Gujarat Technological University (GTU), located in Gujarat, India, is a public state university with 486 affiliated colleges throughout the state. The university boasts a substantial enrollment of approximately 225,000 students, offering a diverse range of programs, including Diplomas, Undergraduate, and Postgraduate degrees, as well as a well-established Doctoral program.

Diploma to Degree CET (DDCET - 2025)

Tentative Important Dates:

Sr. No.	Events	Dates & Time
1	Opening date of online registration	27/01/2025, 1:00 PM
2	Closingdate of online registration	30/3/2025, 12:00 Midnight
3	Admit card download	10/4/2025 onwards
4	Exam Date	April 19, 2025

website : www. gujacpc.admissions.nic.in

GTU Sample Paper with Detailed soultion :https://qualexe.com/ddcetsqp-pdf

DDCET 2024 Paper with Detailed soultion: https://qualexe.com/previous-year-paper/view/ddcet-2024

PAPER SET A SOLUTION - https://qualexe.com/final-paper-set

PAPER SET B SOLUTION - https://qualexe.com/final-paper-setb

Application Fees (Nonrefundable) :

Rs. 250 per Candidate

Selection:

The DDCET Rank will be available online, and the merit will be valid for the respective year only.

Exam Pattern :

Program	Paper Number	Paper	No. of Question	Maximum Marks	Time Duration
Engineering and Technology	BE 01	Basics of Science and Engineering	50	100	150 Minutes
	BE 02	Aptitutde Test (Mathematics and soft skill)	50	100
	Total		100	200

DDCET Syllabus : (Common to all Programmes of Diploma Engineering)

PAPER-1- BE-01

Sr no	Topic	Sub-topic	Weightage (%)
1	Units and Measurement	Physical quantities and units. Interconversion of units MKS (SI) to CGS and vice versa. Errors, Estimation of error, relative error, percentage error, propagation of errors. Measurement with Vernier caliper and micrometer screw gauge.	12
2	Classical Mechanics	Linear motion, velocity, acceleration, force, Newtons laws of motion, linear momentum and impulse of force. Circular motion, angular velocity, angular acceleration, centripetal and centrifugal force. Work, energy, kinetic energy, potential energy, power.	12
3	Electric Current	Ohms Law and application Charge, interaction of charges, Coulombs force. Electric field, electric potential, electric flux, electric current. Resistance, conductance, resistivity, conductivity, series and parallel combination of resistors. Capacitance, parallel plate capacitor, series and parallel combination of capacitors.	12
4	Heat and thermometry	Modes of heat transfer Various temperature scale, conversion of temperature, Kelvin Celsius, Kelvin Fahrenheit, Fahrenheit Celsius and vice versa. Heat capacity and specific heat. Thermal conductivity, coefficient of thermal conductivity, linear thermal expansion.	12
5	Wave motion, optics and acoustics	Types of waves, (progressive, stationary, mechanical, non-mechanical, transverse, longitudinal). Frequency, wavelength, periodic time and their relations. Properties and applications of electromagnetic waves (ordinary light, LASER) and sound waves (ultrasonic wave, audible wave). Amplitude, intensity, phase and wave equations. Reflection, refraction, Snells law, absolute refractive index, relative refractive index, total internal reflection, critical angle, optical fiber (construction, properties and applications). Reverberation, Reverberation time, Sabines formula, echo, absorption coefficient.	12
6	Chemical Reactions and Equations	Chemical Equations: Writing a Chemical Equation, Balanced Chemical Equations. Types of Chemical Reactions: Combination Reaction, Decomposition Reaction, Displacement Reaction, Double Displacement Reaction.	6
7	Acids, Bases and Salts	Understanding the Chemical Properties of Acids and Bases. Reaction of Metallic Oxides with Acids. Reactions of an Acid or a Base in Water Solutions. Importance of pH in Everyday life. Salts: Family of salts, pH of salts	8
8	Metals and Non-metals	Physical properties of Metals and Non-metals. Chemical Properties of Metals. How do Metals and Non-metals React : Properties of Ionic compounds. Corrosion of Metals.	6
9	Computer Practice	Basics of Computer System Introduction to Internet HTML Using MS - Word /MS-Excel/MS-Power Point	10
10	Environmental Sciences	Ecosystem Pollution and its types Climate Change Renewable Sources of Energy such as Hydro, Solar, Wind, Bio-mass, Tidal and Geothermal - their availability and limitations.	10

PAPER-2 BE-02 Aptitude Test

Sr. no	Topics	Sub-topics	Weightage(%)
1	Determinant and Matrices	Determinant and its value up to 3rd order (Without properties) Concept of a Matrix Types of Matrices (Rectangular matrix, Square matrix, Null matrix, Diagonal matrix, Scalar matrix, Identity matrix, Singular and Non-singular matrix) Addition, Subtraction and multiplication by scalar of matrices Product of two matrices Adjoint and Inverse of a matrix of order 2X2. Solution of Simultaneous linear equations of two variables	8
2	Trigonometry	Units of Angles (degree and radian) Trigonometric Functions Periods of Trigonometric functions Allied & Compound Angles, Multiple Submultiples angles Sum and factor formula	6
3	Vectors	Introduction of a Vector Direction and Magnitude Types of vectors (Null vector, Unit Vector) Addition, Subtraction. Scalar product (Dot product) and Vector Product (Cross product) Angle between two Vectors	4
4	Coordinate Geometry	Introduction and slope of a line Equation of a line (Two-point form, Slope point form, Intercept form, General form) Condition of parallel and perpendicular lines Equation of Parallel and Perpendicular lines to the given line Angle between two lines Equation of a circle with centre and radius To find centre and radius from general equation of a circle	4
5	Function & Limit	Function and simple examples Limit of a Function Standard formulae of Limit and related simple examples	6
6	Differentiation and its Applications	Concept of Differentiation Working rule: Sum, Subtraction, Product and Quotient Chain Rule Derivative of Implicit functions, Parametric functions Logarithmic Differentiation Successive Differentiation up to second order Applications: Velocity, Acceleration of given simple functions	8
7	Integration	Concept of Integration Working rules and Integral of standard functions Method of substitution & Integration by parts (simple examples) Definite Integral (simple examples)	8
8	Logarithm	Logarithm as a function Laws of Logarithm and related Simple examples	4
9	Statistics	Mean, Median and Mode for ungrouped data	2
10	Comprehension of Unseen Passage	An unseen passage will be given followed by 5 questions. Students have to read the passage and answer the questions.	10
11	Theory of Communication	Process of Communication Verbal and Non-verbal Communication Barriers to Communication	10
12	Techniques of Writing	Parts of Letter and Email Types of Business Letter (Inquiry, Reply, Order, Complaint, Adjustment) Common Abbreviations used in Business Letter	10
13	Grammar	Parts of Speech 1) Noun 2) Pronoun 3) Adjective 4) Adverb 5) Verb 6) Preposition 7) Connectors 8) Interjection Tenses Subject Verb Agreement	10
14	Correction of Incorrect Words and Sentences	Word Correction: Students have to choose correct spelling of the word from the options given Sentence Correction: Students have to choose grammatically or structurally correct sentence from the options given.	10

Marking System:

Each Correct Answer : 2 Marks
Each Wrong Answer : 0.5 Negative Mark

Qualexe EdTech offers a comprehensive program including:

A lecture video series
Topic-wise MCQ tests
Practice booklet (English / Gujarati)
Tournament quizzes
Test series
Offline Test
Doubt solving bot
Performance analysis

Note:

"Qualexe will offer well-designed test series and tournaments for quality exercise."

Frequently Asked Questions (FAQs) about GTU's Diploma to Degree CET (DDCET):

1. What is DDCET, and how is it relevant to Gujarat Technological University (GTU)

DDCET stands for Diploma to Degree Common Entrance Test, a crucial examination at GTU facilitating the transition from diploma to degree programs in the various disciplines.

2. Can you provide an overview of GTU and its affiliation with DDCET

GTU, located in Gujarat, India, is a public state university with 486 affiliated colleges. DDCET serves as a bridge for students aspiring to shift from diploma courses to degree programs within the university.

3. What are the important dates for the DDCET application process

The online registration for DDCET typically opens in January 2025, and the exam is scheduled to take place on 19/04/2025.

4. How can I apply for the DDCET, and what is the application fee

The registration link for DDCET is mentioned below. Interested candidates can apply online through this link during the specified registration period. The nonrefundable application fee is Rs. 250 per candidate.

Registration link: www. gujacpc.admissions.nic.in

5. What is the selection process for DDCET, and how is merit determined

The DDCET Rank is available online, and the merit obtained in the exam is valid for the respective year only.

6. Could you provide details about the DDCET exam pattern

The DDCET exam consists of two papers: BE 01 (Basics of Science and Engineering) and BE 02 (Aptitude Test - Mathematics and soft skills). Each paper has 50 questions, with a total of 100 questions and 200 marks. The duration for the exam is 150 minutes.

7. How is the DDCET exam marked, and are there negative markings

Each correct answer in DDCET is awarded 2 marks, while each wrong answer incurs a 0.5 negative mark.

8. What additional support or resources are available for DDCET preparation

QUALEXE will offer well-designed test series and tournaments to facilitate quality exercise for DDCET candidates. candidates will be able to appear in DDCET like testseries for better practice and compare their performace with other candicates.

9. Is the DDCET merit valid for multiple years

No, the merit obtained in DDCET is valid for the respective year only.

10. How can I stay updated on any changes or announcements related to DDCET

For the latest and most accurate information, candidates are advised to regularly check the official GTU website and communications from the examination office. Additionally, all the latest updates about the DDCET Exam will be available on the QUALEXE website. So, keep visiting our website regularly for any announcements or changes.

Previous Year Paper

Subject wise analysis

Subject	Number of questions
POWER ELECTRONICS & DRIVES	4
ELECTROMAGNETICS	1
POWER SYSTEM	8
BASIC ELECTRONICS	4
SIGNALS & SYSTEMS	4
ELECTRICAL MACHINES	8
CONTROL SYSTEM ENGINEERING	3
DIGITAL ELECTRONICS	2
ELECTRICAL CIRCUIT ANALYSIS	2
Total	36

Q1.An SCR is considered to be a semi-controlled device because

it can be turned OFF but not ON with a gate pulse
it conducts only during one-half cycle of an alternating current wave
it can be turned ON but not OFF with a gate pulse
it can be turned ON only during one-half cycle of an AC

Correct Ans: C

Q2.The unit of ∇×H is

\(Ampere\)
\(Ampere/meter\)
\(Ampere/meter^2\)
\(Ampere-meter\)

Correct Ans: C

Q3.The total reactance and total susceptance of a lossless overhead EHV line, operating at \(50 \: Hz\), are given by \(0.045 \: pu\) and \(1.2 \: pu\) respectively. If the velocity of wave propagation is \(3 \times 10^5 \: km/s\), then the approximate length of the line is

122 km
222 km
172 km
272 km

Correct Ans: B

Q5.The input impedance of the operational amplifiers is

Infinite
Zero
Very small
Very high but not infinite

Correct Ans: D

Q6.What is the energy of a power signal

Finite
Zero
Infinite
Between 1 & 2

Correct Ans: C

Q8.When the applied voltage per phase is reduced to one-half, the starting torque of a three-phase squirrel cage induction motor becomes

½ of the initial value
¼ of the initial value
Twice of the initial value
4 times of the initial value

Correct Ans: B

Q10.For given base voltage and base volt-amperes, the per unit impedance value of an element is \(x\). What will be the per unit impedance value of this element when voltage and volt-ampere bases are both doubled?

0.5x
2x
4x
x

Correct Ans: A

Q11.The transfer function of a system is given as \(\frac{100}{s^2 + 20s + 100}\). The system is

An overdamped system
A critically damped system
An underdamped system
An unstable system

Correct Ans: B

Q12.A single-phase thyristor-bridge rectifier is fed from a 230V, 50 Hz, single-phase, AC mains. If it is delivering a constant DC current of 10 A, at firing angle of 30°, then value of the power factor at AC mains is

0.87
0.9
0.78
0.45

Correct Ans: C

Q14.A 183-bus power system has 150 PQ buses and 32 PV buses. In the general case, to obtain the load flow solution using Newton-Raphson method in polar coordinates, the minimum number of simultaneous equations to be solved is _____________.

