Mathematics-DDCET MCQ - Electrical Engineering Objective

Q1. If \(h(x) = 3x + 4\), what is \(h^{'}(x)\), the derivative of \(h(x)\) with respect to \(x\)?

3

2

4

0

Q2. \(\cos{(\pi + \cos^{-1}{(\frac{1}{2}}))} = _{----------} \)

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

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

\(-\frac{3}{5}\)

\(\frac{3}{5}\)

Q3. If \(log_{2}{(a)} = 3\) and \(log_{2}{(b)} = 2\), find \(log_{2}{(ab)}\).

3

2

5

6

Q4. What is the fundamental theorem of calculus?

The product rule for differentiation

The chain rule for integration

The relationship between derivatives and integrals

The quotient rule for integration

Q5. If the diagonal elements of a diagonal matrix are all unity it is called

Null matrix

Identity matrix

Row matrix

Column matrix

Q6. Find \(\int_{1}^{2} \frac{1}{x^2} dx\).

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

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

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

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

Q7. What does the definite integral \(\int_{a}^{b} f(x) dx\) represent geometrically?

Area under the curve of \(f(x)\) from \(a \: to \: b\)

Slope of the tangent line to \(f(x)\) at \(x=a\)

Length of the curve of \(f(x)\) from \(a \: to \: b\)

Volume of the solid formed by revolving \(f(x)\) around the x-axis from \(a \: to \: b\)

Q8. What is the product rule for logarithms?

\(log_{b}{(p.q)} = log_{b}{(p)} \times log_{b}{(q)}\)

\(log_{b}{(p.q)} = log_{b}{(p)} + log_{b}{(q)}\)

\(log_{b}{(p.q)} = log_{b}{(p)} - log_{b}{(q)}\)

\(log_{b}{(p.q)} = log_{b}{(p)} / log_{b}{(q)}\)

Q9. What is the integral of \(3 \sqrt{x} + 2 x^{-\frac{1}{2}}\) with respect to \(x\) ?

\( 2 x^{\frac{3}{2}} + 4 x^{\frac{1}{2}} + C\)

\( x^{\frac{3}{2}} + x^{\frac{1}{2}} + C\)

\( 3 x^{\frac{3}{2}} + 2 x^{\frac{1}{2}} + C\)

\( x^{\frac{3}{2}} + 2 x^{\frac{1}{2}} + C\)

Q10. If \(g(x) = e^{(2x)}\), what is \(g''(x)\), the second derivative of \(g(x)\) with respect to \(x?\)

\(4 e^{(2x)}\)

\(-4 e^{(2x)}\)

\(4 e^{(x)}\)

\(4 e^{(2)}\)

MCQ