AP ECET 2026 Electrical and Electronics Engineering Question Paper: Download Answer Key with Solution PDF

In the matrix \[ A=\begin{bmatrix} 1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 4 & 9 \end{bmatrix}, \]
the minor \(M_{23}\) of the element \(a_{23}\) is:

• (A) \(10\)
• (B) \(-10\)
• (C) \(-6\)
• (D) \(6\)

If \[ \begin{vmatrix} 2x & 5 \\
8 & x \end{vmatrix} = \begin{vmatrix} 6 & -2 \\
7 & 3 \end{vmatrix}, \]
then the value of \(x\) is:

• (A) \(3\)
• (B) \(\pm 6\)
• (C) \(-3\)
• (D) \(\pm 2\)

If \(A\) is a square matrix of order \(3\) and \(|A|=5\), then the value of \(\left|2A^T\right|\) is:

• (A) \(-10\)
• (B) \(10\)
• (C) \(40\)
• (D) \(-40\)

Which of the following systems has non-trivial solution?

• (A) \(AX=0,\ |A|=4\)
• (B) \(AX=0,\ |A|=-4\)
• (C) \(AX=0,\ |A|=0\)
• (D) \(AX=B,\ |B|=5\)

If \[ \begin{bmatrix} x+y & 2 \\
1 & x-y \end{bmatrix} = \begin{bmatrix} 4 & 2 \\
1 & 2 \end{bmatrix}, \]
then the values of \(x\) and \(y\) are:

• (A) \(x=3,\ y=1\)
• (B) \(x=1,\ y=3\)
• (C) \(x=2,\ y=3\)
• (D) \(x=1,\ y=1\)

If \[ \frac{x+4}{(x+2)^2(x+3)} = \frac{A}{(x+2)^2} + \frac{B}{x+2} + \frac{C}{x+3}, \]
then \(A+B+C=\)

• (A) \(2\)
• (B) \(1\)
• (C) \(-1\)
• (D) \(3\)

If \[ \frac{x}{(x-1)^2(x+2)} = \frac{A}{(x-1)^2} + \frac{2}{9(x-1)} + \frac{B}{x+2}, \]
then \(A+B=\)

• (A) \(\frac{1}{3}\)
• (B) \(\frac{1}{9}\)
• (C) \(-\frac{1}{3}\)
• (D) \(\frac{2}{3}\)

If \(\tan A=\frac{1}{2}\) and \(\tan B=\frac{1}{3}\), then \(A+B=\)

• (A) \(30^\circ\)
• (B) \(45^\circ\)
• (C) \(60^\circ\)
• (D) \(90^\circ\)

If \(2\sin^{-1}x=\sin^{-1}k\), then \(k=\)

• (A) \(2x\sqrt{1-x^2}\)
• (B) \(2x\)
• (C) \(x^2\)
• (D) \(1-2x^2\)

If \[ \sin^{-1}\frac{5}{x}+\sin^{-1}\frac{12}{x}=\frac{\pi}{2}, \]
then \(x=\)

• (A) \(12\)
• (B) \(7\)
• (C) \(13\)
• (D) \(15\)

The number of solutions of the equation \[ \sin 2x-\cos 2x=2-\sin 2x \]
lying in the interval \([0,\pi]\) is

• (A) \(0\)
• (B) \(1\)
• (C) \(2\)
• (D) \(3\)

If \[ \tan\theta+\sec\theta=\sqrt3, \]
then the principal value of \(\theta\) in \([0,2\pi]\) is

• (A) \(\frac{\pi}{4}\)
• (B) \(\frac{\pi}{6}\)
• (C) \(\frac{\pi}{2}\)
• (D) \(\frac{2\pi}{3}\)

\[ \frac{\tan x-1+\sec x}{\tan x-\sec x+1} = \]

• (A) \(\frac{1-\sin x}{\cos x}\)
• (B) \(\frac{1+\sin x}{\cos x}\)
• (C) \(\frac{1+\cos x}{\sin x}\)
• (D) \(\frac{1-\cos x}{\sin x}\)

\[ \tan 9^\circ-\tan 27^\circ-\tan 63^\circ+\tan 81^\circ= \]

• (A) \(2\)
• (B) \(1\)
• (C) \(4\)
• (D) \(3\)

If \[ \cos\theta=\frac{1}{2}\left(a+\frac{1}{a}\right), \]
then \[ 4\cos^3\theta-3\cos\theta= \]

• (A) \(a^3+\frac{1}{a^3}\)
• (B) \(\frac{1}{2}\left(a^3+\frac{1}{a^3}\right)\)
• (C) \(\frac{1}{4}\left(a^3+\frac{1}{a^3}\right)\)
• (D) \(\frac{1}{3}\left(a^3+\frac{1}{a^3}\right)\)

\[ \cos 6^\circ\sin 24^\circ\cos72^\circ= \]

• (A) \(\frac{1}{4}\)
• (B) \(-\frac{1}{8}\)
• (C) \(-\frac{1}{4}\)
• (D) \(\frac{1}{8}\)

\[ \tan^{-1}1+\tan^{-1}2+\tan^{-1}3= \]

• (A) \(\frac{3\pi}{4}\)
• (B) \(\frac{\pi}{2}\)
• (C) \(\pi\)
• (D) \(2\pi\)

If \[ z_1=4i^{40}-5i^{35}+6i^{17}+2,\qquad z_2=-1+i, \]
then \[ |z_1+z_2|= \]

• (A) \(13\)
• (B) \(5\)
• (C) \(15\)
• (D) \(12\)

The conjugate of \((1+i)^3\) is

• (A) \(1+2i\)
• (B) \(-2+2i\)
• (C) \(-2-2i\)
• (D) \(1-2i\)