Correct Ans: B

Q16.The direction of rotation of a 3-phase induction motor is clockwise when it is supplied with 3-phase sinusoidal voltage having phase sequence A-B-C. For counter clockwise rotation of the motor, the phase sequence of the power supply should be

B-C-A
C-A-B
A-C-B
B-C-A and C-A-B

Correct Ans: C

Q17.The value of \(a_0\) which will ensure that the polynomial \(s^3+3s^2+2s+a_0\) has roots on the left half of the s-plane is

Correct Ans: D

Q18.A linear discrete time systemhas the characteristic equation \(z^3-0.81z = 0\). The system

is stable
is marginally stable
is unstable
None of these

Correct Ans: A

Q19.In the CE configuration of a transistor amplifier, there is

No phase change between input and output voltages
180° phase change between input and output current
No phase change between input and output currents and no phase change between input and output voltages
No phase change between input and output currents and 180° phase change between input and output voltages

Correct Ans: B

Q20.A 50 Hz, 4 pole, 500 MVA, 22 kV turbo-generator is delivering rated megavolt-amperes at 0.8 power factor. Suddenly a fault occurs reducing its electric power output by 40%. Neglect losses and assume constant power input to the shaft. The accelerating torque in the generator in MN-m at the time of the fault will be

1.528
1.018
0.848
0.509

Correct Ans: B

Q22.Which one of the following is not a necessary condition to be satisfied for Synchronizing an incoming alternator to an already operating alternator

Same voltage magnitude
Same Prime mover speed
Same frequency
Same Phase sequence

Correct Ans: B

Q23.In the Bode-plot of a unity feedback control system, the value of phase of \(G(j\omega)\) at the Gain Cross over Frequency is \(-125^o\). The phase margin of the system is

\(-125^o\)
\(-55^o\)
\(55^o\)
\(125^o\)

Correct Ans: C

Q24.An AC induction motor is used for a speed control application. It is driven from an inverter with a constant V/f control. The motor name plate details are as follows:
V= 415V, 3-phase, f=50 Hz, N = 2850 rpm The motor is run with the inverter output frequency set at 40 Hz, and with half the rated slip. The running speed of the motor is

2400 rpm
2280 rpm
2340 rpm
2790 rpm

Correct Ans: C

Q26.For a periodic square wave, which one of the following statements is TRUE?

The Fourier series coefficients do not exist.
The Fourier series coefficients exist but the reconstruction converges at no point.
The Fourier series coefficients exist and the reconstruction converges at most points.
The Fourier series coefficients exist and the reconstruction converges at every points.

Correct Ans: C

Q27.A 555 timer can be used as

An astable multivibrator only
A monostable multivibrator only
A frequency divider only
An astable multivibrator or a
monostable multivibrator or a frequency divider

Correct Ans: D

Q28.In a DC machine, the number of mechanical and electrical degrees will be same when the number of poles on the machine is

Correct Ans: B

Q29.A Buchholz relay is used for

Protection of transformer against all internal faults.
Protection of transformer against all external faults.
Protection of transformer against all internal and external faults.
Protection of induction motors.

Correct Ans: A

Q32.A low-pass filter with a cut-off frequency of 30 Hz is cascaded with a high-pass filter with a cut-off frequency of 20Hz. The resultant system of filters will function as

An all-pass filter
An all-stop filter
An band stop (band-reject) filter
A band-pass filter

Correct Ans: D

Q33.Which of the following are the variable losses in a rotating machine?

Core loss and mechanical loss
Core loss and stray load loss
Copper loss and core loss
Copper loss and stray load loss

Correct Ans: D

Q34.In thermal power plants, the pressure in the working fluid cycle is developed by

feed water pump
superheater
condenser
turbine

Correct Ans: A

Q36.A step up chopper is used to feed a load at 400 V DC from a 250 V DC source. The inductor current is continuous. If the ‘OFF’ time of the switch is 20 \(\mu s\), the switching frequency of the chopper in kHz is

32.95
31.25
20.25
44.80

Correct Ans: B

Q37.It is desired to have 64×8 memory. However if the available memory size is 16×4, then how many such memories are required to fulfill the requirement?

Correct Ans: A

Q38.In a residential electrical connection having load less than 5 kW, the following rating of leakage current for ELCB is suggested

300 mA
30 mA
3 mA
3000 mA

Correct Ans: B

Q41.An 8-pole, 3-phase, 50 Hz induction motor is operating at a speed of 700 rpm. The frequency of the rotor current of the motor in Hz is____________.

3.33 Hz
2.22 Hz
4.44 Hz
1.11 Hz

Correct Ans: A

Q42.Given two coupled inductors \(L_1\) and \(L_2\), their mutual inductance M satisfies

M\(=\sqrt{L_1^2+L_2^2}\)
M\(>\frac{L_1+L_2}{2}\)
M\(>\sqrt{L_1L_2}\)
M\(\leq\sqrt{L_1L_2}\)

Correct Ans: D

Q43.Find the correct combination. <br>
\(\mathbf{List-1 \: - Type \: of \: tariff :}\)

A. Block rate

B. Flat rate

C. Two part tariff

D. Power factor tariff

\(\mathbf{List-2 \: - Type \: of \: consumers:}\)

1. Large industrial

2. Medium industrial

3. Domestic and commercial

4. Agricultural and street lighting

A-3, B-4, C-2, D-1
A-1, B-2, C-3, D-4
A-2, B-3, C-4, D-1
A-4, B-1, C-2, D-3

Correct Ans: A

Q44.A passive 2-port network is in a steady-state condition. Compared to its input, the steady state output can never offer

Higher voltage
Lower impedance
Better regulation
Greater power

Correct Ans: D

Q45.A four bit number is given as 1001. Its 1’s complement is

1001
1110
0110
0111

Correct Ans: C

Q47.In single-phase modulation of PWM inverter, third harmonic can be eliminated if pulse width is equal to

30°
60°
120°
150°

Correct Ans: C

Q49.In transformer, zero voltage regulation at full load is

Not possible
Possible at unity power factor load
Possible at leading power factor load
Possible at lagging power factor load

Correct Ans: C

Q50.A function of one or more variables which conveys information on the nature of physical phenomenon is called

Noise
Interference
System
Signal

Correct Ans: D

Subject wise analysis

Subject	Number of questions
Basics of Science and Engineering (DDCET)	50
Aptitude Test (Mathematics and Soft Skill) DDCET	50
Total	100

Q1.A big piece of glass is first heated and then is allowed to cool. On cooling down, a crack is developed in it. One of the possible reasons for this is ___________ .

High melting point
Large thermal conductivity
Large specific heat
Small thermal conductivity

Correct Ans: D

Solution:

\(\Rightarrow\) When glass cools unevenly due to \(\textbf{small thermal conductivity}\), thermal stress develops, causing cracks. Mathematically, thermal stress \( \sigma = E \alpha \Delta T \), where \( E \) is Young's modulus, \( \alpha \) is thermal expansion coefficient, and \( \Delta T \) is temperature gradient.

Q2.When heat is given to boiling water, the temperature of water ____________ .

increases
decreases
remains constant
None of the above.

Correct Ans: C

Solution:

\(\Rightarrow\) Boiling water maintains constant temperature (\( 100^\circ C \) at 1 atm) because heat energy (\( Q = mL \)) is used for phase change (latent heat of vaporization \( L \)), not increasing kinetic energy. Thus, \( \Delta T = 0 \).

Q3.\(37^\circ\)C = ________\(^\circ\)F.

98.6
98.8
97.6
96.8

Correct Ans: A

Solution:

\(\Rightarrow\) Convert \( 37^\circ C \) to Fahrenheit: \( T_F = \frac{9}{5}T_C + 32 = \frac{9}{5} \times 37 + 32 = 98.6^\circ F \).

Q4.The SI Unit of coefficient of thermal conductivity is _____________ .

j/m K
N/m K
W/mK
mK/W

Correct Ans: C

Solution:

\(\Rightarrow\) Thermal conductivity (\( k \)) measures heat transfer rate per unit area and temperature gradient. SI unit: \( \text{W/mK} \) (Watt per meter per Kelvin). Derived from Fourier's law: \( Q = -kA \frac{dT}{dx} \).

Q5.Audible waves have a frequency range from ______________ .

20 Hz-10 KHz
20 Hz-20 KHz
10 Hz-10 KHz
10 Hz - 20 KHz

Correct Ans: B

Solution:

\(\Rightarrow\) Audible frequency range for humans: \( 20\ \text{Hz} \) (low-pitched) to \( 20\ \text{kHz} \) (high-pitched). Ultrasonic waves (\( >20\ \text{kHz} \)) and infrasonic waves (\( <20\ \text{Hz} \)) are inaudible.

Q6.The speed of light in a vacuum is __________ .

\(3\times10^5\) m/s
\(3\times10^6\) m/s
\(3\times10^7\) m/s
\(3\times10^8\) m/s

Correct Ans: D

Solution:

\(\Rightarrow\) Speed of light in vacuum (\( c \)) is a fundamental constant: \( c = 299,792,458\ \text{m/s} \approx 3 \times 10^8\ \text{m/s} \).

Q7.What is the periodic time of a wave having frequency of 20 Hz?

0.05 sec
0.5 sec
5 sec
50 sec

Correct Ans: A

Solution:

\(\Rightarrow\) Period (\( T \)) and frequency (\( f \)) are inversely related: \( T = \frac{1}{f} = \frac{1}{20\ \text{Hz}} = 0.05\ \text{sec} \).

Q8.LASER is an extremely ______________ radiation.

Unidirectional
Focused
Coherent and Stimulated
All of above

Correct Ans: D

Solution:

\(\Rightarrow\) LASER properties: \(\textbf{Unidirectional}\) - travels in one direction, \(\textbf{Focused}\) - narrow beam, \(\textbf{Coherent}\) in-phase waves, and \(\textbf{Stimulated}\) - emission. Hence, all options are correct.

Q9.A volume of an auditorium is 5000 \(m^3\). The total absorption by the surfaces is 900 O.W.U. Then calculate reverberation time.

8.094
0.729
0.894
1.003

Correct Ans: C

Solution:

\(\Rightarrow\) Reverberation time (\( T \)) is calculated using Sabine's formula: \( T = \frac{0.161V}{A} \), where \( V = 5000\ \text{m}^3 \) (volume) and \( A = 900\ \text{OWU} \) (absorption). Substituting: \( T = \frac{0.161 \times 5000}{900} = 0.894\ \text{sec} \).

Q10.If \(n_1\) and \(n_2\) are refractive indices of core and cladding resp. Then what is the formula for numerical aperture for optical fiber?

\(\sqrt {n^2_2-n^2_1}\)
\(\sqrt {n^2_1-n^2_2}\)
\(\sqrt {n_2-n_1}\)
\(\sqrt {n_1-n_2}\)

Correct Ans: B

Solution:

\(\Rightarrow\) Numerical Aperture (\( NA \)) for optical fiber: \( NA = \sqrt{n_1^2 - n_2^2} \), where \( n_1 \) (core) and \( n_2 \) (cladding) are refractive indices. This determines light-gathering capacity.

Q11.\(CaCO_{3(s)}\) \(\:\xrightarrow[]{heat}\:\) \(CaCO_{3(s)}+ CaCO_{2(g)}\), which kind of reaction is this?

Displacement reaction
Oxidation reaction
Thermal decomposition reaction
Precipitation reaction

Correct Ans: C

Solution:

\(\Rightarrow\) Here, a single element \(CaCO_{3}\) breaks down into two product that is \(CaO\) and \( CO_{2}\).
\(\Rightarrow\) Hence, this is a decomposition process.

Q12.What is the formula of lead sulphate ?

\(Pb_2SO_4\)
\(Pb(SO_4)_2\)
\(PbSO_4\)
\(Pb_2(SO_4)_3\)

Correct Ans: C

Solution:

\(\Rightarrow\) The formula of lead sulphate is:\(PbSO_4\)

where,

\(Pb = Lead\)

\(SO_4 = Sulphate \: ion\)

Q13.Which is the balance equation of \(Al+HCl \rightarrow AlCl_3+ H_2\) ?

\(Al+HCl \rightarrow AlCl_3+ 2H_2\)
\(2Al+6HCl \rightarrow 2AlCl_3+ 3H_2\)
\(2Al+3HCl \rightarrow 2AlCl_3+ 2H_2\)
\(2Al+4HCl \rightarrow 3AlCl_3+ 3H_2\)

Correct Ans: B

Solution:

\(\Rightarrow\) The given chemical equation is
\(\quad \:Al + HCl \rightarrow AlCl_3 + H_2 \)
\(\Rightarrow\) Here, the number of atoms of hydrogen and chlorine is not equal on both the side.

