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Sr. No.  Events  Dates & Time 

1  Opening date of online registration?  6/2/2024, 1:00 PM 
2  Closing?date of online registration  11/3/2024, 12:00 Midnight 
3  Admit card download  1/4/2024 to 5/4/2024 
4  Exam Date  April 7, 2024 
5  Test type  Offline  Paper Based Test 
6  Result Declaration  3rd week of April (Tentative) 
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Rs. 250 per Candidate
The DDCET Rank will be available online, and the merit will be valid for the respective year only.
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 
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Sr no  Topic  Subtopic  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, Newton?s 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 

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, nonmechanical, 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, Snell?s law, absolute refractive index, relative refractive index, total internal reflection, critical angle, optical fiber (construction, properties and applications). ? Reverberation, Reverberation time, Sabine?s formula, echo, absorption coefficient. 
12 
6  Chemical Reactions and Equations 

6 
7  Acids, Bases and Salts 

8 
8  Metals and Nonmetals 

6 
9  Computer Practice 

10 
10  Environmental Sciences 

10 
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Sr. no  Topics  Subtopics  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 Nonsingular 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 (Twopoint 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 Nonverbal 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 
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Marking System:
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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.
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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.
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3. What are the important dates for the DDCET application process?
??? The online registration for DDCET typically opens in February 2024, and the exam is scheduled to take place on any Sunday of March 2024.
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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: https://acpc.gujarat.gov.in/ddcet#
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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.
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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 120 minutes.
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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.
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8. What additional support or resources are available for DDCET preparation?
? ? QUALEXE will offer welldesigned 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.
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9. Is the DDCET merit valid for multiple years?
??? No, the merit obtained in DDCET is valid for the respective year only.
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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.
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 
Correct Ans: C
Correct Ans: C
Correct Ans: B
Correct Ans: D
Correct Ans: C
Correct Ans: B
Correct Ans: A
Correct Ans: B
Correct Ans: C
Correct Ans: B
Correct Ans: C
Correct Ans: D
Correct Ans: A
Correct Ans: B
Correct Ans: B
Correct Ans: B
Correct Ans: C
Correct Ans: C
Correct Ans: C
Correct Ans: D
Correct Ans: B
Correct Ans: A
Correct Ans: D
Correct Ans: D
Correct Ans: A
Correct Ans: B
Correct Ans: A
Correct Ans: B
Correct Ans: A
Correct Ans: D
Correct Ans: A
Correct Ans: D
Correct Ans: C
Correct Ans: C
Correct Ans: C
Correct Ans: D
Subject  Number of questions 

Basics of Science and Engineering (DDCET)  50 
Aptitude Test (Mathematics and Soft Skill) DDCET  50 
Total  100 
Correct Ans: C
Solution:
\(\Rightarrow\) Burning of coal involves the main component, carbon, reacting with oxygen \((O_2)\) in the air to form carbon dioxide\( (CO_2)\).
\(\Rightarrow\) This is a combination reaction where two elements or compounds combine to form a new substance.
Correct Ans: B
Solution:
\(\Rightarrow\) Double displacement reactions are reactions in which the reactants undergo an exchange of ions.
\(\Rightarrow\) The example of a double displacement reaction is given below:
\(\quad \quad Na_2SO_4 + NaCl_2 \rightarrow BaSO_4 + 2NaCl\)
\(\Rightarrow\) Here \(Cl_2\) and \(SO_4\) are undergo exchange.
\(\Rightarrow\) This equation can be expressed in a generalized form as follows: \(AC + BD \rightarrow AD+ BC\)
Correct Ans: C
Solution:
\(\Rightarrow\) In the balanced equation,the quantity of atoms for each element stays constant, both before and after a chemical reaction.
\(\Rightarrow\) Here in option C, the atoms of each elements are equal on both the side
Correct Ans: D
Solution:
\(\Rightarrow\) The outer layer of the teeth is madeup of calcium phosphate.
Correct Ans: A
Solution:
\(\Rightarrow\) This is a salt formed by a strong acid \((HNO_3)\) and a strong base \((KOH)\).
\(\Rightarrow\) When strong acids and strong bases react, they tend to neutralize each other, resulting in a solution with a pH close to 7.
Correct Ans: B
Solution:
\(\Rightarrow\) Metal oxides have a basic nature, so when an acid interacts with a metal oxide, they cancel each other out.
\(\Rightarrow\) This results in the formation of salt and water during the reaction.
Correct Ans: B
Solution:
\(\Rightarrow\) The Chemical formula for this compound is \(Na_2ZnO_2\)
Correct Ans: B
Solution:
\(\Rightarrow\) The atomic number is 9. So it has 2 electrons in the innermost shell and 7 electrons in the outer shell.