The equation of a circle whose Centre is \((-3,2)\) and area is \(176\) units is

• (A) \(x^2+y^2+6x-4y-36=0\)
• (B) \(x^2+y^2+6x-4y-43=0\)
• (C) \(x^2+y^2-6x+4y-36=0\)
• (D) \(x^2+y^2-6x+4y-43=0\)

The equation of a circle whose Centre is \((2,-1)\) and which passes through the point \((3,6)\) is

• (A) \(x^2+y^2+4x+2y-45=0\)
• (B) \(x^2+y^2-2x+2y-50=0\)
• (C) \(x^2+y^2+2x+2y-50=0\)
• (D) \(x^2+y^2-4x+2y-45=0\)

If the parabola \(y^2=4ax\) passes through the point \((3,2)\), then the length of its latus rectum is:

• (A) \(\frac{4}{3}\)
• (B) \(4\)
• (C) \(\frac{2}{3}\)
• (D) \(\frac{1}{3}\)

The line \(y=mx+2\) is a tangent to the parabola \(y^2=8x\) if

• (A) \(m=1\)
• (B) \(m=2\)
• (C) \(m=3\)
• (D) \(m=4\)

The length of the latus rectum and eccentricity of the Hyperbola \[ 9x^2-16y^2=144 \]
are

• (A) \(\left(\frac{9}{4},\frac{5}{4}\right)\)
• (B) \(\left(\frac{9}{2},\frac{5}{4}\right)\)
• (C) \(\left(\frac{9}{2},\frac{5}{2}\right)\)
• (D) \(\left(9,\frac{5}{2}\right)\)

The equation of the ellipse with foci at \((\pm3,0)\) and the eccentricity as \(\frac{1}{3}\) is:

• (A) \(\frac{x^2}{81}+\frac{y^2}{72}=1\)
• (B) \(\frac{x^2}{9}+\frac{y^2}{8}=1\)
• (C) \(\frac{x^2}{8}+\frac{y^2}{9}=1\)
• (D) \(\frac{x^2}{3}+\frac{y^2}{2}=1\)

\[ \lim_{x\to\infty}\left(1+\frac{1}{x}\right)^x= \]

• (A) \(0\)
• (B) \(1\)
• (C) \(e\)
• (D) \(\infty\)

\[ \lim_{x\to 0}\frac{\sqrt{1+x}-1}{x}= \]

• (A) \(0\)
• (B) \(\frac{1}{2}\)
• (C) \(1\)
• (D) \(\infty\)

If \[ y=\frac{a\cos x+b\sin x+c}{\sin x}, \]
then \[ \frac{dy}{dx}= \]

• (A) \(-a cosec^2x-c cosec x\cot x\)
• (B) \(-a\)
• (C) \(-a cosec^2x+b\sec^2x+c cosec x\cot x\)
• (D) \(a cosec^2x-c cosec x\cot x\)

If \[ y=\sqrt{x+\sqrt{x+\sqrt{x+\cdots\infty}}}, \]
then \[ \frac{dy}{dx}= \]

• (A) \(\frac{1}{2y}\)
• (B) \(\frac{1}{1-2y}\)
• (C) \(\frac{1}{2(1-2y)}\)
• (D) \(\frac{-1}{1-2y}\)

Slope of the tangent to the curve \[ y=9x^2+7x^4+5 \]
at the point \(x=1\) is

• (A) \(28\)
• (B) \(16\)
• (C) \(46\)
• (D) \(\frac{1}{46}\)

If \[ f(x)= \begin{cases} 4(5^x), & x<0
8k+x, & x\geq 0 \end{cases} \]
then \(f'(-1)=\)

• (A) \(\frac{2}{5}\log 5\)
• (B) \(\frac{4}{5}\log 5\)
• (C) \(\frac{3}{5}\log 5\)
• (D) \(20\log 5\)

If \[ 2^x+2^y=2^{x+y}, \]
then \[ \frac{dy}{dx}= \]

• (A) \(1-2^y\)
• (B) \(1-\frac{1}{2^y}\)
• (C) \(1+2^{-y}\)
• (D) \(1+2^y\)

If \[ y+\sin^{-1}(1-x^2)=e^x, \]
then \[ \frac{dy}{dx}= \]

• (A) \(e^x-\frac{2}{\sqrt{2-x^2}}\)
• (B) \(e^x-\frac{2}{\sqrt{2+x^2}}\)
• (C) \(e^x+\frac{2}{\sqrt{2-x^2}}\)
• (D) \(e^x+\frac{2}{\sqrt{2+x^2}}\)

If \(y(x)=x^x,\ x>0\), then \[ y''(2)-2y'(2)= \]

• (A) \(4\log_e2-2\)
• (B) \(4\log_e2+2\)
• (C) \(4(\log_e2)^2+2\)
• (D) \(4(\log_e2)^2-2\)

If \[ z=x^2y^3+e^y\sin x, \]
then \[ \frac{\partial^2 z}{\partial x\partial y}= \]

• (A) \(6xy^2+e^y\cos x\)
• (B) \(3x^2y^2+e^y\sin x\)
• (C) \(3x^2y^2+e^y\cos x\)
• (D) \(6xy^2+e^y\sin x\)

\[ \int \frac{dx}{\sin^2x\cos^2x}= \]

• (A) \(\tan x+\cot x+c\)
• (B) \(\tan x-\cot x+c\)
• (C) \(\tan x\cot x+c\)
• (D) \(\tan x+\sec x+c\)

\[ \int \frac{dx}{\sqrt{x+1}+\sqrt{x}}= \]