\(\text {Step 1:}\) Balance \(Cl\) both side as it has maximum atoms.
\(\Rightarrow\) To do this multiply 3 with \(HCl\) on the reactant side
\(\implies Al + 3HCl \rightarrow AlCl_3 + H_2 \)

\(\text {Step 2:}\) Balance \(H\) both side.
\(\Rightarrow\) Reactant have 3 atoms and product have 2 atoms of \(H\), which can be balanced out as follow:
\(\implies Al + 2\times 3 HCl \rightarrow AlCl_3 + 3\times H_2 \)
\(\implies Al + 6HCl \rightarrow AlCl_3 + 3H_2 \)

\(\text {Step 3:}\) Now, we need to balance \(Cl\) again.
\(\Rightarrow\) Reactant have 6 atoms and product have 3 atoms of \(Cl\), which can be balanced out as follow:
\(\implies Al + 6HCl \rightarrow 2AlCl_3 + 3H_2 \)

\(\text {Step 4:}\) Finally, we need to balance \(Al\).
\(\Rightarrow\) Reactant have 1 atoms and product have 2 atoms of \(Al\), which can be balanced out as follow:
\(\implies 2Al + 6HCl \rightarrow 2AlCl_3 + 3H_2 \)

Q14.Which main product is obtained by reaction of sodium hydroxide with zinc metal?

\(NaZnO_2\)
\(NaZn_2O\)
\(Na_2ZnO_2\)
\(Zn(OH)_2\)

Correct Ans: C

Solution:

\(\Rightarrow\) Sodium zincate - \(Na_2ZnO_2\).
\(\Rightarrow\) It is formed when zinc reacts with sodium hydroxide \((NaOH)\) in an aqueous solution.
\(\Rightarrow\) It is often used in galvanizing and electroplating processes and can also be found in some types of batteries.

Q15.Which type of oxides is called basic oxide ?

Non-metallic oxide
Metallic oxide
(A) and (B) both
Inactive oxide

Correct Ans: B

Solution:

\(\Rightarrow\) Basic oxides are metal oxides that react with water to form a base or with acids to form a salt and water.
\(\Rightarrow\) They are typically ionic compounds formed by the reaction of metals with oxygen.

Q16.Which of the following is known as milk of magnesia?

\(Mn(OH)_2\)
\(Mg(OH)_2\)
\(MgO\)
\(Mg(OH)\)

Correct Ans: B

Solution:

\(\Rightarrow\) Magnesium hydroxide \((Mg(OH)_2)\) - a milky white liquid is known as milk of magnesia.

Q17.Which of the following is the chemical formula of bleaching powder?

\(Ca(OH)_2\)
\(CaOCl_2\)
\(Ca_2OCl\)
\(CaCO_3.2H_2O\)

Correct Ans: B

Solution:

\(\Rightarrow\) Bleaching powder is also known as calcium hypochlorite, and its formula is \(CaOCl_2\).

Q18.Which of the following is the lustrous non-metal?

Iodine
Carbon
Nirtogen
Bromine

Correct Ans: A

Solution:

\(\Rightarrow\) lodine is non metal having lustrous appearance.

Q19.Which of the following metals neither reacts with cold nor hot water, but reacts with vapour?

Aluminium
Iron
Zinc
All of the above

Correct Ans: D

Solution:

The correct answer is: Aluminium (Al)

\(\Rightarrow\) Among metals, aluminium does not react with cold or hot water due to the formation of a passive oxide layer \(Al_2 O_3\) on its surface. However, it does react with steam (water vapour) at high temperatures to form aluminium oxide and hydrogen gas:

\[
2Al + 3H_2O (g) \rightarrow Al_2O_3 + 3H_2 \uparrow
\]

Other metals comparison:

\(\rightarrow\) Sodium (Na) and Potassium (K): React vigorously with cold water.

\(\rightarrow\) Calcium (Ca) and Magnesium (Mg): React with cold or hot water.

\(\rightarrow\) Iron (Fe): Reacts slowly with steam.

\(\rightarrow\) Zinc (Zn): Also reacts with steam.

\(\therefore\) Aluminium fits the condition best — no reaction with cold or hot water, but reacts with steam

Q20.Which of the following is correct order of reactivity of metals?

\(Mg > Al > Zn > Fe\)
\(Mg > Fe > Zn > Al\)
\(Fe > Zn >Al > Mg\)
\(Mg > Al > Fe> Zn\)

Correct Ans: A

Solution:

\(\Rightarrow\) The figure shows the list of elements arranged according to their reactivity.

Q21.The smallest unit of data in a computer is called a:

Byte
Bit
Nibble
GB

Correct Ans: B

Solution:

\(\Rightarrow\) A single bit can only have two possible values: 0 or 1. Computers rely on these values to store and handle information.
\(\Rightarrow\) Bits are usually combined to create bigger units of data like bytes, which consist of 8 bits, or kilobytes, which contain 1024 bytes.

Q22.Pressing Ctrl + Home keys on the Keyboard moves the cursor to the _______ in MS-Word.

End of the document
Beginning of the line
Beginning of the paragraph
Beginning of the document

Correct Ans: D

Solution:

In MS Word, Pressing
\(\Rightarrow\) \(\text{Ctrl + End}\) moves the cursor to the end of the document .
\(\Rightarrow\) Only \(\text{Home}\) moves it to the beginning of the current line.
\(\Rightarrow\) \(\text{Ctrl +Up arrow} (\uparrow)\) jumps to the beginning of the current paragraph.
\(\Rightarrow\) \(\text{Ctrl + Home}\) returns to the very start of the document.

Q23.Which of the following can be classified as a relative link in the HTML?

All of the above

Correct Ans: B

Solution:

\(\Rightarrow\) \(\text{Relative}\) URLs omit the scheme/host and specify a path relative to the current document (or its parent directories).
\(\Rightarrow\) \(\text{Absolute}\) URLs include a scheme (e.g. http:// or https://) and usually a host name.

Q24.To find the total value of the cell values in A2, B2, C2 and D2 in MS-Excel, the correct formula is:

sum (A2:D2)
sum (A2, B2, C2, D2)
Both (A) and (B)
None of the above

Correct Ans: C

Solution:

The correct choice is \(\text{Both (A) and (B)}\).
\(\Rightarrow\) \(\text{=SUM(A2:D2)}\) uses a continuous range from A2 through D2.
\(\Rightarrow\) \(\text{=SUM(A2, B2, C2, D2)}\) explicitly lists each cell and add them up.

Q25.Which of the following is an incorrect option in the view menu of a Microsoft Power point presentation ?

Tree view
Outline view
Notes page
Reading view

Correct Ans: A

Solution:

In MS Powerpoint,
\(\Rightarrow\) \(\text{Outline view}\) shows only the text content of your slides in a collapsible, linear outline on the left pane.
\(\Rightarrow\) \(\text{Notes page}\) displays a single slide at the top and its speaker notes below, formatted as a printable “notes page."
\(\Rightarrow\) \(\text{Reading view}\) runs your presentation in a window (not full‑screen) so you can step through slides as a viewer would.

\(\Rightarrow\) PowerPoint doesn’t include any option in view menu named \(\text{Tree View}\).

Q26.The green plants manufacture their own food are known as __________.

Heterotrophs
Autotrophs
Saprotrophs
Omnivores

Correct Ans: B

Solution:

\(\Rightarrow\) Autotrophs are organisms capable of producing their own food, often through photosynthesis, using light energy, water, and carbon dioxide.

Q27.Bag filters are used to ____________ .

reduce noise pollution
reduce sludge from waste water
remove particulate matter for a contaminated gas stream
reduce soil pollution

Correct Ans: C

Solution:

\(\Rightarrow\) A bag filter is an air pollution control device that uses fabric bags to trap particulate matter (dust and other small particles) from polluted gas streams.
\(\Rightarrow\) It's commonly used in industrial settings like boiler houses, factories, and power plants to reduce emissions and improve air quality.

Q28.The process of producing energy by utilizing heat trapped inside the earth surface is known as ____________ .

Geo-Thermal energy
Hydrothermal energy
Solar energy
Wave energy

Correct Ans: A

Solution:

\(\Rightarrow\) The process of producing energy by utilizing heat trapped inside the Earth's surface is called geothermal energy.

Q29.__________ is a device that converts solar energy directly into electricity.

Fuel cell
Hydrogen cell
Solar array
Photovoltaic cell

Correct Ans: D

Solution:

\(\Rightarrow\) A solar cell (also known as a photovoltaic cell) is a device that converts solar energy directly into electricity.

Q30.The goal of the Paris Agreement is to keep the increase in global temperature well below ____________ above Preindustrial levels.

\(1.0^\circ C\)
\(1.5^\circ C\)
\(2.0^\circ C\)
\(2.5^\circ C\)

Correct Ans: C

Solution:

\(\Rightarrow\) The Paris Agreement aims to keep the increase in global temperature well below 2 degrees Celsius.

Q31.Number of significant digits in 2025 is __________ .

Correct Ans: B

Solution:

\(\Rightarrow\) Significant digits in 2025: All non-zero digits (2, 0, 2, 5) are significant. Zero (0) between non-zero digits is also significant.

Q32.Zero error is an example of _______ error.

Systematic
Random
Maximum
Minimum

Correct Ans: A

Solution:

\(\Rightarrow\) Zero error is \(\textbf{systematic}\) because it arises from instrument calibration (e.g., micrometer screw gauge not starting at zero) and is repeatable. Random errors vary unpredictably.

Q33.I joule =________ erg.

\(10^3\)
\(10^5\)
\(10^7\)
\(10^9\)

Correct Ans: C

Solution:

\(\Rightarrow\) Energy unit conversion: \( 1\ \text{J} = 10^7\ \text{erg} \).
Derived from \( 1\ \text{J} = 1\ \text{kg m}^2/\text{s}^2 \) and \( 1\ \text{erg} = 1\ \text{g cm}^2/\text{s}^2 \).

Q34.Density of water in CGS system is ________.

1000
100
10
1

Correct Ans: D

Solution:

\(\Rightarrow\) Density of water in CGS: \( \rho = 1\ \text{g/cm}^3 \) (at \( 4^\circ C \)). In SI: \( 1000\ \text{kg/m}^3 \).

Q35.In equation density \(s=\frac{m}{V}\) if percentage error in mass m is 0.3% and for radius r is 0.5% then percentage error in density of a Sphere is __________%.

Correct Ans: A

Solution:

\(\Rightarrow\) For a sphere (\( V = \frac{4}{3}\pi r^3 \)), \% error in density (\( s \)): \( \Delta s\% = \Delta m\% + 3 \times \Delta r\% = 0.3\% + 3 \times 0.5\% = 1.8\% \).

Q36.The pitch of micrometer screw is 1 mm. There are 100 divisions on it's circular scale. What will be the least count of the micrometer screw.

1 mm
0.1 mm
0.01 mm
0.001 mm

Correct Ans: C

Solution:

\(\Rightarrow\) Least Count = \( \frac{\text{Pitch}}{\text{Divisions}} = \frac{1\ \text{mm}}{100} = 0.01\ \text{mm} \). Ensures precision in micrometer measurements.

Q37.The SI Unit of linear momentum is ___________ .

Kgs/m
Kg m/s
ms/Kg
Kg s m

Correct Ans: B

Solution:

\(\Rightarrow\) Linear momentum: \( p = mv \). SI unit: \( \text{kg m/s} \).

Q38.The centripetal force always acts ____________ .

Away from the centre
In tangential direction
Perpendicular to the motion
Towards the centre

Correct Ans: D

Solution:

\(\Rightarrow\) Centripetal force (\( F_c = \frac{mv^2}{r} \)) always points \(\textbf{towards the centre}\) of circular motion, perpendicular to velocity.

Q39.When external force acting on a body is zero then its acceleration is __________ .

increases
decreases
equal to zero
remains constant

Correct Ans: C

Solution:

\(\Rightarrow\) Newton's First Law: If net force \( F = 0 \), acceleration \( a = 0 \) (object remains at rest or moves uniformly).