Correct Ans: C
Solution:
\(\Rightarrow\) Applying a layer of zinc on an iron frying pan can prevent it from rusting.
\(\Rightarrow\) This technique is called Electroplating.
\(\Rightarrow\) As zinc is more reactive than iron, oxygen in the air reacts with the surface of zinc first, and iron remains intact.
Correct Ans: A
Solution:
\(\Rightarrow\) Malleability defines material's capacity to undergo permanent deformation under compression without breaking.
\(\Rightarrow\) Gold has an atomic structure that enables it to be hammered into extremely thin sheets, which are so delicate that they appear almost transparent.
\(\Rightarrow\) This is commonly referred to as gold leaf.
Correct Ans: C
Solution:
\(\Rightarrow\) In Excel, "label" is a word that's used for text entries that usually act as headers or identifiers in a spreadsheet, but it's not seen as a separate data type.
\(\Rightarrow\) "Character" is also not visible directly in the MS Excel data type. It is included in "text" data type.
Correct Ans: A
Solution:
\(\Rightarrow\) Powerpoint can zoom in up to 400% and zoom out to a minimum of 10%.
Correct Ans: B
Solution:
\(\Rightarrow\) Magic tool is not available in MSWord.
Correct Ans: A
Solution:
\(\Rightarrow\) The CPU (Central Processing Unit) typically consists of two main components:
\(\Rightarrow\) ALU (Arithmetic Logic Unit): Responsible for performing arithmetic and logical operations on data.
\(\Rightarrow\) CU (Control Unit): Manages the execution of instructions and coordinates the activities of the other hardware components.
Correct Ans: D
Solution:
\(\Rightarrow\) Microsoft Office is not an operating system (OS).
\(\Rightarrow\) It is a suite of productivity software applications developed by Microsoft for use in offices and businesses.
Correct Ans: D
Solution:
\(\Rightarrow\) Blue baby syndrome is often linked to nitrate pollution.
\(\Rightarrow\) Nitrate can pollute sources of drinking water, and when babies drink water that has high levels of nitrate, it can cause a condition where the blood's ability to carry oxygen is decreased.
\(\Rightarrow\) This can result in the skin turning a bluish color.
Correct Ans: B
Solution:
\(\Rightarrow\) Clouds are primarily present in the troposphere, which is the lowest layer of the Earth's atmosphere.
Correct Ans: C
Solution:
\(\Rightarrow\) CFCs (Chlorofluorocarbons) are not recommended to be used in refrigerators because they deplete the ozone layer.
Correct Ans: B
Solution:
\(\Rightarrow\) The approximate efficiency range of modern solar photovoltaic (PV) panels in converting sunlight into electricity varies, but it typically falls between 15% to 20%.
\(\Rightarrow\) However, some highefficiency panels can achieve efficiencies upwards of 20% or even higher.
Correct Ans: C
Solution:
\(\Rightarrow\) Particulate matter (PM10) is primarily responsible for causing respiratory problems and cardiovascular diseases in humans.
\(\Rightarrow\) PM10 refers to inhalable particles with diameters that are generally 10 micrometers and smaller.
Correct Ans: C
Solution:
\(\Rightarrow\) The SI unit of power is the watt (W) which is equal to one joule per second.
Correct Ans: D
Solution:
Given data:
\(\Rightarrow\) Pitch distance of screw =0.5 mm
\(\Rightarrow\) Number of total division on circular scale = 50
\(\Rightarrow\) \(LC=\frac{pitch\:distance\:of\:screw}{number \:of\:total\:division\:on\:circular\:scale}\)
\(\Rightarrow\) \(LC=\frac{0.5}{50}=0.01\:mm\)
Correct Ans: B
Solution:
Relation between newton (N) and dyne:
\(1\: N=10^5\:dyne\)
\(1\:dyne=10^{5}\:N\)
\(10\:dyne=10 \times10^{5}\:N=10^{4}\:N\)
Correct Ans: The correct answer does not align perfectly with the provided options
Solution:
\(\Rightarrow\) In the CGS (CentimeterGramSecond) system, the unit of energy is the erg. The erg is a small unit of energy.
\(\Rightarrow\) In the MKS (MeterKilogramSecond) system and SI (International System of Units), the unit of energy is the joule.
\(\Rightarrow\) The relationship between the erg and the joule:
\(1\) erg\(=10^{7}\) joules \(\implies\) 1 joule \(= 10^7\) erg
Correct Ans: The correct answer does not align perfectly with the provided options
Solution:
\(\Rightarrow\) Standard value of refractive index of water = 1.333
Absolute differences:
1.30  1.333 = 0.033
1.32  1.333 = 0.013
1.34  1.333 = 0.007
1.35  1.333 = 0.017
1.31  1.333 = 0.023
Mean Absolute Error = (0.033+0.013+0.007+0.017+0.023) / 5= 0.093 / 5=0.0186
Correct Ans: A
Solution:
\(\Rightarrow\) Vernier caliper is used to measure "Inner diameter of the ring.