• (A) \(\frac{2}{3}\left[(x+1)^{\frac{3}{2}}-x^{\frac{3}{2}}\right]+c\)
• (B) \(\frac{2}{3}\left[(x+1)^{\frac{3}{2}}+x^{\frac{3}{2}}\right]+c\)
• (C) \(\frac{3}{2}\left[(x+1)^{\frac{3}{2}}-x^{\frac{3}{2}}\right]+c\)
• (D) \(\frac{3}{2}\left[(x+1)^{\frac{3}{2}}+x^{\frac{3}{2}}\right]+c\)

If \[ \int \frac{\sin^3x+\cos^3x}{\sin^2x\cos^2x}\,dx = A\sec x+B cosec x+c, \]
then \((A,B)\) are

• (A) \((1,1)\)
• (B) \((-1,-1)\)
• (C) \((1,-1)\)
• (D) \((-1,1)\)

The integral of \(f(x)=1+x^2+x^4\) with respect to \(x^2\) is

• (A) \(x+\frac{x^3}{3}+\frac{x^5}{5}+C\)
• (B) \(\frac{x^2}{3}+\frac{x^4}{5}+C\)
• (C) \(x^2+\frac{x^4}{4}+\frac{x^6}{6}+C\)
• (D) \(x^2+\frac{x^4}{2}+\frac{x^6}{3}+C\)

\[ \int_0^{\frac{\pi}{2}} \frac{\sin^{100}x}{\sin^{100}x+\cos^{100}x}\,dx = \]

• (A) \(\frac{\pi}{2}\)
• (B) \(\frac{\pi}{4}\)
• (C) \(100\)
• (D) \(50\)

\[ \int_0^1 x\sqrt{x^2+4}\,dx= \]

• (A) \(\frac{1}{3}[5\sqrt5-4]\)
• (B) \(\frac{1}{2}[5\sqrt5-8]\)
• (C) \(\frac{1}{3}[5\sqrt5-8]\)
• (D) \(\frac{1}{3}[5\sqrt5+4]\)

\[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin^5x\cos^3x}{x^4}\,dx= \]

• (A) \(\frac{\pi}{2}\)
• (B) \(\frac{\pi}{4}\)
• (C) \(0\)
• (D) \(1\)

\[ \int \frac{dx}{\sqrt{16-25x^2}}= \]

• (A) \(\frac{1}{5}\sin^{-1}\left(\frac{5x}{4}\right)+c\)
• (B) \(\sin^{-1}\left(\frac{5x}{4}\right)+c\)
• (C) \(\frac{1}{5}\sin^{-1}\left(\frac{x}{4}\right)+c\)
• (D) \(\frac{1}{5}\sin^{-1}\left(\frac{4x}{5}\right)+c\)

The solution of the differential equation \[ x\frac{dy}{dx}+y=0 \]
passing through the point \((1,1)\) is \(y=\)

• (A) \(x^2\)
• (B) \(x^{-1}\)
• (C) \(x^{-2}\)
• (D) \(x\)

Degree of the differential equation \[ y=x\frac{dy}{dx}+a\sqrt{1+\left(\frac{dy}{dx}\right)^2} \]
is

• (A) \(4\)
• (B) \(3\)
• (C) \(2\)
• (D) \(1\)

The order of the differential equation of all circles passing through the origin and having their centres on the \(x\)-axis is

• (A) \(4\)
• (B) \(3\)
• (C) \(2\)
• (D) \(1\)

If \(a\) and \(b\) are arbitrary constants, then the differential equation representing the family of curves \[ y=a\sin(x+b) \]
is

• (A) \(\frac{d^2y}{dx^2}-y=0\)
• (B) \(\frac{d^2y}{dx^2}+y=0\)
• (C) \(\frac{d^2y}{dx^2}-y^2=0\)
• (D) \(\frac{dy}{dx}-y=0\)

The differential equation is \[ \frac{dy}{dx}+\frac{y}{x}=0 \]
and \(y(1)=2\). Then the value of \(y(3)\) is

• (A) \(2\)
• (B) \(3\)
• (C) \(\frac{2}{3}\)
• (D) \(1\)

The general solution of the differential equation \[ \frac{dy}{dx}=e^{x-y}+x^2e^{-y} \]
is

• (A) \(e^{-y}=e^x+\frac{x^3}{3}+c\)
• (B) \(e^y=e^x+\frac{x^3}{3}+c\)
• (C) \(e^y=e^x+x^3+c\)
• (D) \(e^y=e^x+c\)

The differential equation is \[ \frac{dy}{dx}+y\tan x=\sec x \]
and \(y(0)=1\). Then the value of \(y\left(\frac{\pi}{4}\right)\) is

• (A) \(0\)
• (B) \(\sqrt2\)
• (C) \(1\)
• (D) \(-1\)

If \(P=Fv\sin\beta t\), where \(F\) is force and \(v\) is velocity, then the dimensions of \(P\) and \(\beta\) are

• (A) \(ML^2T^{-3},\ T^{-1}\)
• (B) \(MLT^{-2},\ T^{-2}\)
• (C) \(ML^2T^{-1},\ T^{-1}\)
• (D) \(ML^2T^3,\ T^{-2}\)

If velocity \(V\), energy \(E\), and time \(T\) are chosen as fundamental quantities, then dimensional representation of surface tension in this system will be

• (A) \(E^1V^{-2}T^{-2}\)
• (B) \(E^1V^{-1}T^{-2}\)
• (C) \(E^{-2}V^{-1}T^{-3}\)
• (D) \(E^1V^{-2}T^{-1}\)

If \(|\vec A+\vec B|=|\vec A-\vec B|\), then the angle between the two vectors \(\vec A\) and \(\vec B\) is

• (A) \(0^\circ\)
• (B) \(180^\circ\)
• (C) \(120^\circ\)
• (D) \(90^\circ\)

An aeroplane is moving in a circular path with a speed of \(450\ kmph\). What is the change in velocity in half revolution?