Q40.The formula for angular velocity of a body moving with a constant speed v in a circle of radius r, is given by _________

\(v/r\)
\(vr\)
\(vr^2\)
\(vr^3\)

Correct Ans: A

Solution:

\(\Rightarrow\) Angular velocity (\( \omega \)) for circular motion: \( \omega = \frac{v}{r} \) (radians/second).

Q41.A body having 10 kg mass and 9.8 \(m/s^2\) acceleration produces how much force ?

9.8 newton
98 newton
0.98 newton
980 newton

Correct Ans: B

Solution:

\(\Rightarrow\) Force (\( F \)) via Newton's Second Law:
\( F = ma = 10\ \text{kg} \times 9.8\ \text{m/s}^2 = 98\ \text{N} \).

Q42.If an object having mass 50 kg rotated in a circle with a radius of 2 m with a constant speed of 60 m/s then what is the value of centripetal acceleration?

\(6000 m/s^2\)
\(3000 m/s^2\)
\(1800 m/s^2\)
\(1500 m/s^2\)

Correct Ans: C

Solution:

\(\Rightarrow\) Centripetal acceleration (\( a_c \)): \( a_c = \frac{v^2}{r} = \frac{(60\ \text{m/s})^2}{2\ \text{m}} = 1800\ \text{m/s}^2 \).

Q43.The SI Unit of electric flux is __________ .

\(C^2/Nm\)
\(Nm/C\)
\(Nm/C^2\)
\(Nm^2/C\)

Correct Ans: D

Solution:

\(\Rightarrow\) Electric flux (\( \Phi \)) SI unit: \( \text{Nm}^2/\text{C} \).
From Gauss's law: \( \Phi = \oint \mathbf{E} \cdot d\mathbf{A} \).

Q44.The electric field lines are _________ .

Imaginary
Real
Ideal
None of the above

Correct Ans: A

Solution:

\(\Rightarrow\) Electric field lines are \(\textbf{imaginary}\) curves representing the direction of the electric field (\( \mathbf{E} \)) at each point.

Q45.How many electrons are in 1 coulomb charge ?

\(6.25 \times 10^{17}\)
\(6.25 \times 10^{18}\)
\(6.25 \times 10^{19}\)
\(6.25 \times 10^{20}\)

Correct Ans: B

Solution:

\(\Rightarrow\) Number of electrons in 1 Coulomb: \( n = \frac{Q}{e} = \frac{1\ \text{C}}{1.6 \times 10^{-19}\ \text{C}} = 6.25 \times 10^{18} \).

Q46.The capacitance of a capacitor ___________ if an insulating dielectric material is placed between two plates of it.

increases
decreases
remains constant
becomes zero

Correct Ans: A

Solution:

\(\Rightarrow\) Capacitance (\( C \)) with dielectric: \( C = \kappa C_0 \), where \( \kappa \) (dielectric constant) \( >1 \). Thus, \( C \) \(\textbf{increases}\).

Q47.If the distance between two charges is doubled then electric force between them becomes ______________ .

half
double
one fourth
four times

Correct Ans: C

Solution:

\(\Rightarrow\) Coulomb's Law: \( F \propto \frac{1}{r^2} \). If distance \( r \) doubles, force reduces to \( \frac{1}{4} \).

Q48.What is the effective value of resistance when three resistors \(5\: \Omega, \: 10 \:\Omega\) and \(15\: \Omega \) are connected in series combination?

\(10 \:\Omega\)
\(30 \:\Omega\)
\(20 \:\Omega\)
\(5.5 \:\Omega\)

Correct Ans: B

Solution:

\(\Rightarrow\) Series resistance: \( R_{\text{total}} = R_1 + R_2 + R_3 = 5\ \Omega + 10\ \Omega + 15\ \Omega = 30\ \Omega \).

Q49.Heat capacity of a body per unit mass is known as ______________ .

Specific heat
Relative heat
\(C_p)\)
\(C_v)\)

Correct Ans: A

Solution:

\(\Rightarrow\) Specific heat capacity (\( c \)): Heat required per unit mass to raise temperature by \( 1^\circ C \). SI unit: \( \text{J/kg K} \).

Q50.1 KCal= _________ J.

4.186
4186
41.86
418.6

Correct Ans: B

Solution:

\(\Rightarrow\) Energy conversion: \( 1\ \text{kcal} = 4186\ \text{J} \) (exact: \( 1\ \text{cal} = 4.186\ \text{J} \)).

Q51.The Centre of the circle \((x+3)^2+y^2-2=0\) is___.

(3,0)
(0,3)
(-3,0)
(0,-3)

Correct Ans: C

Solution:

\[
(x + 3)^2 + y^2 - 2 = 0
\]
\[
(x + 3)^2 + y^2 = 2
\]

Standard form:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:

- \((h, k)\) is the centre of the circle

- \(r\) is the radius

Compare:
\[
(x + 3)^2 + y^2 = (x - (-3))^2 + (y - 0)^2
\]

\(\therefore h = -3 \: \& \: k = 0\)

\(\therefore\) The centre of the circle is \((-3, 0)\).

Q52.If \(f(x)=e^{log x}\), then \(f(1)=\)___

0
1
e
-e

Correct Ans: B

Solution:

\[
f(x) = e^{\log x}
\]
\[where, \quad
e^{\log_e x} = x \quad \text{(for } x > 0 \text{ and natural log)}
\]

\[\therefore
f(x) = x
\]

\[\therefore
f(1) = 1
\]

Q53.\(\lim_{x \to 0} \frac{\sin 2x}{\tan x}\) = _____

Correct Ans: C

Solution:

\[
\lim_{x \to 0} \frac{\sin 2x}{\tan x}
\]

\[
\sin 2x = 2 \sin x \cos x
\quad \text{and} \quad
\tan x = \frac{\sin x}{\cos x}
\]

\[
\frac{2 \sin x \cos x}{\frac{\sin x}{\cos x}} = 2 \sin x \cos x \cdot \frac{\cos x}{\sin x}
\]

\[
= 2 \cancel{\sin x} \cos x \cdot \frac{\cos x}{\cancel{\sin x}} = 2 \cos^2 x
\]

Take the limit as \(x \to 0\)

\[
2 \cos^2 x = 2 \cdot 1 = 2
\]

Q54.\(\lim_{n \to \infty} (1+\frac{5}{2n})^{8n}\) =_____

\(e^{13}\)
\(e^{4}\)
\(e^{10}\)
\(e^{20}\)

Correct Ans: D

Solution:

\[
\lim_{n \to \infty} \left(1+\frac{5}{2n}\right)^{8n}
\]

\(\rightarrow\) Standard exponential limit identity:

\[
\lim_{n \to \infty} \left(1 + \frac{k}{n}\right)^n = e^k
\]
\(\rightarrow\) Rewrite the expression:

\[
\left(1 + \frac{5}{2n}\right)^{8n}
= \left[\left(1 + \frac{5}{2n}\right)^{2n}\right]^4
\]

\[
\left(1 + \frac{5}{2n}\right)^{2n} \to e^5 \quad \text{as } n \to \infty
\]

\[\therefore
\left[\left(1 + \frac{5}{2n}\right)^{2n}\right]^4 \to (e^5)^4 = e^{20}
\]

Q55.\(\frac{d}{dx}(log 5 + \sin \frac{\pi}{3})\) = ____

\(0\)
\(\frac{1}{5}+\cos \frac{\pi}{3}\)
\(\frac{1}{5}-\cos \frac{\pi}{3}\)
\(\cos \frac{\pi}{3}\)

Correct Ans: A

Solution:

\[
\frac{d}{dx}\left(\log 5 + \sin \frac{\pi}{3}\right)
\]

\(\rightarrow\) \(\log 5\) is a constant (natural log of 5)

\(\rightarrow\) \(\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\), also a constant

\(\therefore\) Derivative of a constant is 0

\[
\frac{d}{dx}(\text{constant}) = 0
\]

Q56.\(\frac{d}{dx}(x^e+e^x-e^e)\) = ___

\(e^x\)
\(e x^e+e^x\)
\(e x^{e-1}+e^x\)
\(e x^{e-1}+e^x-e^{e-1}\)

Correct Ans: C

Solution:

\[
\frac{d}{dx}(x^e + e^x - e^e)
\]

Differentiate each term:

1. \(\frac{d}{dx}(x^e) = e x^{e-1}\)

(Since \(e\) is a constant exponent)

2. \(\frac{d}{dx}(e^x) = e^x\)

3. \(\frac{d}{dx}(e^e) = 0\)

(Because it is a constant)

\[
\frac{d}{dx}(x^e + e^x - e^e) = e x^{e-1} + e^x
\]

Q57.\(\frac{d}{dx} \log (\sin x)\) =____

\(\cot x\)
\(-\cot x\)
\(\tan x\)
\(-\tan x\)

Correct Ans: A

Solution:

\[
\frac{d}{dx} \log (\sin x)
\]

\(\rightarrow\) Apply the chain rule:

The derivative of \(\log(u)\) with respect to \(x\) is:

\[
\frac{d}{dx} \log(u) = \frac{1}{u} \cdot \frac{du}{dx}
\]

Here, \(u = \sin x\).

\[
\frac{d}{dx} \sin x = \cos x
\]

\[
\frac{d}{dx} \log (\sin x) = \frac{1}{\sin x} \cdot \cos x
\]

\[
\frac{\cos x}{\sin x} = \cot x
\]

Q58.If \(x+y=-2\) then \(\frac{dy}{dx}=\)____

0
1
2
-1

Correct Ans: D

Solution:

\[
x + y = -2
\]

\(\Rightarrow\) Differentiate both sides:

\[\rightarrow
\frac{d}{dx}(x + y) = \frac{d}{dx}(x) + \frac{d}{dx}(y) = 1 + \frac{dy}{dx}
\]

\[\rightarrow
\frac{d}{dx}(-2) = 0
\]

\[\therefore
1 + \frac{dy}{dx} = 0
\]

Q59.\(\int \frac{1}{e^x} dx =\) ____ \(+C\)

\(e^{-x}\)
\(-e^{-x}\)
\(e^{x}\)
\(-e^{x}\)

Correct Ans: B

Solution:

\[
\int \frac{1}{e^x} \, dx
\]

\[where, \:\:
\frac{1}{e^x} = e^{-x}
\]

\[
\int e^{-x} \, dx
\]

\(\rightarrow\) The integral of \(e^{ax}\) with respect to \(x\) is \(\frac{e^{ax}}{a}\), where \(a\) is a constant. Here, \(a = -1\).

\[\therefore
\int e^{-x} \, dx = \frac{e^{-x}}{-1} = -e^{-x}
\]

\[\therefore
\int \frac{1}{e^x} \, dx = -e^{-x} + C
\]

Q60.\(\int\frac{3}{5x^4} dx=\) ___\(+C\)

\(\frac{-3}{5x^3}\)
\(\frac{-12}{5x^5}\)
\(\frac{3}{20x^3}\)
\(\frac{-1}{5x^3}\)

Correct Ans: D

Solution:

\[
\int \frac{3}{5x^4} \, dx
\]

\[
\int \frac{3}{5} x^{-4} \, dx = \frac{3}{5} \int x^{-4} \, dx
\]
Use the power rule

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} \quad \text{for } n \neq -1
\]

Here, \(n = -4\), so:

\[
\int x^{-4} \, dx = \frac{x^{-3}}{-3} = -\frac{1}{3x^3}
\]

\[\therefore
\frac{3}{5} \cdot \left(-\frac{1}{3x^3}\right) = -\frac{1}{5x^3}
\]

Q61.\(\int \frac{4x-10}{x^2-5x+1} dx=\)_____\(+C\)

\(2 log \vert 2x-5 \vert\)
\(2 log \vert x^2-5x+1 \vert\)
\(\frac{2}{ log \vert 2x-1 \vert}\)
\(\frac{2}{ log \vert x^2-5x+1 \vert}\)

Correct Ans: B

Solution:

\[
\int \frac{4x - 10}{x^2 - 5x + 1} \, dx
\]

Let:
\[
u = x^2 - 5x + 1 \Rightarrow du = (2x - 5)\,dx
\]

\[\therefore
\frac{4x - 10}{x^2 - 5x + 1} \, dx = \frac{2(2x - 5)}{u} \, dx = 2 \cdot \frac{du}{u}
\]

\[
\int 2 \cdot \frac{1}{u} \, du = 2 \ln |u| + C
\]

Substitute back: \(u = x^2 - 5x + 1\):

\[=
2 \ln |x^2 - 5x + 1| + C
\]

Q62.\(\int_{-\pi}^{\pi} x^2 \sin x \: dx = \)_____

\(0\)
\(1\)
\(-1\)
\(-2 \pi\)

Correct Ans: A

Solution:

\[
\int_{-\pi}^{\pi} x^2 \sin x \, dx
\]

\(\rightarrow x^2\) is even: \(x^2 = (-x)^2\)

\(\rightarrow \sin x\) is odd: \(\sin(-x) = -\sin x\)

\[\therefore
x^2 \sin x \text{ is the product of even and odd functions ⇒ an odd function}
\]

\(\rightarrow\) Use symmetry of definite integrals.