Correct Ans: C
Solution:
Newton's second law of motion:
\(\Rightarrow\) Newton's second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
\(\Rightarrow\) Formula: \(F=m \times a\)
Correct Ans: B
Solution:
Given data:
\(\Rightarrow\) \(F= 30 \:N\)
\(\Rightarrow\) \(m=5 \:kg\)
Force acting on the object \(F=m \times a\)
\(a=F/m\)
\(a=30/5=6\:\:m/s^2\)
Correct Ans: C
Solution:
Impulse of Force:
\(\Rightarrow\) Impulse of force is the change in momentum of an object and it depends on the force applied and the time duration of the force.
\(\Rightarrow\) Formula: Impulse of Force = force \(\times\) time
\(\Rightarrow\) SI unit: newtonsecond (N s)
\(\Rightarrow\) CGS unit: dynesecond.
\(\Rightarrow\) It is a vector quantity.
Examples:
1. China wares wrapped in paper while packing.
2. Bogies of a train are provided with buffers.
Therefore, from the above explanation the correct option is (C).
Correct Ans: C
Solution:
\(\Rightarrow\) A body moving in vertical circular motion experiences these three forces like Force of gravity, Centripetal force and Centrifugal force.
\(\Rightarrow\) A body moving in vertical circular motion does not experience Friction force.
Correct Ans: D
Solution:
\(\Rightarrow\) Field forces are any forces that act on an object without direct physical contact.
\(\Rightarrow\) There are three main types:1. Gravitational force, 2. Magnetic force, 3. Electrical force
Therefore, from the above explanation the correct option is (D) All of above.
Correct Ans: A
Solution:
\(\Rightarrow\) The work done by the external force on a system equals the change in total energy.
Correct Ans: B
Solution:
Given data:
\(\Rightarrow\) \(V=6\: V\)
\(\Rightarrow\) \(I=0.4\:mA=0.4 \times 10^{3}\:A\)
\(V=I \times R\)
\(6=0.4 \times 10^{3} \times R \implies R=15000\: \Omega=15\:k \Omega\)
Correct Ans: D
Solution:
According to Coulomb's law
The magnitude of the electrostatic force \((F)\) between two point charges
\(F=k \frac{Q_1 Q_2}{d^2}\)
\(F=\frac{1}{4\pi \epsilon_0
} \frac{Q_1 Q_2}{d^2}\)
\(\epsilon_0= \frac{Q_1 Q_2}{4 \pi \times F \times d^2}=\frac{C^2}{Nm^2}\)
Hence, option (D) is correct.
Correct Ans: D
Solution:
\(\Rightarrow\) The Electric flux depends on the Electric field intensity, Area and Angle between the surface and the electric field.
Electric flux (\(\phi\)) is a measure of the electric field passing through an area.
Calculation: \(\phi= E \times A \cos \theta\)
Where,
\(E\)  Magnitude of the electric field intensity
\(A\)  Area of the surface
\(\theta\)  Angle between the surface and the electric field.
Therefore, from the above explanation the correct option is (D) All of these.
Correct Ans: C
Solution:
\(\mathbf{Resistance:}\)
\(\Rightarrow\) Resistance of the conductor is the opposition to the flow of current. It is denoted by R.
\(\Rightarrow\) Unit : \(\Omega\)
\(\mathbf{Conductance:}\)
\(\Rightarrow\) Conductance is the offered by the conductor to the flow of current. It is denoted by G.
\(\Rightarrow\) Unit : \(\mho\) or S (siemens)
Hence, Inverse of Resistance is known as conductance means Conductance is the reciprocal of resistance (\(G=\frac{1}{R}\))
Correct Ans: D
Solution:
Given data:
\(\Rightarrow\) \(R_1=10\:\Omega\)
\(\Rightarrow\) \(R_2=20\:\Omega\)
Effective value of resistance (\(R_{eq}\)) when two resistors are connected in parallel combination
\(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\)
\(R_{eq}=\frac{R_1 \times R_2}{R_1 +R_2}\)
\(R_{eq}=\frac{10 \times 20}{10 +20}=6.66\:\Omega\)
Correct Ans: B
Solution:
Capacitance:
\(\Rightarrow\) Capability of a capacitor to store electrical charge is called capacitance.
\(\Rightarrow\) Unit of capacitance is Farad or coulomb/volts and is denoted by F.
\(\Rightarrow\) \(Q \propto V,\:Q =CV,\:C =\frac{Q}{V}=\frac{coulomb}{volts}\) .