• (A) \(0\ kmph\)
• (B) \(450\ kmph\)
• (C) \(250\ kmph\)
• (D) \(900\ kmph\)

The ratio between maximum and minimum values of two vectors \(\vec A\) and \(\vec B\), where \(A>B\), is \(4:1\). Then the ratio between the magnitudes of two vectors is

• (A) \(3:2\)
• (B) \(5:3\)
• (C) \(2:3\)
• (D) \(3:5\)

The magnitudes of three vectors \(\vec A,\vec B,\vec C\) are \(12,5\), and \(13\) units respectively and \(\vec A+\vec B=\vec C\). The angle between \(\vec A\) and \(\vec B\) is

• (A) \(0^\circ\)
• (B) \(120^\circ\)
• (C) \(90^\circ\)
• (D) \(45^\circ\)

A body falling from height \(H\) takes time \(T\) seconds to reach the ground. The time taken to cover the second half of height is

• (A) \(\frac{T}{\sqrt2}\)
• (B) \(\sqrt2T\)
• (C) \(\frac{\sqrt2-1}{\sqrt2}T\)
• (D) \(\frac{1}{\sqrt2-1}T\)

With what speed should a body be thrown upwards so that the distances covered in the \(5^{th}\) second and \(6^{th}\) second are equal?

• (A) \(75\ m/s\)
• (B) \(\sqrt{98}\ m/s\)
• (C) \(49\ m/s\)
• (D) \(19.8\ m/s\)

A body of mass \(1\ kg\) starts moving from rest under the action of a force which varies with displacement as \(F=2x+5\) in newtons. The work done by this force to displace the body from \(x=0\) to \(x=2\ m\) is

• (A) \(8\ J\)
• (B) \(10\ J\)
• (C) \(12\ J\)
• (D) \(14\ J\)

The potential energy of a particle is given by \(U(x)=20+(x-2)^2\), where \(U\) is in joules and \(x\) is in meters. The minimum potential energy and the position where it occurs are

• (A) \(20\ J at x=2\)
• (B) \(2\ J at x=20\ m\)
• (C) \(22\ J at x=2\ m\)
• (D) \(0\ J at x=2\ m\)

Power supplied to a particle of mass \(2\ kg\) varies with time as \[ P=\frac{3t^2}{2}\ watt, \]
where \(t\) is in seconds. If velocity at \(t=0\) is zero, the velocity at \(t=2\ s\) is

• (A) \(1\ m/s\)
• (B) \(2\ m/s\)
• (C) \(\sqrt2\ m/s\)
• (D) \(4\ m/s\)

A pump is used to deliver water at a certain rate from a given pipe. To obtain twice the volume of water from the same pipe in the same time, by what factor must the power of the motor pump be increased? Assume ideal conditions.

• (A) \(4\)
• (B) \(8\)
• (C) \(16\)
• (D) \(32\)

Two identical piano wires, when tuned to a fundamental frequency of \(400\ Hz\), produce no beats. One wire is then slightly tightened, and the beat frequency heard is \(2\ Hz\). What is the new fundamental frequency of the tightened wire?

• (A) \(398\ Hz\)
• (B) \(402\ Hz\)
• (C) \(404\ Hz\)
• (D) \(396\ Hz\)

A source of sound of frequency \(500\ Hz\) is moving towards an observer with velocity \(30\ m/s\). The speed of sound is \(330\ m/s\). The frequency heard by the observer will be

• (A) \(450\ Hz\)
• (B) \(550\ Hz\)
• (C) \(600\ Hz\)
• (D) \(500\ Hz\)

In acoustics, ``Noise'' is generally characterized by

• (A) Irregular and non-periodic vibrations
• (B) A constant pitch and frequency
• (C) Vibrations that follow a harmonic series
• (D) Regular and periodic vibrations

If the volume of a room is doubled and the total absorption is halved, the reverberation time will

• (A) Remain unchanged
• (B) Be doubled
• (C) Become four times
• (D) Be halved

In a closed hall of volume \(5000\ m^3\), the total absorption of the interior surfaces is \(200\) metric sabin. The reverberation time is

• (A) \(1\ s\)
• (B) \(2\ s\)
• (C) \(3\ s\)
• (D) \(4\ s\)

In an isothermal process

• (A) Internal energy of the system never remains constant
• (B) Total heat energy of the system remains constant
• (C) Volume of the system remains constant
• (D) Temperature of the system remains constant

If the pressure of an ideal gas is doubled and its absolute temperature is halved, the volume will become

• (A) \(\frac{1}{4}\) of initial volume
• (B) \(\frac{1}{2}\) initial volume
• (C) Same as initial volume
• (D) \(2\) times of initial volume

At constant temperature, the product \(PV\) is plotted against pressure \(P\) for an ideal gas. The graph obtained is

• (A) Straight line parallel to \(P\)-axis
• (B) Straight line with positive slope
• (C) Straight line through origin
• (D) Parabola

A bubble of an ideal gas rises from the bottom of a lake to the surface. At the bottom, the pressure is \(3\ atm\) and the temperature is \(7^\circ C\). At the surface, the pressure is \(1\ atm\) and the temperature is \(27^\circ C\). If the initial volume of the bubble was \(V_0\), what is its volume \(V\) at the surface?