\(\rightarrow\) The integral of an odd function over a symmetric interval \([ -a, a ]\) is always zero:

\[
\int_{-a}^{a} \text{(odd function)} \, dx = 0
\]

Q63.\(\frac{log 125}{log 5}\)=_____

\(log 125 - log 5\)
\(log 120 \)
\(25\)
\(3\)

Correct Ans: D

Solution:

\[
\frac{\log 125}{\log 5}
\]

\[where, \:
\log 125 = \log (5^3) = 3 \log 5
\]

\[
\frac{\log 125}{\log 5} = \frac{3 \log 5}{\log 5}
\]

\[
= 3
\]

Q64.\(log 2 + 2 log 3\) =_____

\(2 log 6\)
\(log 8\)
\(log 18\)
\(log 12\)

Correct Ans: C

Solution:

\[
\log 2 + 2 \log 3
\]

\[where, \:
2 \log 3 = \log (3^2) = \log 9
\]

\[\therefore
\log 2 + \log 9 = \log (2 \cdot 9) = \log 18
\]

Q65.The mean of the first five negative integers is ___.

15
-15
3
-3

Correct Ans: D

Solution:

The first five negative integers are:
\[
-1,\ -2,\ -3,\ -4,\ -5
\]

\[\therefore
\text{Mean} =\frac{sum}{number \: of \: terms}= \frac{-15}{5} = -3
\]

Q66.\(\begin{bmatrix}
\tan x & -\csc x \\
-\sin x & -\cot x
\end{bmatrix} =\) _____

0
-1
-2
-3

Correct Ans: C

Solution:

\[
\begin{bmatrix}
\tan x & -\csc x \\
-\sin x & -\cot x
\end{bmatrix}
\]

\[\therefore
\det = (\tan x)(-\cot x) - (-\csc x)(-\sin x)
\]

\[\therefore
\det = \left( \frac{\sin x}{\cos x} \right) \left( -\frac{\cos x}{\sin x} \right) - \left( -\frac{1}{\sin x} \right)(-\sin x)
\]

\[\therefore
\det = -1 - 1 = -2
\]

Q67.The matrix \(\begin{bmatrix}
3 & 1 & -2 \\
1 & 0 & 5 \\ -2 & 5 & 4
\end{bmatrix} \) is a ____ matrix.

Singular
Symmetric
Skew-symmetric
Diagonal

Correct Ans: B

Solution:

\[Given:
A = \begin{bmatrix}
3 & 1 & -2 \\
1 & 0 & 5 \\
-2 & 5 & 4
\end{bmatrix}
\]

\(\quad 1.\) Symmetric Matrix:

A matrix is symmetric if \( A = A^T \) (transpose equals the original).

\[
A^T = \begin{bmatrix}
3 & 1 & -2 \\
1 & 0 & 5 \\
-2 & 5 & 4
\end{bmatrix}
= A
\]

\(\therefore\) A is symmetric.

\(\quad 2.\) Skew-symmetric Matrix:

For a matrix to be **skew-symmetric**, \( A^T = -A \).

Here, since \( A = A^T \), it is **not** skew-symmetric.

\(\quad 3.\) Diagonal Matrix:

A diagonal matrix has non-zero entries only on the main diagonal and zeros elsewhere.

This matrix has non-zero off-diagonal elements (like 1 and -2), so it's not diagonal.

\(\quad 4.\) Singular Matrix:

A matrix is singular if its determinant is 0.

\[
\text{det}(A) =
3 \begin{vmatrix} 0 & 5 \\ 5 & 4 \end{vmatrix}
- 1 \begin{vmatrix} 1 & 5 \\ -2 & 4 \end{vmatrix}
+ (-2) \begin{vmatrix} 1 & 0 \\ -2 & 5 \end{vmatrix}
\]

\[
\text{det}(A) = -75 - 14 - 10 = -99 \neq 0
\]

\(\therefore\) It is not singular.

Q68.If \(A=\begin{bmatrix}3 & 1 & -2 \end{bmatrix} \) and \(B= \begin{bmatrix}-5 \\ 0 \\ 4 \end{bmatrix} \) then \(AB=\)____

\(\begin{bmatrix}-2 & 1 & 6 \end{bmatrix} \)
\(\begin{bmatrix}-15 & 0 & 8 \end{bmatrix} \)
\(\begin{bmatrix}-7 \end{bmatrix} \)
\(None\)

Correct Ans: D

Solution:

\[
A = \begin{bmatrix} 3 & 1 & -2 \end{bmatrix}, \quad B = \begin{bmatrix} -5 \\ 0 \\ 4 \end{bmatrix}
\]

\(\rightarrow\) \(A\) is a 1×3 row matrix, and \(B\) is a 3×1 column matrix,

\(\therefore\) The product \(AB\) is defined and will result in a 1×1 matrix.

\[\therefore
AB = (3)(-5) + (1)(0) + (-2)(4)
= -15 + 0 - 8 = -23
\]

Q69.\(A=\begin{bmatrix}
4 & 5 \\
-2 & -3
\end{bmatrix} \) then \(A^{-1}=\) ____

\(\begin{bmatrix}
-3 & -5 \\
2 & -4
\end{bmatrix} \)
\(\frac{1}{2}\begin{bmatrix}
-3 & -5 \\
2 & 4
\end{bmatrix} \)
\(\frac{-1}{2}\begin{bmatrix}
-4 & -5 \\
-2 & 3
\end{bmatrix} \)
\(\frac{-1}{2}\begin{bmatrix}
-3 & -5 \\
2 & 4
\end{bmatrix} \)

Correct Ans: D

Solution:

\[
A = \begin{bmatrix} 4 & 5 \\ -2 & -3 \end{bmatrix}
\]
\[\implies
A^{-1} = \frac{1}{\det(A)} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}
\quad \text{for} \quad A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}
\]

\[\therefore
\det(A) = ad - bc = (4)(-3) - (5)(-2) = -12 + 10 = -2
\]

\[\therefore
A^{-1} = \frac{1}{-2} \begin{bmatrix} -3 & -5 \\ 2 & 4 \end{bmatrix}
= \begin{bmatrix} \frac{3}{2} & \frac{5}{2} \\ -1 & -2 \end{bmatrix}
\]

Q70.\(225^\circ = \)____ \(radian.\)

\(\frac{3 \pi}{4}\)
\(\frac{5 \pi}{4}\)
\(\frac{7 \pi}{4}\)
\(\frac{9 \pi}{4}\)

Correct Ans: B

Solution:

\[
\text{Radians} = \text{Degrees} \times \frac{\pi}{180}
\]

\[\implies
225^\circ = 225 \times \frac{\pi}{180} = \frac{225\pi}{180}=\frac{5\pi}{4}
\]

Q71.If \(\sin \theta = \frac{2}{\sqrt{5}}\), then \(\cot \theta=\) _____

\(1\)
\(\frac{1}{2}\)
\(2\)
\(\frac{1}{\sqrt{5}}\)

Correct Ans: B

Solution:

\[
\sin \theta = \frac{2}{\sqrt{5}}
\]

\[where, \:
\sin^2 \theta + \cos^2 \theta = 1
\]

\[\therefore
\left( \frac{2}{\sqrt{5}} \right)^2 + \cos^2 \theta = 1\] \[\Rightarrow \frac{4}{5} + \cos^2 \theta = 1
\Rightarrow \cos^2 \theta = 1 - \frac{4}{5} = \frac{1}{5}
\Rightarrow \cos \theta = \pm \frac{1}{\sqrt{5}}
\]
\[\therefore
\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{\pm \frac{1}{\sqrt{5}}}{\frac{2}{\sqrt{5}}} = \pm \frac{1}{2}
\]

Q72.Peripheral period of \(cos (3+4x)=\)____

\(\frac{\pi}{4}\)
\(\frac{-\pi}{4}\)
\(\frac{\pi}{2}\)
\(\frac{-\pi}{2}\)

Correct Ans: C

Solution:

\[Given:
\cos(3 + 4x)
\]

\[
\text{Period} = \frac{2\pi}{|B|}
\quad \text{for} \quad \cos(Bx + C)
\]

\(\rightarrow\) The function is in the form \(\cos(Bx + C)\), with:

\(\rightarrow\) \(B = 4\)

\(\rightarrow\) \(C = 3\)

\[
\text{Period} = \frac{2\pi}{|4|} = \frac{2\pi}{4} = \frac{\pi}{2}
\]

Q73.\(\vert\hat{i} - 2\hat{j} - 2\hat{k}\vert = \)______

\(3\)
\(-3\)
\(\pm3\)
\(9\)

Correct Ans: A

Solution:

\[
\vec{A} = \hat{i} - 2\hat{j} - 2\hat{k}
\]

\[
|\vec{A}| = \sqrt{a^2 + b^2 + c^2}
\]

\[
|\vec{A}| = \sqrt{1^2 + (-2)^2 + (-2)^2}
= \sqrt{1 + 4 + 4}
= \sqrt{9}
= 3
\]

Q74.\((\hat{i} \times \hat{j}) \circ \hat{k}=\)____

\(\hat{i}\)
\(\hat{k}\)
\(0\)
\(1\)

Correct Ans: D

Solution:

\[Given:
(\hat{i} \times \hat{j}) \circ \hat{k}
\]
Cross product:
\[
\hat{i} \times \hat{j} = \hat{k}
\]
Dot product:
\[
\hat{k} \cdot \hat{k} = 1
\]

\[
(\hat{i} \times \hat{j}) \circ \hat{k} = 1
\]

Q75.If the lines \(x-2y=3\) and \(3y+px-1=0\) are perpendicular to each other then \(p=\)____

\(\frac{3}{2}\)
\(\frac{-3}{2}\)
\(6\)
\(-6\)

Correct Ans: C

Solution:

Given:

1. \(x - 2y = 3\)

2. \(3y + px - 1 = 0\)
\[
x - 2y = 3 \Rightarrow -2y = -x + 3 \Rightarrow y = \frac{1}{2}x - \frac{3}{2}
\]

\(\therefore\) slope \(m_1 = \frac{1}{2}\)

Line 2:

\[
3y + px = 1 \Rightarrow 3y = -px + 1 \Rightarrow y = \frac{-p}{3}x + \frac{1}{3}
\]

\(\therefore\) slope \(m_2 = \frac{-p}{3}\)

\(\Rightarrow\) The condition for perpendicular lines:
\[
m_1 \cdot m_2 = -1
\]

\[
\frac{1}{2} \cdot \left( \frac{-p}{3} \right) = -1
\Rightarrow \frac{-p}{6} = -1
\Rightarrow p = 6
\]

Q76.A letter of adjustment is generally written in response to _______________.

letter of inquiry
request letter
order letter
complaint letter

Correct Ans: D

Solution:

\(\Rightarrow\) A letter of adjustment is written in response to a \(\textbf{complaint letter}\) to address grievances or resolve issues.

Q77.Which of the following statement is correct about letter of inquiry?

written to offer a product.
written to seek details about product or service.
written to start investigation..
written to raise a complaint.

Correct Ans: B

Solution:

\(\Rightarrow\) A letter of inquiry (B) seeks details about products/services, distinct from complaints or offers.

Q78.Which of the following is an essential part of business letter?

Executive summary
Identification initials.
Inside address
Carbon copy notation

Correct Ans: C

Solution:

\(\Rightarrow\) The \(\textbf{inside address}\) (recipient's address) is essential in business letters for formal communication.

Q79.Which of the following parts is used to take a courteous leave from a letter?

Greetings
Salutation
Complimentary close
Enclosure

Correct Ans: C

Solution:

\(\Rightarrow\) The \(\textbf{complimentary close}\) (e.g., "Sincerely") is the courteous farewell in a letter.

Q80.Give the full form of 'PS' used in letter writing.