Therefore, from the above explanation the correct option is (B) \(C/V\)
Correct Ans: A
Solution:
\(\Rightarrow\) The correct order of these metals in increasing order of thermal conductivity is:
Iron, Aluminium, Copper, Silver.
Note:
\(\Rightarrow\) Iron: Has a thermal conductivity of 50–80 W/m·K
\(\Rightarrow\) Aluminum: Has a thermal conductivity of 205–235 W/m·K
\(\Rightarrow\) Copper: Has a thermal conductivity of 390–400 W/m·K
\(\Rightarrow\) Silver: Has a thermal conductivity of 430 W/m·K
Correct Ans: C
Solution:
Relation between Fahrenheit scale and Celsius scale:
\(T_F=\frac{9}{5} T_C+32\)
Where,
\(T_F=\) Temperature on Fahrenheit scale
\(T_C=\) Temperature on Celsius scale
Consider \(T_C=40^\circ C\), this value put in above equation
\(T_F=\frac{9}{5} \times(40)+32\)
\(T_F=72+32\)
\(T_F=40^\circ F\)
Correct Ans: D
Solution:
Heat Capacity
\(\Rightarrow\) It is the ratio of the amount of heat \((Q)\) given to a body to a change in its temperature \((\Delta T)\).
\(\Rightarrow\) \(H_C = \frac{Q}{\Delta T}\)
\(\Rightarrow\) SI Unit: \(J/K\)
\(\Rightarrow\) Other Unit: \(Cal/K \:or\:J/^\circ C\:or\:Cal/^\circ C\)
Therefore, from the above explanation the correct option is (D) All of above.
Correct Ans: B
Solution:
Correct Ans: A
Solution:
The mathematical formula for specific heat:
\(C=\frac{Q}{m\Delta T}\)
Where,
\(C\) Specific heat
\(Q\) Heat energy transferred
\(m\) Mass of the substance
\(\Delta T\) Change in temperature
Correct Ans: B
Solution:
Relation between Fahrenheit scale and Celsius scale:
\(T_F=\frac{9}{5} T_C+32\)
Where,
\(T_F=\) Temperature on Fahrenheit scale
\(T_C=\) Temperature on Celsius scale
\(T_F=\frac{9}{5} T_C+32\)
\(104=\frac{9}{5} T_C+32\)
\(104 \times 5=(9 \times T_C)+(32 \times 5)\)
\(T_C=\frac{(104 \times 5) (32 \times 5)}{9}=40^\circ C\)
Correct Ans: A
Solution:
\(\Rightarrow\) Sound wave is not a type of electromagnetic wave; it is a mechanical wave that requires a medium (such as air, water, or solid material) for propagation.
Correct Ans: B
Solution:
\(\Rightarrow\) Light waves are classified as nonmechanical type of waves (transverse waves.).
\(\Rightarrow\) They do not require any medium for propagation, they can propagate through vacuum also.
Note:
Longitudinal wave
\(\Rightarrow\) The particles of the medium move parallel to the direction of propagation of wave.
\(\Rightarrow\) Examples: Sound waves, etc.
Transverse wave
\(\Rightarrow\) The particles of the medium move perpendicular to the direction of propagation of wave.
\(\Rightarrow\) Examples: Light waves (electromagnetic waves), Water surface waves, etc.
Therefore, from the above explanation the correct option is (B) Transverse.
Correct Ans: D
Solution:
Given data:
\(\Rightarrow\) \(f=2\:kHz=2000\:Hz\)
\(\Rightarrow\) \(\lambda=2\:m\)
\(v = f· \lambda \)
\(v = 2000 \times 2=4000\:m/s \)
Note:
Frequency:
\(\Rightarrow\) It is the number of oscillations or cycles of a wave that occur in a unit of time.
\(\Rightarrow\) It is denoted by \(f\)
\(\Rightarrow\) Unit: hertz (Hz), cycle per second (c/s)
Wavelength:
\(\Rightarrow\) It is defined as the distance between two successive points that are in phase.
\(\Rightarrow\) It is denoted by \(\lambda\)
\(\Rightarrow\) Unit: meter (m) or Angstrom unit \((1\:A^\circ=10^{10}\:m)\)
Correct Ans: C
Solution:
\(\Rightarrow\) Divergent is not a characteristic of LASER (Light Amplification by Stimulated Emission of Radiation).
Correct Ans: A
Solution:
\(\Rightarrow\) Optical fibre works on the principle of total internal reflection.