• (A) \(3V_0\)
• (B) \(3.21V_0\)
• (C) \(0.9V_0\)
• (D) \(5.4V_0\)

The R.M.S. speed of oxygen molecules at \(27^\circ C\) is \(v\). At \(927^\circ C\), the rms speed will be:

• (A) \(v\)
• (B) \(\frac{v}{2}\)
• (C) \(2v\)
• (D) \(4v\)

In a photoelectric experiment, the stopping potential for incident light of wavelength \(4000\ Å\) is \(2\ V\). If the wavelength is changed to \(3000\ Å\), the new stopping potential will be approximately \[ (Use h=4.14\times10^{-15}\ eV s,\ c=3\times10^8\ m/s) \]

• (A) \(2\ V\)
• (B) \(3.03\ V\)
• (C) \(4.14\ V\)
• (D) \(1.5\ V\)

In Optical Fiber communication, the signal is transmitted in the form of:

• (A) Electrical pulses
• (B) Light pulses
• (C) Radio waves
• (D) Sound waves

In a superconducting ring, a persistent current has been flowing without decay for years. This is possible because:

• (A) Resistance is exactly zero and flux is quantized
• (B) Resistance is very small but finite
• (C) The ring is at absolute zero temperature
• (D) Magnetic field lines are expelled

The pair of orbitals with electron density maximum along the axes is

• (A) \(d_{xy}, d_{yz}\)
• (B) \(d_{z^2}, d_{x^2-y^2}\)
• (C) \(d_{xz}, d_{z^2}\)
• (D) \(d_{xz}, p_z\)

The angular momentum of an electron in an orbit \(X\) of hydrogen atom is \(\frac{2h}{\pi}\). Maximum number of orbitals possible in \(X\) is

• (A) \(4\)
• (B) \(9\)
• (C) \(16\)
• (D) \(25\)

The four quantum numbers for the electron in the outermost orbital of potassium \((Z=19)\) are

• (A) \(n=4,\ l=2,\ m=-1,\ s=+\frac{1}{2}\)
• (B) \(n=4,\ l=0,\ m=0,\ s=+\frac{1}{2}\)
• (C) \(n=3,\ l=0,\ m=1,\ s=+\frac{1}{2}\)
• (D) \(n=4,\ l=3,\ m=-2,\ s=-\frac{1}{2}\)

In which of the following, the number of bonding electrons and non-bonding electrons are in \(3:2\) ratio?

• (A) \(N_2\)
• (B) \(O_2\)
• (C) \(HCl\)
• (D) \(F_2\)

Which one of the following statements is not correct?

• (A) Ionic bond is non-directional bond
• (B) The maximum number of bond pairs between two atoms is \(3\)
• (C) Covalent compounds conduct electricity in fused state
• (D) Ionic compounds are generally soluble in water

\(12.6\ g\) of oxalic acid, \(H_2C_2O_4\cdot2H_2O\) \((M.wt. 126)\), is present in \(1500\ mL\) of solution. The normality of that solution is

• (A) \(0.266\ N\)
• (B) \(0.133\ N\)
• (C) \(0.399\ N\)
• (D) \(0.430\ N\)

Which of the following has highest equivalent weight? Given: At.wt. \(H=1,\ C=12,\ O=16,\ S=32,\ Na=23,\ Ca=40\)

• (A) Sulphuric acid
• (B) Sodium carbonate
• (C) Sodium sulphate
• (D) Calcium carbonate

Identify the pair of gases which have same number of molecules at S.T.P.?

• (A) \(11\ g of CO_2\) and \(14\ g of N_2\)
• (B) \(16\ g of O_3\) and \(16\ g of CH_4\)
• (C) \(5\ g of H_2\) and \(40\ g of CH_4\)
• (D) \(28\ g of N_2\) and \(22\ g of CO_2\)

\(100\ mL\) of \(0.1M\ HCl\) and \(100\ mL\) of \(0.05M\ H_2SO_4\) are mixed and the solution is diluted to \(2.0\ L\) by adding water. The pH of the resulting solution is

• (A) \(1\)
• (B) \(3\)
• (C) \(2\)
• (D) \(4\)

According to Arrhenius theory of acids and bases, which of the following is an example of Arrhenius base?

• (A) \(H_2SO_4\)
• (B) \(NH_3\)
• (C) \(NaOH\)
• (D) \(CaO\)

Electrolysis of an aqueous solution of \(Na_2SO_4\) between Pt electrodes liberates a gas \(X\) at anode and gas \(Y\) at cathode. \(X\) and \(Y\) respectively are

• (A) \(H_2,\ O_2\)
• (B) \(O_2,\ H_2\)
• (C) \(SO_2,\ H_2\)
• (D) \(H_2,\ SO_2\)

The wrong statement regarding Galvanic cell is

• (A) In this spontaneous redox reaction occurs
• (B) Salt bridge maintains electrical neutrality between the two solutions
• (C) Anode is represented by \((+)\) and cathode by \((-)\)
• (D) At anode oxidation occurs

Which of the following is a weak electrolyte?

• (A) \(H_2CO_3\)
• (B) \(H_2SO_4\)
• (C) \(NaCl\)
• (D) \(NaOH\)

The exhausted anion-exchange resin is regenerated with

• (A) dilute \(NaOH\) solution
• (B) dilute \(NaCl\) solution
• (C) dilute \(HCl\) solution
• (D) dilute \(Na_2SO_4\) solution

A sample of water is known to contain \(Mg(HCO_3)_2=7.3\ mg/L\), \(Ca(HCO_3)_2=8.1\ mg/L\), and \(27.2\ mg/L\) of \(CaSO_4\). The total hardness associated with water sample in ppm in equivalents of \(CaCO_3\) is \[ (At.wt. H=1,\ C=12,\ O=16,\ Mg=24,\ Ca=40,\ S=32) \]

• (A) \(20\)
• (B) \(25\)
• (C) \(30\)
• (D) \(40\)

The type of functional group associated with cation exchange resin is

• (A) \(-OH\)
• (B) \(-SO_3H\)
• (C) \(-NH_2\)
• (D) \(-CHO\)

Identify the incorrect statement about the corrosion.