Please
Post Service
Personnel Service
Post Script

Correct Ans: D

Solution:

\(\Rightarrow\) "PS" stands for \(\textbf{Post Script}\), used to add information after the main message.

Q81.The talented singer danced quickly. (Identify the adverb)

talented
quickly
danced
singer

Correct Ans: B

Solution:

\(\Rightarrow\) The adverb \(\textbf{quickly}\) modifies the verb "danced," describing how the action was performed.

Q82.The captain along with ten players ______________ arrived at the stadium. (Select the correct option)

has
have
is
are

Correct Ans: A

Solution:

\(\Rightarrow\) With "captain along with," the singular verb \(\textbf{has}\) agrees with the subject "captain."

Q83.None of the products _____________ up to the mark, so we returned them all. (Select the correct option)

is
are
was
were

Correct Ans: D

Solution:

\(\Rightarrow\) "None" with plural "products" requires plural verb \(\textbf{were}\) in past tense.

Q84.There is a church ___________ the lake. (Select the correct option)

over
on
between
above

Correct Ans: B

Solution:

\(\Rightarrow\) The church is located \(\textbf{on}\) the lake's edge (surface contact), not above/over.

Q85.He ____________ to the gym every morning before work. (Select the correct option)

goes
went
is going
go

Correct Ans: A

Solution:

\(\Rightarrow\) Present simple tense \(\textbf{goes}\) indicates habitual action ("every morning").

Q86.Select the correct spelling.

Fahrenhit
Ferrenhit
Fahrenheit
Fahrenheat

Correct Ans: C

Solution:

\(\Rightarrow\) Correct spelling: \(\textbf{Fahrenheit}\), named after physicist Daniel Fahrenheit.

Q87.Select the correct spelling.

Inconvenience
Inconveninse
Inconvinience
Inconviniance

Correct Ans: A

Solution:

\(\Rightarrow\) Correct spelling: \(\textbf{Inconvenience}\) (meaning "trouble" or "hardship").

Q88.Identify the correct sentence.

The criminals arrested by police.
The police are arrested the criminals.
The police were arrested the criminals.
The police arrested the criminals.

Correct Ans: D

Solution:

\(\Rightarrow\) Active voice correct: \(\textbf{"The police arrested the criminals"}\). Others are passive/grammatically incorrect.

Q89.Identify the correct sentence.

Shreya is tired as she had worked since 7 o'clock.
Shreya is tired as she has been working since 7 o'clock.
Shreya was tired as she has worked since 7 o'clock.
Shreya is tired as she working since 7 o'clock.

Correct Ans: B

Solution:

\(\Rightarrow\) Present perfect continuous \(\textbf{"has been working"}\) shows ongoing action from past to present.

Q90.Identify the correct sentence.

The father purchased a vividly illustrated children's dictionary for his daughter.
The father purchased a child's vividly illustrated dictionary for her daughter.
The father purchased a children's vividly illustrated dictionary for his daughter.
The father purchased an illustrated child's vivid dictionary for his daughter.

Correct Ans: A

Solution:

\(\Rightarrow\) Correct phrasing: \(\textbf{"vividly illustrated children's dictionary"}\) (proper adjective-noun order).

Q91.Read the following passage carefully and answer the questions:

The ancient stepwell, Chand Baori, descended into the earth like a forgotten dream. Its geometric steps, thousand precise cuts into the Sandstone, spiraled down towards the emerald depths of the water. The air within its shadowed walls was cool, a welcome respite from the scorching Rajasthani sun. Villagers, their colourful turbans and saris vibrant against the stone, gathered at the upper levels, drawing water in earthen pots. Legends whispered of a hidden chamber deep within the stepwell, a place where the spirits of the desert dwelled, guarding secrets of forgotten Kings.
A traveling musician, his sitar echoing through the vast space, played haunting ragas, his melodies blending with the gentle splash of water. A lone scholar, his spectacles perched on his nose, meticulously studied the intricate carvings on the walls,searching for clues to the stepwell's mysterious origins and the stories etched into its sandstone heart.

What was the purpose of the steps in Chand Baori?

To provide seating for spectators
To create a maze for tourists
To allow access to the water deep below
To form a decorative pattern

Correct Ans: C

Solution:

\(\Rightarrow\) Steps allow \(\textbf{access to water}\) in the stepwell, as described in the passage.

Q92.The "cool shadowed walls" of the stepwell provide:

A place for loud celebrations.
A relief from the desert heat.
A place for modern art display.
A site for industrial activity.

Correct Ans: B

Solution:

\(\Rightarrow\) "Cool shadowed walls" provide \(\textbf{relief from desert heat}\), contrasting the "scorching sun."

Q93.According to legends, what was hidden deep within the stepwell?

A treasure vault
Sacred water
A secret passage to the fort
A chamber of desert spirit

Correct Ans: D

Solution:

\(\Rightarrow\) Legends mention a \(\textbf{chamber of desert spirits}\) guarding secrets.

Q94.The phrase "forgotten dream" used to describe Chand Baori suggests:

The stepwell's historical significance and potential obscurity.
The stepwell's modern architectural design.
The stepwell's role as a tourist attraction.
The stepwell's frequent use by villagers.

Correct Ans: A

Solution:

\(\Rightarrow\) "Forgotten dream" implies \(\textbf{historical significance and obscurity}\), not modern use.

Q95.What was the scholar searching for in the carvings?

Precious gems
Ancient map of desert
Clues to stepwell's origin
Hidden doorways

Correct Ans: C

Solution:

\(\Rightarrow\) The scholar studies carvings for \(\textbf{clues to the stepwell's origin}\).

Q96.While communicating, the process of understanding the original idea of the message is called ______________ .

Decoding
Feedback
Encoding
Transmission

Correct Ans: A

Solution:

\(\Rightarrow\) \(\textbf{Decoding}\) is interpreting the sender's message by the receiver.

Q97.____________ is the study of body language and its effect on communication including facial expression, gestures, etc.

Proxemics
Chronemics
Paralanguage
Kinesics

Correct Ans: D

Solution:

\(\Rightarrow\) \(\textbf{Kinesics}\) studies body language (gestures, expressions).

Q98.Which of the following is not an example of verbal communication ?

A manager giving instructions to workers orally.
A man shaking hand with a foreigner.
A student writing a letter to the principal.
An oldman reading a news paper.

Correct Ans: B

Solution:

\(\Rightarrow\) \(\textbf{Shaking hands}\) is non-verbal; others involve spoken/written words.

Q99.What is common result of socio-cultural barrier to communication?

Enhanced comprehension.
Improved content clarity.
Misinterpretation of intent.
Enriched social connection.

Correct Ans: C

Solution:

\(\Rightarrow\) Socio-cultural barriers often cause \(\textbf{misinterpretation}\) due to differing norms.

Q100.Factors such as person's emotions, anxiety, stress and fear can form ____________ barrier to communication.

Personal Barrier
Psychological Barrier
Physical Barrier
Neurological Barrier

Correct Ans: B

Solution:

\(\Rightarrow\) Emotions like anxiety create \(\textbf{psychological barriers}\) to effective communication.

Subject wise analysis

Subject	Number of questions
Basics of Science and Engineering (DDCET)	50
Aptitude Test (Mathematics and Soft Skill) DDCET	50
Total	100

Q1.Burning of coal is a which type of process ?

Double displacement
Decomposition
Combination
Displacement

Correct Ans: C

Q2.\(Na_2SO_{4 (aq)} + BaCl_2(aq) \rightarrow BaSO_{4(aq)} + NaCl_{(aq)}\). Which type of reaction is this?

Combination
Double displacement
Decomposition
None of above

Correct Ans: B

Q3.Reaction of Zinc with Sulphuric acid gives Zinc Sulphate and Hydrogen. Which is the balanced equation for this chemical Change?

\(Zn+ 2H_2SO_4 \rightarrow 2ZnSO_4 + H_2\)
\(2Zn+ H_2SO_4 \rightarrow ZnSO_4 + 2H_2\)
\(Zn+ H_2SO_4 \rightarrow ZnSO_4 + H_2\)
None of above

Correct Ans: C

Q4.The outer layer of the teeth is made-up of

Calcium nitrate
Potassium phosphate
Calcium chloride
) Calcium phosphate

Correct Ans: D

Q5.The pH of aqueous solution of which salt is 7.0 ?

\(KNO_3\)
\(NH_4CL\)
\(CH_3COONa\)
\(Na_2CO_3\)

Correct Ans: A

Q6.Metal oxide + Acid \(\rightarrow\) _____

Base + Water
Salt+ Water
Acid + Salt
None of these

Correct Ans: B

Q7.State the molecular formula of Sodium Zincate.

\(Na_2ZnO_3\)
\(Na_2ZnO_2\)
\(NaZnO_2\)
\(Na_2Zn_2O_2\)

Correct Ans: B

Q8.How many electrons are present in the outermost shell of fluorine?

Correct Ans: B

Q9.Which of the following methods is suitable for preventing an iron frying pan from rusting?

Applying grease
Applying paint
Applying a coating of zinc
All of the above.

Correct Ans: C

Q10.Which of following metals is highly malleable?

Gold
Lead
Both (A) and (B)
None of these

Correct Ans: A

Q11._____ is not valid data type in MS-Excel.

Number
Character
Label
Date/time

Correct Ans: C

Q12.What is the max zoom percentage in MS-PowerPoint?

Correct Ans: A

Q13.Which is not in MS-Word ?

ltalic
Magic tool
Font
Bold

Correct Ans: B

Q14.CPU consist of

ALU + CU
ROM + ALU
RAM + ROM
None of the above

Correct Ans: A

Q15.Which of the following is not OS (Operating System)

UNIX
MS-DOS
LINUX
Microsoft Office

Correct Ans: D

Q16.Which pollutant is commonly associated with "blue baby Syndrome" in infants?

Lead
Arsenic
Mercury
Nitrate

Correct Ans: D

Q17.Clouds are present in _______ layers of atmosphere?

Stratosphere
Troposphere
Mesosphere
Thermosphere

Correct Ans: B

Q18.CFCs are not recommended to be used in refrigerators because they_______

Increase temperature
Affect environment
Deplete ozone
Affect human body

Correct Ans: C

Q19.What is the approximate efficiency range of modern solar photovoltaic (PV) panels in converting Sunlight in to electricity?

5- 10%
15 -20%
20 -30%
40 - 50%

Correct Ans: B

Q20.Which pollutant is primarily responsible for causing respiratory problems and cardiovascular diseases in humans?

Lead
Benzene
Particulate matter (PM10)
Carbon Monoxide (CO)

Correct Ans: C

Q21.What is the S.I unit of power?

Joule
Volt
Watt
Ampere

Correct Ans: C

Q22.The pitch of micrometer screw is 0.5 mm. There are 50 divisions on it's circular scale. What will be the least count of the screw?

0.1 mm
0.001 mm
1 mm
0.01 mm

Correct Ans: D

Q23.10 dyne= ________N?

\(10^{-5}\)
\(10^{-4}\)
\(10^{5}\)
\(10^{7}\)

Correct Ans: B

Q24.What is the unit of Energy in CGS.

Newton
Watt
Joule
Arg

Correct Ans: The correct answer does not align perfectly with the provided options

Q25.The refractive index of water is found to have the values 1.30, 1.32, 1.34, 1.35, 1.31. Calculate the mean absolute error.

0.01254
0.1254
1.254
0.001254

Correct Ans: The correct answer does not align perfectly with the provided options

Q26.Which instrument is used to measure "Inner diameter of the ring"?

Vernier caliper
Micrometer screw
Spherometer
Physical balance

Correct Ans: A

Q27.The mathematical expression for Newton's second law is___________

\(F=mv\)
\(P=mv\)
\(F=ma\)
\(P=ma\)

Correct Ans: C

Q28.Find the acceleration produced by applying a force of \(30\: N\) on an object of mass of \(5\: kg\).

\(0.6\:m/s^2\)
\(6\:m/s^2\)
\(6\:m/s\)
\(0.6\:m/s\)

Correct Ans: B

Q29.__________are the examples of impulse of force.

China wares are wrapped in paper while packing.
Bogies of a train are provided with the buffers.
Both (A) and (B)
None of above

Correct Ans: C

Q30.A body is moving in a vertical circular motion, which one of the following forces does not experience?

Force of gravity
Centripetal force
Friction force
Centrifugal force

Correct Ans: C

Q31.___________is the field force.