Correct Ans: B
Solution:
Given data:
\(\Rightarrow\) \(V=6000 \:m^3\)
\(\Rightarrow\) \(A=1000\:O.W.U\)
\(RT=\frac{0.161 \times 6000}{1000}=0.966\:seconds\)
Sabine's formula for reverberation of time:
\(RT=\frac{0.161 \times V}{A}\)
Where,
\(V\) is the volume of the room in cubic meters
\(A\) is the total absorption in the room in \(O.W.U.\)
\(RT\) is the reverberation time in seconds
Correct Ans: D
Solution:
\(\lim_{x \rightarrow 0} (\frac{10^x5^x}{x}) =\frac{0}{0}\)
This is of the form \(\frac{0}{0}\), so by L’Hospital’s rule and differentiate the numerator and denominator:
\(\implies\) \( \lim\limits_{x \to 0} (\frac{10^xlog_e105^xlog_e5}{1}) \)
\(\implies\) \( log_e10log_e5 \)
\(\implies\) \( log_e5+log_e2 log_e5 \)
\(\implies\) \( log_e2 \)
Correct Ans: B
Solution:
\(\lim_{n \rightarrow \infty} \frac{3n^2  11n 13}{(4n5)(76n)}\)
Divide numerator and denominator by \(n^2\)
\(= \lim_{n \rightarrow \infty} \frac{3  \frac{11}{n} \frac{13}{n^2}}{(4\frac{5}{n})(\frac{7}{n}6)}\)
\(= \frac{3  0 0}{(40)(06)}\)
\(= \frac{1}{8}\)
Correct Ans: A
Solution:
\(f(x)=log_4(x)\) then
\(f(64)=log_4(64)\)
\(f(64)=log_44^3\)
\(f(64)=3log_44\)
\(f(64)=3\)
Correct Ans: B
Solution:
\(\Rightarrow\) For \(f(x) = \cos^2 x\),
\(\implies f^{'}(x) = \frac{d(\cos^2 x)}{dx} = 2 \cos x \: \frac{d}{dx} \cos x\)
\(\therefore f^{'}(x) =2 \cos x (\sin x) =  \sin (2x)\)
Correct Ans: D
Solution:
\(\Rightarrow\) For \(f(x) =\log (\sqrt{x^29}) = \frac{1}{2} \log ({x^29}) \),
\(\implies f^{'}(x) = \frac{1}{2}[\frac{1}{x^29} \frac{d}{dx}(x^29)] \)
\(\implies f^{'}(x) = \frac{1}{2}[\frac{1}{x^29} \times 2x] \)
\(\implies f^{'}(x) = \frac{x}{x^29}\)
Correct Ans: A
Solution:
\(\Rightarrow x=\csc \theta \quad \therefore \frac{dx}{d \theta} = \cot \theta \:\csc \theta \)
\(\Rightarrow y=\cot \theta \quad \therefore \frac{dy}{d \theta} = \csc^2 \theta \)
\(\rightarrow \frac{dy}{dx} = \frac{\frac{dy}{d \theta}}{\frac{dx}{d \theta}} = \frac{ \csc^2 \theta}{ \cot \theta \:\csc \theta}\)
\(\therefore \frac{dy}{dx} = \sec \theta\)
Correct Ans: A
Solution:
\(\Rightarrow\) If the function \(f(x)\) get that \(f^{"}(x)<0\), then the function will have maximum value.
\(\Rightarrow\) If the function \(f(x)\) get that \(f^{"}(x)>0\), then the function will have minimum value.
Correct Ans: C
Solution:
\(\Rightarrow\) Let's consider, \(u=10x17 \quad \implies du = 10 dx\)
\(\therefore \int \cos (10x17) dx = \frac{1}{10}\int \cos u \:du \)
\(=\frac{1}{10} \sin u + c = \frac{1}{10} \sin (10x17) + c\)
Correct Ans: B
Solution:
\(\Rightarrow f(x) = \sin^5 x \cos^8 x\)
\(f(x) = \sin^5 (x) \cos^8 (x) =  \sin^5 x \: \cos^8 x =  f(x)\)
\(\therefore\) The given function f(x) is an \(\text{Odd}\) function.