• (A) In the composition type of galvanic cell, metal with lower standard reduction potential undergoes corrosion
• (B) In stress cell type of galvanic cell, corrosion occurs at the stressed area of the metal
• (C) The rate of corrosion is more, when the area of cathode is smaller
• (D) In concentration cell type of galvanic cell, the metal below the water level undergoes corrosion readily

In galvanised iron

• (A) Zn acts as anode and Fe acts as cathode
• (B) Zn acts as cathode and Fe acts as anode
• (C) Sn acts as anode and Fe acts as cathode
• (D) Sn acts as cathode and Fe acts as anode

During vulcanization of raw rubber, the chemical added to it is

• (A) Sulphur
• (B) Phosphorus
• (C) Iodine
• (D) Sodium

Which of the following is a natural polymer?

• (A) Cellulose
• (B) Teflon
• (C) Polyvinylchloride
• (D) Neoprene rubber

The structure of Buna-S polymer is

• (A) \(\left[-CH_2-CH=CH-CH_2-CH(C_6H_5)-CH_2-\right]_n\)
• (B) \(\left[-CH_2-CH=CH-CH_2-CH(CN)-CH_2-\right]_n\)
• (C) \(\left[-CH_2-C(Cl)=CH-CH_2-\right]_n\)
• (D) \(\left[-NH-CO-NH-CH_2-\right]_n\)

The polymer used in making gaskets and non-stick coating utensils is

• (A) Polyvinyl chloride
• (B) Polystyrene
• (C) Polytetrafluoroethylene
• (D) Polythene

Which of the following is not to be considered as a primary fuel?

• (A) Wood
• (B) Petroleum
• (C) Coke
• (D) Coal

The oxide of nitrogen responsible for depletion of ozone layer is

• (A) \(N_2O\)
• (B) \(NO_2\)
• (C) \(NO\)
• (D) \(N_2O_3\)

The BOD of highly polluted water is

• (A) \(17\ ppm\)
• (B) \(10\ ppm\)
• (C) \(8\ ppm\)
• (D) \(12\ ppm\)

Ohm's law states that

• (A) Current is directly proportional to resistance
• (B) Current is directly proportional to voltage
• (C) Current is inversely proportional to voltage
• (D) Resistance is directly proportional to current

The unit of electrical resistance is

• (A) Ampere
• (B) Volt
• (C) Ohm
• (D) Watt

Kirchhoff's current law is based on the conservation of

• (A) Energy
• (B) Charge
• (C) Momentum
• (D) Power

Kirchhoff's voltage law is based on the conservation of

• (A) Charge
• (B) Energy
• (C) Current
• (D) Resistance

The material having nearly zero temperature coefficient of resistance is

• (A) Copper
• (B) Aluminium
• (C) Manganin
• (D) Carbon

The reciprocal of resistance is called

• (A) Conductance
• (B) Reactance
• (C) Impedance
• (D) Susceptance

The dielectric material between the plates of a capacitor is

• (A) Copper
• (B) Aluminium
• (C) Iron
• (D) Insulating material

In a capacitor, energy is stored in the form of

• (A) Magnetic field
• (B) Electric field
• (C) Heat energy
• (D) Mechanical energy

The equivalent capacitance of capacitors connected in parallel is

• (A) Less than the smallest capacitance
• (B) Equal to the reciprocal sum
• (C) Sum of individual capacitances
• (D) Zero

The equivalent capacitance of capacitors connected in series is

• (A) \(C_1+C_2+C_3\)
• (B) \(\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\)
• (C) \(\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}\)
• (D) Greater than the largest capacitance

The unit of inductance is

• (A) Henry
• (B) Farad
• (C) Ohm
• (D) Weber

Energy stored in an inductor is given by

• (A) \(\frac{1}{2}CV^2\)
• (B) \(\frac{1}{2}LI^2\)
• (C) \(VI\)
• (D) \(I^2R\)

The opposition offered by an inductor to alternating current is called

• (A) Resistance
• (B) Capacitive reactance
• (C) Inductive reactance
• (D) Conductance

The opposition offered by a capacitor to alternating current is called

• (A) Capacitive reactance
• (B) Inductive reactance
• (C) Resistance
• (D) Conductance

In a purely inductive circuit, current

• (A) Leads voltage by \(90^\circ\)
• (B) Lags voltage by \(90^\circ\)
• (C) Is in phase with voltage
• (D) Leads voltage by \(180^\circ\)

In a purely capacitive circuit, current

• (A) Lags voltage by \(90^\circ\)
• (B) Leads voltage by \(90^\circ\)
• (C) Is in phase with voltage
• (D) Is zero

The power factor of a purely resistive AC circuit is

• (A) Zero
• (B) Unity
• (C) Lagging
• (D) Leading

The power factor of a purely inductive circuit is

• (A) Unity
• (B) Zero lagging
• (C) Zero leading
• (D) One leading

The power factor of a purely capacitive circuit is

• (A) Unity
• (B) Zero lagging
• (C) Zero leading
• (D) One lagging

At resonance in a series RLC circuit, the impedance is

• (A) Maximum
• (B) Minimum
• (C) Infinite
• (D) Zero

At resonance in a series RLC circuit, current is

• (A) Minimum
• (B) Maximum
• (C) Zero
• (D) Infinite always

The resonant frequency of a series RLC circuit is

• (A) \(\frac{1}{2\pi LC}\)
• (B) \(\frac{1}{2\pi\sqrt{LC}}\)
• (C) \(2\pi\sqrt{LC}\)
• (D) \(\frac{L}{C}\)

The form factor of a sinusoidal alternating current is

• (A) \(1.11\)
• (B) \(1.414\)
• (C) \(0.707\)
• (D) \(0.637\)