Gravitational force
Magnetic force
Electrical force
All of above

Correct Ans: D

Q32.The work done by the external forces on a system equals the changes in___________

Total energy
Kinetic energy
Potential energy
None of these

Correct Ans: A

Q33.\(6\:V\) battery is connected across a resistance \(R\). The current through \(R\) is \(0.4\: mA\). What will be the value of \(R\)?

\(10\: k\Omega\)
\(15\: k\Omega\)
\(20\: k\Omega\)
\(24\: k\Omega\)

Correct Ans: B

Q34.___________is the Unit of permitivity.

\( N m^2 /C^2\)
\(A/m\)
\(N /m^2C\)
\(C^2 / N m^2\)

Correct Ans: D

Q35.The Electric flux depends on the__________

Electric field intensity
Area
Angle between the surface and the electric field.
All of these

Correct Ans: D

Q36.Inverse of Resistance is known as__________

current
specific resistance
conductance
voltage

Correct Ans: C

Q37.What is the effective value of resistance when two resistors \(10\:\Omega\) and \(20\:\Omega\) are connected in parallel combination?

\(10\:\Omega\)
\(20\:\Omega\)
\(30\:\Omega\)
\(6.6\:\Omega\)

Correct Ans: D

Q38.The Unit of capacitance is__________

Correct Ans: B

Q39.Arrange the metals Aluminium, Copper, Iron and Silver in increasing order of thermal conductivity.

Iron, Aluminium, Copper, Silver
Aluminium, Iron, Copper, Silver
Copper, Iron, Silver, Aluminium
Iron, Copper, Aluminium, Silver

Correct Ans: A

Q40.At what temperature are Celsius and Fahrenheit equal?

\(40^\circ C\)
\(40^\circ F\)
\(-40^\circ C\) and \(-40^\circ F\)
None of above

Correct Ans: C

Q41.Unit of heat capacity is

\(J/K\)
\(Cal/K\)
\(Cal/^\circ C\)
All of above

Correct Ans: D

Q42.With rising temperatures, the thermal conductivity will be_________

Decreased
Increased
Remain constant
Zero

Correct Ans: The correct answer does not align perfectly with the provided options

Q43.The mathematical formula of specific heat is___________

\(C = Q / m \Delta T\)
\(Q = C / m \Delta T\)
\(H_c = Q / \Delta L\)
\(Q = H_c / \Delta L\)

Correct Ans: A

Q44.A person is having temperature of \(104^\circ F\). Convert it in Celsius.

\(38^\circ C\)
\(40^\circ C\)
\(-40^\circ C\)
\(-38^\circ C\)

Correct Ans: B

Q45.Which of the following is not a type of electromagnetic wave?

Sound wave
Light wave
Gamma Ray
Micro wave

Correct Ans: A

Q46.Which type of wave is a light wave?

Longitudinal
Transverse
Both (A) and (B)
None of the above

Correct Ans: B

Q47.The frequency of sound wave is \(2\:kHz\) and it's wave length is \(2\:m\). What is the speed of sound wave?

\(2000 \:m/s\)
\(400 \:m/s\)
\(200 \:m/s\)
\(4000 \:m/s\)

Correct Ans: D

Q48.__________is not the characteristics of LASER.

Coherent
Monochromatics
Divergent
High intensity

Correct Ans: C

Q49.Optical fibre works on the principle of___________

Total internal reflection
Polarization
Refraction
Differaction

Correct Ans: A

Q50.A volume of an auditorium is \(6000 \: m^3\) . The total absorption by the surfaces is \(1000\: O.W.U.\) Then calculate reverberation time.

9 second
0.966 second
90 second
9.6 second

Correct Ans: B

Q51.\(\lim_{x \rightarrow 0} (\frac{10^x-5^x}{x})\) = _____

\(\log_e \frac{1}{2}\)
\(\log_e 10\)
\(\log_e 5\)
\(\log_e 2\)

Correct Ans: D

Q52.\(\lim_{n \rightarrow \infty} \frac{3n^2 - 11n -13}{(4n-5)(7-6n)}\) = _____

\(\frac{1}{4}\)
\(-\frac{1}{8}\)
\(\frac{1}{6}\)
\(-\frac{1}{4}\)

Correct Ans: B

Q53.If \(\text{f(x)=\(log_4\)(x) then f(64) = ____ }\)

\(3\)
\(-3\)
\(6\)
\(\frac{1}{3}\)

Correct Ans: A

Q54.\(\frac{d}{dx} (\cos^2 x)\) = _____

\(\sin 2x\)
\(-\sin 2x\)
\(\cos 2x\)
\(-\cos 2x\)

Correct Ans: B

Q55.\(\frac{d}{dx} [\log (\sqrt{x^2-9})]\) = _____

\(\frac{1}{\sqrt{x^2-9}}\)
\(\frac{x}{\sqrt{x^2-9}}\)
\(\frac{9}{{x^2-9}}\)
\(\frac{x}{{x^2-9}}\)

Correct Ans: D

Q56.If \(x=\csc \theta\) and \(y=\cot \theta\) then \(\frac{dy}{dx}\) = ____

\(\sec \theta\)
\(\csc \theta\)
\(\sin \theta\)
\(\cos \theta\)

Correct Ans: A

Q57.The necessary condition for the function \(f(x)\) to be minimum at \(x=a\) is _____

\(f^{"} (a) >0\)
\(f^{"} (a) <0\)
\(f^{'} (a) >0\)
\(f^{'} (a) <0\)

Correct Ans: A

Q58.\(\int \cos (10x-17) dx\) =____ \(+ c\)

\(10 \sin (10x-17)\)
\(-10 \sin (10x-17)\)
\(\frac{1}{10} \sin (10x-17)\)
\(-\frac{1}{10} \sin (10x-17)\)

Correct Ans: C

Q59.\(\int_{-1}^1 \sin^5 x \cos^8 x \: dx\) = ____

\(-1\)
\(0\)
\(\frac{1}{2}\)
\(\frac{1}{4}\)

Correct Ans: B

Q60.\(\int e^x (\csc^2 x- \cot x) dx\) =____\(+c\)

\(e^x \csc^2 x\)
\(-e^x \csc^2 x\)
\(e^x \cot x\)
\(-e^x \cot x\)

Correct Ans: D

Q61.\(\int \frac{x-3}{x^2-6x+40} dx\) = ____\(+c\)

\(\frac{1}{2} \log \: \lvert x^2-6x+40\rvert \)
\(-\frac{1}{2} \log \: \lvert x^2-6x+40\rvert \)
\(2 \log \: \lvert x^2-6x+40\rvert \)
\(-2 \log \: \lvert x^2-6x+40\rvert \)

Correct Ans: A

Q62.\(\log_{\frac{1}{81}} \frac{1}{9}\) = ____

\(9\)
\(\frac{1}{9}\)
\(\frac{1}{2}\)
\(-\frac{1}{2}\)

Correct Ans: C

Q63.\(4^{log_2 3} + 2^{log_8 27} =\) ____

Correct Ans: D

Q64.If the mean of the observations \(\text{19,15,12,k,8,3}\) is \(11\), then \(\text{k}=\)___

Correct Ans: B

Q65.If \(A= \begin{bmatrix} 1 & -1 \\ 1 & 2 \end{bmatrix}\) and \(B= \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}\) then \((AB)^T\)= \(_{…..........}\)

\( \begin{bmatrix} 3 & -2 \\ 7 & 0 \end{bmatrix}\)
\( \begin{bmatrix} 3 & 0 \\ -2 & 7 \end{bmatrix}\)
\( \begin{bmatrix} 3 & -2 \\ 0 & 7 \end{bmatrix}\)
\( \begin{bmatrix} 3 & 0 \\ 7 & -2 \end{bmatrix}\)

Correct Ans: B

Q66.If \(A= \begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 3 \\ 1 & 1 & 0 \end{bmatrix} \) then \( |A|= _{----------}.\)

-3
3
-4
4

Correct Ans: D

Q67.If \(A= \begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix}\) then \(A^{-1}= _{----------}.\)

\( \frac{1}{5} \begin{bmatrix} 1 & 1 \\ -3 & 2 \end{bmatrix}\)
\( \frac{1}{5} \begin{bmatrix} 2 & 1 \\ -3 & 1 \end{bmatrix}\)
\( \frac{1}{5} \begin{bmatrix} 1 & -1 \\ 3 & 2 \end{bmatrix}\)
\( \frac{1}{5} \begin{bmatrix} -2 & 3 \\ -1 & -1 \end{bmatrix}\)

Correct Ans: A

Q68.If \(A= \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}\) and \(B= \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}\) then \(3B-2A=_{…..........}.\)

\( \begin{bmatrix} 4 & -3 \\ -1 & 6 \end{bmatrix}\)
\( \begin{bmatrix} 4 & -3 \\ -1 & -6 \end{bmatrix}\)
\( \begin{bmatrix} -1 & 2 \\ 4 & -9 \end{bmatrix}\)
\( \begin{bmatrix} -1 & 2 \\ 4 & 9 \end{bmatrix}\)

Correct Ans: D

Q69.\(\sin{(225^\circ)}= _{…..........}.\)

\(\frac{-1}{\sqrt{2}}\)
\(\frac{1}{\sqrt{2}}\)
\(\frac{\sqrt{3}}{2}\)
\(\frac{-1}{2}\)

Correct Ans: A

Q70.If \(\tan{\theta}=-\frac{12}{5}, \: \: \frac{3 \pi}{2}<\theta <2 \pi \) then \(\cos{\theta}= _{…..........}.\)

\(\frac{-12}{13}\)
\(\frac{12}{13}\)
\(\frac{5}{13}\)
\(\frac{-5}{13}\)

Correct Ans: C

Q71.\(\cos^{-1} (-\frac{\sqrt{3}}{2})= _{…..........}.\)

\(\frac{2\pi}{3}\)
\(\frac{-\pi}{6}\)
\(\frac{5\pi}{3}\)
\(\frac{5\pi}{6}\)

Correct Ans: D

Q72.If \(|\overline{x} \times \overline{y}| = |\overline{x}| = |\overline{y}|= \sqrt{2}\) then \((\angle {\overline{x}, \overline{y}})= _{…..........}.\)

\(\frac{\pi}{3}\)
\(\frac{\pi}{4}\)
\(\frac{\pi}{6}\)
\(\frac{\pi}{2}\)

Correct Ans: B

Q73.If vectors \(( 2,\: 3,\: a )\) and \(( 3,\: -1,\: 4 )\) are perpendicular then \(a= _{…..........}.\)

\(\frac{-3}{4}\)
\(\frac{3}{4}\)
\(\frac{4}{3}\)
\(\frac{-4}{3}\)

Correct Ans: A

Q74.If the centre of the circle \(x^2+y^2-6my+11=0\) is \((0,\: -3)\) then \(m = _{…..........}.\)

2
-2
1
-1

Correct Ans: D

Q75.Equation of the line passing through the points \((1, \: -1)\) and \((-1, \: 1)\) is \(_{…..........}.\)

\(2x+y-1=0 \)
\( x+2y-1=0 \)
\( x+y=0 \)
\( x+2y+1=0 \)

Correct Ans: C

Q76.Which of the following is not a part of the business letter?

Photo
Salutation
Date
Signature

Correct Ans: A

Q77.A letter is incomplete and worthless without_________.

Signature
Postscript
Enclosure
Photo

Correct Ans: A

Q78.Give the full form of C.O.D.

Cash on delay
Cash on delivery
Cash on order
Cash on distance

Correct Ans: B

Q79.Hurrah! I have passed the examination. Identify the interjection.

Examination
Passed
Hurrah!
The whole sentence.

Correct Ans: C

Q80.The dog is sitting _________ the cot. Select appropriate option.

under
into
between
up

Correct Ans: A

Q81.The Sun __________ in the East. Select appropriate option.

raise
rises
rise
raised

Correct Ans: B

Q82.Your family __________ a happy family. Select appropriate option.

are
is
has
have

Correct Ans: B

Q83.Do you have ____________ doubt in this question paper? Select appropriate option.

some
any
many
much

Correct Ans: B

Q84.Select the correct spelling.

Playwright
Playwrite
Playright
Playrite

Correct Ans: A

Q85.Select the correct spelling.

Enterpeneur
Entrepreneur
Enterpreneur
Entrepeneur

Correct Ans: B

Q86.Choose the correct grammatical sentence.