\(\therefore \int_{1}^1 f(x) dx = 0\)
Correct Ans: D
Solution:
\(\Rightarrow \int e^x [f(x)+f^{'} (x)] dx = e^x f(x) + c \quad ...(i)\)
\(Given : f(x) = (\csc^2 x \cot x) = (\cot x + (\csc^x))\)
\(\therefore f(x) = \cot x \quad \implies f^{'} (x) =  csc^x \)
\(\rightarrow\) From equation (i),
\(\therefore \int e^x (\csc^2 x \cot x) dx =  \int e^x [(\cot x + (\csc^x))] dx\)
\(implies \int e^x (\csc^2 x \cot x) dx =  e^x \cot x + c\)
Correct Ans: A
Solution:
\(\Rightarrow Let's \: consider\),
\(u = x^26x+40 \quad \implies du = (2x  6) dx = \frac{1}{2} (x3) dx\)
\(\therefore \int \frac{x3}{x^26x+40} dx = \frac{1}{2} \int \frac{1}{u} \: du\)
\(= \frac{1}{2} ln \: \lvert u \rvert + c = \frac{1}{2} ln \lvert (x^26x+40) \rvert + c\)
Correct Ans: C
Solution:
\(Given: \log_{\frac{1}{81}} \frac{1}{9} = \log_{\frac{1}{9^2}} \frac{1}{9}\)
\(= \log_{9^{2}} 9^{1} = \frac{1}{2} \:log_9 \:9 = \frac{1}{2}\)
Correct Ans: D
Solution:
\(Given: 4^{log_2 3} + 2^{log_8 27} = 2{^2}^{log_2 3} + {8^{\frac{1}{3}}}^{log_8 27}\)
\(= 2^{log_2 3^2} + 8^{log_8 27^{\frac{1}{3}}} = 2^{log_2 \: 9} +8^{log_8 \: 3} \)
\(=9 + 3 = 12\)
Correct Ans: B
Solution:
\(Observations: \text{19,15,12,k,8,3}\)
\(Mean = \frac{19+15+12+k+8+3}{6}\)
\(\implies 11 = \frac{57 + k}{6}\)
\(\implies 66 = 57 + k\)
\(\therefore k = 9\)
Correct Ans: B
Solution:
If \(A= \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix}\) and \(B= \begin{bmatrix} 2 & 1 \\ 1 & 3 \end{bmatrix}\) then :
\(AB = \begin{bmatrix} 1 & 1 \\ 1 & 2 \end{bmatrix} . \begin{bmatrix} 2 & 1 \\ 1 & 3 \end{bmatrix}\)
\(AB = \begin{bmatrix} (1)(2) +(1)(1) & (1)(1) +(1)(3) \\ (1)(2) + (2)(1) & (1)(1) + (2)(3) \end{bmatrix} \)
\(AB = \begin{bmatrix} 2 +1 & 1 3 \\ 2 2 & 1 + 6 \end{bmatrix} \)
\(AB = \begin{bmatrix} 3 & 2 \\ 0 & 7 \end{bmatrix} \)
Now, \((AB)^T = \begin{bmatrix} 3 & 2 \\ 0 & 7 \end{bmatrix} ^T\)
\((AB)^T = \begin{bmatrix} 3 & 0 \\ 2 & 7 \end{bmatrix}\)
Correct Ans: D
Solution:
For \(A= \begin{bmatrix} 1 & 2 & 1 \\ 2 & 1 & 3 \\ 1 & 1 & 0 \end{bmatrix} \)
\( A = 1((1)(0)(3)(1)) 2((2)(0)(3)(1)) +1((2)(1)(1)(1))\)
\( A = 1(03) 2(03) +1(21)\)
\( A = 3 +6 +1\)
\( A = 4\)
Correct Ans: A
Solution:
If \(A= \begin{bmatrix} 2 & 1 \\ 3 & 1 \end{bmatrix}\)
Adjoint of a Matrix \(A \) (two by two) can be found by changing values of diagonal elements and changing signs of offdiagonal elements.
\(Adj(A) = \begin{bmatrix}1 & 1 \\ 3 & 2 \end{bmatrix} \)
Determinant \(A = \begin{vmatrix} 2 & 1 \\ 3 & 1 \end{vmatrix}= 5\)
Inverse of matrix \(A\) is given by:
\( (A)^{1} = \frac{Adj(A)}{A} = \frac{ \begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix}}{A}\)
\( (A)^{1} = \frac{1}{5} \begin{bmatrix} 1 & 1 \\ 3 & 2 \end{bmatrix} \)
Correct Ans: D
Solution:
If \(A= \begin{bmatrix} 2 & 1 \\ 1 & 0 \end{bmatrix}\) and \(B= \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}\) then :
\( \implies 3B 2A = 3 \times \begin{bmatrix} 1 & 0 \\ 2 & 3 \end{bmatrix}  2\times \begin{bmatrix} 2 & 1 \\ 1 & 0 \end{bmatrix} \)
\( \implies 3B 2A = \begin{bmatrix} 3 & 0 \\ 6 & 9 \end{bmatrix}  \begin{bmatrix} 4 & 2 \\ 2 & 0 \end{bmatrix} \)
\( \implies 3B 2A = \begin{bmatrix} 1 & 2 \\ 4 & 9 \end{bmatrix} \)
Correct Ans: A
Solution:
\(\sin{(225^\circ)} \)
\(= \sin{(180^\circ+45^\circ)}\)
\(=\sin{45}\)
\(=\frac{1}{\sqrt{2}}\)
Correct Ans: C
Solution:
\(sec^2\thetatan^2\theta=1\)
\(sec^2\theta=1+ tan^2\theta\)
\(sec^2\theta=1+ \frac{12}{5}^2\)
\(sec^2\theta=1+ \frac{144}{25}\)
\(sec^2\theta= \frac{169}{25}\)
\(sec\theta= \frac{13}{5}\)
\(\implies \cos\theta= \frac{5}{13}\)
Correct Ans: D
Solution:
In \(\cos^{1} (\frac{\sqrt{3}}{2})\), \((\frac{\sqrt{3}}{2})<0\), and \(cos\theta<0\) in \(2^{nd}\) and \(3^{rd}\) quadrant.