The peak factor of a sinusoidal alternating current is

• (A) \(1.11\)
• (B) \(1.414\)
• (C) \(0.707\)
• (D) \(0.637\)

The average value of a sinusoidal alternating current over one complete cycle is

• (A) Maximum value
• (B) RMS value
• (C) Zero
• (D) Half of maximum value

The RMS value of a sinusoidal alternating current is

• (A) \(0.637I_m\)
• (B) \(0.707I_m\)
• (C) \(1.414I_m\)
• (D) \(I_m\)

The average value of sinusoidal alternating current over half cycle is

• (A) \(0.637I_m\)
• (B) \(0.707I_m\)
• (C) \(1.414I_m\)
• (D) Zero

In a three-phase balanced system, the phase difference between any two phases is

• (A) \(60^\circ\)
• (B) \(90^\circ\)
• (C) \(120^\circ\)
• (D) \(180^\circ\)

In star connection, line voltage is related to phase voltage as

• (A) \(V_L=V_{ph}\)
• (B) \(V_L=\sqrt3V_{ph}\)
• (C) \(V_{ph}=\sqrt3V_L\)
• (D) \(V_L=3V_{ph}\)

In delta connection, line current is related to phase current as

• (A) \(I_L=I_{ph}\)
• (B) \(I_L=\sqrt3I_{ph}\)
• (C) \(I_{ph}=\sqrt3I_L\)
• (D) \(I_L=3I_{ph}\)

What is the major disadvantage of an auto transformer?

• (A) High cost
• (B) Low efficiency
• (C) Lack of electrical isolation between primary and secondary
• (D) Very heavy weight

If an alternator has a flux per pole of \(0.05\ Wb\), a frequency of \(50\ Hz\), and \(100\) turns per phase (assume pitch factor and distribution factor is \(1\)), the RMS phase emf is approximately

• (A) \(222\ V\)
• (B) \(1110\ V\)
• (C) \(555\ V\)
• (D) \(444\ V\)

Which method provides the most accurate results for the voltage regulation of a non-salient pole alternator?

• (A) EMF method
• (B) MMF method
• (C) Poitier Triangle method
• (D) Direct loading test

Two alternators A and B are in parallel. Alternator A is adjusted to have a leading power factor. This will cause Alternator B to

• (A) Also have a leading power factor
• (B) Have a lagging power factor
• (C) Stop rotating
• (D) Carry zero current

A Synchronous motor used specifically for power factor correction (running at no load and over excited) is called a

• (A) Synchronous generator
• (B) Synchronous condenser
• (C) Induction generator
• (D) Variable speed drive

In the V-curve of a Synchronous motor, the minimum point of the curve corresponds to

• (A) Lagging power factor
• (B) Unity power factor
• (C) Minimum speed
• (D) Leading power factor

What is a Pony motor in the context of starting a Synchronous motor?

• (A) A motor that runs on DC only
• (B) A small auxiliary motor used to bring the main motor up to speed
• (C) The main cooling fan
• (D) A motor used to reverse the direction

A motor has synchronous speed of \(1000\ rpm\) and runs at \(950\ rpm\). If the torque at this slip is \(10\ Nm\). What is the torque if the slip is doubled? (assume low slip region)

• (A) \(5\ Nm\)
• (B) \(10\ Nm\)
• (C) \(20\ Nm\)
• (D) \(40\ Nm\)

In an Induction motor, the rotor copper loss is equal to

• (A) Slip \(\times\) rotor input power
• (B) \((1-slip)\times\) rotor input power
• (C) Rotor input power/slip
• (D) Slip\(^2\times\) rotor input power

The pole changing method of speed control is only applicable to which type of motor?

• (A) Slip ring induction motor
• (B) Squirrel cage induction motor
• (C) Synchronous motor
• (D) DC shunt motor

Regenerative braking occurs only when the motor speed \(N\)

• (A) Is less than the synchronous speed
• (B) Is greater than the synchronous speed
• (C) Is exactly equal to synchronous speed
• (D) Is zero

A single phase induction motor is

• (A) Inherently self-starting
• (B) Not inherently self-starting
• (C) Self-starting only at high voltages
• (D) Always started by a DC motor

A universal motor is designed to operate on

• (A) DC supply only
• (B) AC supply only
• (C) Both AC and DC supply
• (D) 3-phase supply only

In a BLDC motor, the windings are placed on the

• (A) Rotor
• (B) Stator
• (C) Shaft
• (D) Commutator

The number of pulses applied to a Stepper motor determines the

• (A) Speed of rotation
• (B) Torque produced
• (C) Total angle or distance of rotation
• (D) Direction of rotation

Which type of generating station is best suited for peak load operation due to its quick starting ability?

• (A) Nuclear power plant
• (B) Gas turbine power plant
• (C) Thermal power plant
• (D) Solar power plant

Which of the following is a byproduct of coal combination that can be repurposed by the construction industry?

• (A) Flue gas
• (B) Fly ash
• (C) Nitrogen oxide
• (D) Sludge

If the area under a \(24\) hour daily load curve is \(480\ MWh\). The average load for that day is

• (A) \(10\ MW\)
• (B) \(20\ MW\)
• (C) \(40\ MW\)
• (D) \(480\ MW\)

Which tariff is most suitable for industrial consumers with a significant reactive power load?

• (A) Flat rate tariff
• (B) Block rate tariff
• (C) Maximum demand tariff
• (D) KVA maximum demand tariff

A factory has a load of \(400\ kW\) at a power factor of \(0.8\) lagging. If the power factor is to be improved to unity, the required KVAR of the capacitor bank is

• (A) \(400\ KVAR\)
• (B) \(300\ KVAR\)
• (C) \(500\ KVAR\)
• (D) \(100\ KVAR\)

Which circuit breaker is preferred for high voltage up to \(765\ kV\) and extra high voltage system?