People were coming, going and ignorant him.
People were coming, going and ignoring him.
People where coming, going and ignoring him
People were coming, going and ignored him.

Correct Ans: B

Q87.Choose the correct grammatical sentence.

I like drawing my coworkers and my cat.
I Like drawing, my coworkers and my cat.
I like drawing, my coworkers, and, my cat.
I, Like, drawing, my coworkers, and, my, cat.

Correct Ans: B

Q88.Choose the correct grammatical sentence.

The ship was wrecked, and every man, woman and child have drowned.
The ship was wrecked, and every man, woman, and child are drowned.
The ship was wrecked, and every man, woman and child is drowned.
The ship was wrecked, and every man, woman and child was drowned.

Correct Ans: D

Q89.\(\textbf{Read the following passage carefully and answer the questions: (Q.No. 089 to 093)}\)

The science of fireworks is technically called 'pyrotechnics' from the Greek word 'pyr' meaning fire and 'technics' meaning an art. Pyrotechnics includes not only fireworks but also whole range of devices that use similar materials and principles, from safety matches that we use every day to solid fuel rocket boosters of space shuttle. The household match is considered a special pyrotechnic device, as all the pyrotechnic effect heat, smoke, light, gas and sound are present in it.

Some historians say that 'black powder', the basic material used in fireworks, was invented in India, Shukranti, written more than two thousand years ago, has references to weapons similar to guns and projectile weapons. However, the Chinese are generally considered the pioneers of pyrotechnics. They are said to have developed, black powered more than one thousand years ago. It took at least two thousand years for the knowledge to spread to the West, and it was only in 1242 that an English Monk. Roger Bacon, revealed the formula for "black powder". He considered it such a dangerous substance that he wrote of it in a code language.

\(\mathbf{Ques.}\) As per some historians 'Black Powder was invented in _________.

India
China
Greek
None of the above

Correct Ans: A

Q90.Roger Bacon was _________.

a Chinese writer
an Indian historian
an English Monk
a Greek philosopher

Correct Ans: C

Q91.Who wrote about 'Black Powder in code language?

Shukranti
Roger Bacon
Chinese
Greek

Correct Ans: B

Q92.When was Shukranti written?

One thousand years ago
In 1242
Two thousand years ago
Modern times

Correct Ans: C

Q93.Pyrotechnics word is from

Indian language
Greek language
Chinese language
None of the above

Correct Ans: B

Q94.Verbal communication can be in __________ form.

written
oral and written
oral
none of these

Correct Ans: B

Q95.Tone of voice, voice quality, style of speaking, stress, intonation are part of _________

body language
sign language
paralanguage
code language

Correct Ans: C

Q96.The process of communication is a __________.

two way
three way
one way
single way

Correct Ans: A

Q97. "During the process of communication at every stage, there is hindrance which disturbs communication process." Such hindrance is known as

barrier
noise
sender
receiver

Correct Ans: A

Q98.Our physical appearance is an example of ____________ communication.

oral
written
verbal
non-verbal

Correct Ans: D

Q99.What is written at the top of a business letter on the left hand side.

Sender's address
Receiver's address
Date
Salutation

Correct Ans: A

Q100.Where is the salutation placed in a business letter?

Just above the date
Just below the date
Along with the subject
None of these

Correct Ans: D

Test Series

Hurry-Up - Attend 1 Free and 29 Paid Test Series In Just ₹ 149 ₹ 499 Only.

Free Mock test – 1 Total Number

Free Mock test – Complete Paper

Free Mock Test DDCET 2025

Paid Mock test – 29 Total Number

Buy Now

Paid Mock test – Subject Wise

Determinant and Matrix

30 Questions

60 Marks

45 Mins

19, Nov 2024

Determinant and Matrix

Trigonometry

17 Questions

34 Marks

26 Mins

23, Nov 2024

Trigonometry

Vectors

15 Questions

30 Marks

23 Mins

27, Nov 2024

Vectors

Coordinate Geometry

15 Questions

30 Marks

23 Mins

30, Nov 2024

Coordinate Geometry

Function and Limits

20 Questions

40 Marks

30 Mins

02, Dec 2024

Function and Limits

Differentiation and its Application

18 Questions

36 Marks

27 Mins

05, Dec 2024

Differentiation and its Application

Integration

18 Questions

36 Marks

27 Mins

08, Dec 2024

Integration

Logarithm

20 Questions

40 Marks

30 Mins

10, Dec 2024

Logarithm

Statistics

10 Questions

20 Marks

15 Mins

12, Dec 2024

Statistics

Chemical Reactions and Equations

15 Questions

30 Marks

23 Mins

02, Dec 2024

Chemical Reactions and Equations

Acids Bases and Salts

15 Questions

30 Marks

23 Mins

05, Dec 2024

Acids Bases and Salts

Metals and Nonmetals

15 Questions

30 Marks

23 Mins

09, Dec 2024

Metals and Nonmetals

Units and Measurement

15 Questions

30 Marks

23 Mins

17, Dec 2024

Units and Measurement

Classical Mechanics

15 Questions

30 Marks

23 Mins

20, Dec 2024

Classical Mechanics

Electric Current

15 Questions

30 Marks

23 Mins

24, Dec 2024

Electric Current

Heat and thermometry

15 Questions

30 Marks

23 Mins

27, Dec 2024

Heat and thermometry

Wave motion, optics and acoustics

15 Questions

30 Marks

23 Mins

31, Dec 2024

Wave motion, optics and acoustics

Computer Practices - BSE

20 Questions

40 Marks

30 Mins

06, Feb 2025

Computer Practices

Comprehension of Unseen Passage

15 Questions

30 Marks

23 Mins

03, Mar 2025

Comprehension of Unseen Passage

Theory of Communication

20 Questions

40 Marks

30 Mins

03, Mar 2025

Theory of Communication

Techniques of Writing

20 Questions

40 Marks

30 Mins

03, Mar 2025

Techniques of Writing

Grammar

15 Questions

30 Marks

23 Mins

03, Mar 2025

Grammar

Correction of Incorrect Words and Sentences

15 Questions

30 Marks

23 Mins

03, Mar 2025

Correction of Incorrect Words and Sentences

BSE - Environmental Sciences

20 Questions

40 Marks

30 Mins

04, Mar 2025

BSE - Environmental Sciences

Paid Mock test – Multiple Subject Wise

SECTION-BSE-2025

50 Questions

100 Marks

75 Mins

15, Mar 2025

SECTION-BSE-2025

SECTION-AT-2025

50 Questions

100 Marks

75 Mins

18, Mar 2025

SECTION-AT-2025

Paid Mock test – Complete Paper

Full Length Test 1 - 2025

100 Questions

200 Marks

150 Mins

21, Mar 2025

Full Length Test 1 - 2025

Full Length Test 2 - 2025

100 Questions

200 Marks

150 Mins

25, Mar 2025

Full Length Test 2 - 2025

Full Length Test 3 - 2025

100 Questions

200 Marks

150 Mins

29, Mar 2025

Full Length Test 3 - 2025

Test Series

Hurry-Up - Attend 1 Free and 5 Paid Test Series In Just ₹ 99 ₹ 199 Only.

Free Mock test – 1 Total Number

Free Mock test – Complete Paper

Free Mock Test DDCET 2025

100 Questions

200 Marks

150 Mins

29, Jul 2024

Free Mock Test

Paid Mock test – 5 Total Number

Buy Now

Paid Mock test – Multiple Subject Wise

SECTION-BSE-2025

50 Questions

100 Marks

75 Mins

15, Mar 2025

SECTION-BSE-2025

SECTION-AT-2025

50 Questions

100 Marks

75 Mins

18, Mar 2025

SECTION-AT-2025

Paid Mock test – Complete Paper

Full Length Test 1 - 2025

100 Questions

200 Marks

150 Mins

21, Mar 2025

Full Length Test 1 - 2025

Full Length Test 2 - 2025

100 Questions

200 Marks

150 Mins

25, Mar 2025

Full Length Test 2 - 2025

Full Length Test 3 - 2025

100 Questions

200 Marks

150 Mins

29, Mar 2025

Full Length Test 3 - 2025

Test Series

Hurry-Up - Attend 0 Free and 1 Paid Test Series In Just ₹ 19 ₹ 49 Only.

Paid Mock test – 1 Total Number

Buy Now

Paid Mock test – Subject Wise

BSE - Environmental Sciences

20 Questions

40 Marks

30 Mins

04, Mar 2025

BSE - Environmental Sciences

Test Series

Hurry-Up - Attend 0 Free and 5 Paid Test Series In Just ₹ 99 ₹ 199 Only.

Paid Mock test – 5 Total Number

Buy Now

Paid Mock test – Subject Wise

Comprehension of Unseen Passage

15 Questions

30 Marks

23 Mins

03, Mar 2025

Comprehension of Unseen Passage

Theory of Communication

20 Questions

40 Marks

30 Mins

03, Mar 2025

Theory of Communication

Techniques of Writing

20 Questions

40 Marks

30 Mins

03, Mar 2025

Techniques of Writing

Grammar

15 Questions

30 Marks

23 Mins

03, Mar 2025

Grammar

Correction of Incorrect Words and Sentences

15 Questions

30 Marks

23 Mins

03, Mar 2025

Correction of Incorrect Words and Sentences

Test Series

Hurry-Up - Attend 0 Free and 1 Paid Test Series In Just ₹ 19 ₹ 49 Only.

Paid Mock test – 1 Total Number

Buy Now

Paid Mock test – Subject Wise

Computer Practices - BSE

20 Questions

40 Marks

30 Mins

06, Feb 2025

Computer Practices

Test Series

Hurry-Up - Attend 0 Free and 5 Paid Test Series In Just ₹ 99 ₹ 199 Only.

Paid Mock test – 5 Total Number

Buy Now

Paid Mock test – Subject Wise

Units and Measurement

15 Questions

30 Marks

23 Mins

17, Dec 2024

Units and Measurement

Classical Mechanics

15 Questions

30 Marks

23 Mins

20, Dec 2024

Classical Mechanics

Electric Current

15 Questions

30 Marks

23 Mins

24, Dec 2024

Electric Current

Heat and thermometry

15 Questions

30 Marks

23 Mins

27, Dec 2024

Heat and thermometry

Wave motion, optics and acoustics

15 Questions

30 Marks

23 Mins

31, Dec 2024

Wave motion, optics and acoustics

Test Series

Hurry-Up - Attend 0 Free and 3 Paid Test Series In Just ₹ 49 ₹ 99 Only.

Paid Mock test – 3 Total Number

Buy Now

Paid Mock test – Subject Wise

Chemical Reactions and Equations

15 Questions

30 Marks

23 Mins

02, Dec 2024

Chemical Reactions and Equations

Acids Bases and Salts

15 Questions

30 Marks

23 Mins

05, Dec 2024

Acids Bases and Salts

Metals and Nonmetals

15 Questions

30 Marks

23 Mins

09, Dec 2024

Metals and Nonmetals

Test Series

Hurry-Up - Attend 0 Free and 9 Paid Test Series In Just ₹ 99 ₹ 199 Only.

Paid Mock test – 9 Total Number

Buy Now

Paid Mock test – Subject Wise

Determinant and Matrix

30 Questions

60 Marks

45 Mins

19, Nov 2024

Determinant and Matrix

Trigonometry

17 Questions

34 Marks

26 Mins

23, Nov 2024

Trigonometry

Vectors

15 Questions

30 Marks

23 Mins

27, Nov 2024

Vectors

Coordinate Geometry

15 Questions

30 Marks

23 Mins

30, Nov 2024

Coordinate Geometry

Function and Limits

20 Questions

40 Marks

30 Mins

02, Dec 2024

Function and Limits

Differentiation and its Application

18 Questions

36 Marks

27 Mins

05, Dec 2024

Differentiation and its Application

Integration

18 Questions

36 Marks

27 Mins

08, Dec 2024

Integration

Logarithm

20 Questions

40 Marks

30 Mins

10, Dec 2024

Logarithm

Statistics

10 Questions

20 Marks

15 Mins

12, Dec 2024

Statistics

Test Series

Hurry-Up - Attend 1 Free and 0 Paid Test Series In Just ₹ 0 ₹ 29 Only.

Free Mock test – 1 Total Number

Free Mock test – Complete Paper

Free Mock Test DDCET 2025

100 Questions

200 Marks

150 Mins

29, Jul 2024

Free Mock Test