Means \( \cos^{1} (\frac{\sqrt{3}}{2})\) lies in \(2^{nd}\) and \(3^{rd}\) quadrant.
Now \(\cos^{1} (\frac{\sqrt{3}}{2}) =\frac{\pi}{6} \)
So, \(\cos^{1} (\frac{\sqrt{3}}{2})= (\pi + \frac{\pi}{6}) \: or \: (\pi  \frac{\pi}{6})\)
\(\cos^{1} (\frac{\sqrt{3}}{2})= ( \frac{7\pi}{6}) \: or \: (\frac{5\pi}{6})\)
Correct Ans: B
Solution:
\(\overline{x} \times \overline{y} = \overline{x} \overline{y} \sin{\theta_{xy}}\)
It is given that \(\overline{x} \times \overline{y} = \overline{x} = \overline{y}= \sqrt{2}\)
\(\implies \sqrt{2} =\sqrt{2} \sqrt{2} \sin{\theta_{xy}}\)
\(\implies \sin{\theta_{xy}} =\frac{1}{\sqrt{2}}\)
\(\implies \theta_{xy}=\frac{\pi}{4}\)
Correct Ans: A
Solution:
If vectors \(( 2,\: 3,\: a )\) and \(( 3,\: 1,\: 4 )\) are perpendicular then \( ( 2,\: 3,\: a ) \cdot ( 3,\: 1,\: 4 ) = 0 \)
\( \implies ( 2,\: 3,\: a ) \cdot ( 3,\: 1,\: 4 ) =0 \)
\( 63+4a = 0\)
\( 3+4a=0\)
\(a= \frac{3}{4}\)
Correct Ans: D
Solution:
For the general equation of circle \( x^2+y^2+2gx+2fy +c =0 \), the center of the circle is:
\((g,\: f)\)
By comparing it with given equation we get:
\(g=0\), \(f=3m\)
the center of the circle is given as \((0,\: 3)\):
\(\implies f=3m=3\)
\( \implies m=1\)
Correct Ans: C
Solution:
\(\Rightarrow\) Twopoint form of line joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\(\frac{y−y_1}{y2−y1} = \frac{x−x1}{x2−x1}\)
By placing given two points \((1, \: 1)\) and \((1, \: 1)\), above equation can be written as:
\(\implies\) \( \frac{y−(1)}{1−(1)} = \frac{x−1}{(1)−1}\)
\(\implies\) \( \frac{y+1}{2} = \frac{x−1}{2}\)
\(\implies\) \( 2y2 = 2x−2\)
\(\implies\) \( 2x+2y=0\)
\(\implies\) \(x+y=0\)
Correct Ans: A
Solution:
\(\Rightarrow\) A photo is not typically a part of a standard business letter. Therefore, among the options provided, "Photo" is not a part of the business letter format.
\(\Rightarrow\) The other elements listed (Salutation, Date, Signature) are commonly included in a business letter.
Correct Ans: A
Solution:
\(\Rightarrow\) A letter is incomplete and worthless without a signature.
\(\Rightarrow\) The signature is a crucial element that indicates authenticity and authorship, confirming the sender's identity and agreement with the content of the letter. Therefore, "Signature" is the correct answer.
Correct Ans: B
Solution:
\(\Rightarrow\) The full form of C.O.D. is "Cash on Delivery." It refers to a payment method where payment is made upon the delivery of goods rather than in advance.
Correct Ans: C
Solution:
\(\Rightarrow\) Interjections are words or phrases used to express emotions or sentiments and are often followed by an exclamation mark. In this case, "Hurrah!" expresses joy or excitement about passing the examination.
Correct Ans: A
Solution:
\(\Rightarrow\) The appropriate option to complete the sentence is "under." Therefore, the sentence would be: "The dog is sitting under the cot." This option indicates the location of the dog in relation to the cot.
Correct Ans: B
Solution:
\(\Rightarrow\) The appropriate option to complete the sentence is "rises." Therefore, the complete sentence is: "The Sun rises in the East." This option correctly conjugates the verb "rise" to agree with the subject "Sun" and the present tense of the sentence.
Correct Ans: B
Solution:
\(\Rightarrow\) In this sentence, "Your family" is the subject, and it refers to a singular entity, even though it consists of multiple individuals. "Is" is the appropriate verb to use with a singular subject in the present tense.
Correct Ans: B
Solution:
\(\Rightarrow\) The appropriate option to complete the sentence is "any." Therefore, the complete sentence is: "Do you have any doubt in this question paper?"
\(\Rightarrow\) The word "any" is used in questions to inquire about the existence or presence of something, especially when the answer could be affirmative or negative. In this context, it is asking whether there is doubt in the question paper, implying that the speaker is open to the possibility of either answer.
Correct Ans: A
Solution:
\(\Rightarrow\) A "playwright" is a person who writes plays. The term "playwright" combines the word "play," referring to a dramatic work meant for performance on a stage, and "wright," which historically meant a craftsman or someone who creates something. So, a playwright is essentially someone who crafts or creates plays.
Correct Ans: B
Solution:
\(\Rightarrow\) The correct spelling is "Entrepreneur."
Correct Ans: B
Solution:
\(\Rightarrow\) The correct grammatical sentence is: "People were coming, going and ignoring him."
\(\Rightarrow\) This sentence uses the correct verb form "ignoring" to match the progressive tense of the sentence ("were coming, going"). The verb "ignoring" is in the present participle form, which is appropriate for indicating ongoing action in the past tense.
Correct Ans: B
Solution:
\(\Rightarrow\) The grammatically correct sentence is:
I like drawing, my coworkers and my cat.
\(\Rightarrow\)
Here's why the other options are incorrect:
\(\rightarrow\) I Like drawing my coworkers and my cat.  No proper use of comma.
\(\rightarrow\) I like drawing, my coworkers, and, my cat.  This one has unnecessary commas.
\(\rightarrow\) I, Like, drawing, my coworkers, and, my, cat.  This one uses unnecessary commas and capitalization.
\(\Rightarrow\) In optionB, sentence consists of a simple subject ("I"), a verb ("like"), and a direct object ("drawing my coworkers and my cat"). This structure is clear, concise, and grammatically correct.
Correct Ans: D
Solution:
\(\Rightarrow\) The correct grammatical sentence is: "The ship was wrecked, and every man, woman, and child was drowned."
\(\Rightarrow\) In this sentence: "The ship was wrecked" is in the past tense, which matches the action of the shipwreck.
"Every man, woman, and child" is a collective noun that refers to a singular group, so it requires a singular verb form, "was drowned," to match.
\(\Rightarrow\) Therefore, the correct form is "was drowned," making the sentence grammatically accurate.
Correct Ans: A
Solution:
\(\Rightarrow\) Black Powder was invented in India.
Correct Ans: C
Solution:
\(\Rightarrow\) Roger Bacon was an English Monk.
Correct Ans: B
Solution:
\(\Rightarrow\) Roger Bacon wrote about 'Black Powder' in code language.
Correct Ans: C
Solution:
\(\Rightarrow\) Shukranti was written "Two thousand years ago."
Correct Ans: B
Solution:
\(\Rightarrow\) The word "pyrotechnics" is from the Greek language.
Correct Ans: B
Solution:
\(\Rightarrow\) Verbal communication refers to using words to convey information. This can be done through both speaking (oral) and writing.
Correct Ans: C
Solution:
\(\Rightarrow\) Tone of voice, voice quality, style of speaking, stress, and intonation are part of "paralanguage."
\(\Rightarrow\) Paralanguage refers to the nonverbal elements of speech, such as tone, pitch, volume, and rhythm, which convey meaning alongside spoken words.
Correct Ans: A
Solution:
\(\Rightarrow\) The process of communication is a "two way" process. This implies that communication involves both sending and receiving messages between two or more parties.
Correct Ans: A
Solution:
\(\Rightarrow\) The hindrance that disturbs the communication process at every stage is known as a "Barrier." Noise can be considered as one of the barrier.
Correct Ans: D
Solution:
\(\Rightarrow\) Our physical appearance is an example of "nonverbal" communication. Nonverbal communication includes gestures, facial expressions, body language, posture, and other aspects of appearance that convey messages without the use of words.
Correct Ans: A
Solution:
\(\Rightarrow\) At the top of a business letter on the lefthand side, you typically find the "Sender's address." This includes the sender's name, street address, city, state, and postal code.
Correct Ans: D
Solution:
\(\Rightarrow\) The salutation in a business letter is typically placed "Just above the body of the letter." It is the greeting that addresses the recipient of the letter.
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