• (A) Vacuum Circuit Breaker (VCB)
• (B) Air Circuit Breaker
• (C) \(SF_6\) Circuit Breaker
• (D) Miniature Circuit Breaker (MCB)

Why are current limiting reactors usually ``Air-cored'' rather than ``Iron-cored''?

• (A) To reduce weight
• (B) To improve cooling
• (C) To avoid magnetic saturation during heavy fault currents
• (D) To decrease the cost of iron

Which type of distance relay is inherently ``directional'' and does not require an additional directional unit?

• (A) Impedance relay
• (B) Reactance relay
• (C) MHO relay
• (D) Plain offset relay

Bus bar protection is usually not provided for which type of system?

• (A) Extra high voltage systems
• (B) Small distribution substation
• (C) Power house bus bars
• (D) \(132\ kV\) substations

Which type of lightning arrester is also known as a ``Surge Diverter''?

• (A) Rod gap
• (B) Horn gap
• (C) Expulsion type
• (D) Valve type

If the radius of a conductor in a transmission line is doubled while keeping spacing constant, the inductance of the line will

• (A) Increase
• (B) Decrease
• (C) Remain unchanged
• (D) Double

The sending end voltage of a line is \(33\ kV\) and the receiving end voltage is \(30\ kV\). The voltage regulation of the line is

• (A) \(3%\)
• (B) \(5%\)
• (C) \(10%\)
• (D) \(11%\)

A long transmission line is energized at the sending end but kept open circuited at the receiving end. If the sending end voltage is \(100\ kV\), the receiving end voltage is likely to be

• (A) \(90\ kV\)
• (B) \(100\ kV\)
• (C) \(105\ kV\)
• (D) \(0\ kV\)

What happens to the corona effect if the spacing between conductors is increased?

• (A) Corona increases
• (B) Corona decreases
• (C) Corona is absent
• (D) No effect

The converter used at the sending end of an HVDC system acts as a

• (A) Inverter
• (B) Rectifier
• (C) Cycloconverter
• (D) Chopper

If the length of the span between two level supports is increased by \(20%\), the sag will increase by approximately

• (A) \(20%\)
• (B) \(40%\)
• (C) \(44%\)
• (D) \(50%\)

A string of \(3\) discs can withstand a total voltage of \(25.76\ kV\). If each unit can individually withstand a maximum of \(11\ kV\), then the string efficiency is

• (A) \(68.75%\)
• (B) \(65%\)
• (C) \(78%\)
• (D) \(85%\)

A \(10\ km\) long cable has an insulation resistance of \(2\ M\Omega\). What will be the insulation resistance for a \(50\ km\) length of the same cable?

• (A) \(10\ M\Omega\)
• (B) \(0.4\ M\Omega\)
• (C) \(0.2\ M\Omega\)
• (D) \(1\ M\Omega\)

In a substation Single Line Diagram (SLD), which equipment is typically placed closest to the incoming line?

• (A) Circuit breaker
• (B) Current transformer
• (C) Surge arrester
• (D) Power transformer

A single phase AC distributor has a total resistance of \(0.2\ \Omega\) and a reactance of \(0.3\ \Omega\). If the load current is \(100\ A\) at \(0.8\) p.f. lagging, the approximate voltage drop is

• (A) \(16\ V\)
• (B) \(34\ V\)
• (C) \(50\ V\)
• (D) \(25\ V\)

Which of the following is the standard electrification system used by Indian railways for mainline trains?

• (A) \(1500\ V DC\)
• (B) \(33\ kV AC,\ 50\ Hz\)
• (C) \(25\ kV AC,\ 50\ Hz\)
• (D) \(11\ kV DC\)

The distance between two stops is \(5\ km\), the average speed is \(50\ km/h\), and the stop time is \(2\) minutes. Find the scheduled speed.

• (A) \(37.5\ km/h\)
• (B) \(42.5\ km/h\)
• (C) \(30\ km/h\)
• (D) \(50\ km/h\)

The unit of Specific Energy Consumption (SEC) is

• (A) Watt-hours
• (B) \(kWh/km\)
• (C) Watt hours/\((tonne-km)\)
• (D) Joules/Tonne

A compressor in an electric locomotive is driven by an auxiliary motor to provide air for

• (A) Air conditioning only
• (B) Air brakes, horns, and sanders
• (C) Turbine rotation
• (D) Pantograph lowering only

In which type of wiring system is highly skilled labor required?

• (A) Cleat wiring
• (B) Casing--Capping wiring
• (C) Conduit wiring
• (D) Batten wiring

A fuse in domestic wiring is always connected in the

• (A) Neutral wire
• (B) Earth wire
• (C) Live wire
• (D) Both neutral and earth wire

The main purpose of earthing in electrical installation is

• (A) To increase voltage
• (B) To reduce power consumption
• (C) To provide safety against electric shock
• (D) To increase current rating

Which type of earthing is commonly used in domestic installations?

• (A) Plate earthing
• (B) Pipe earthing
• (C) Rod earthing only
• (D) Strip earthing only

In an NPN transistor, the region which is heavily doped is

• (A) Collector
• (B) Base
• (C) Emitter
• (D) Substrate

In a common emitter transistor configuration, the current gain \(\beta\) is given by

• (A) \(\frac{I_B}{I_C}\)
• (B) \(\frac{I_C}{I_B}\)
• (C) \(\frac{I_E}{I_C}\)
• (D) \(\frac{I_C}{I_E}\)

Lissajous patterns on a CRO are used to measure

• (A) Voltage and current only
• (B) Frequency and phase difference
• (C) Resistance and inductance
• (D) Power factor only

In a CRO, focusing of the electron beam is done by

• (A) Deflection plates
• (B) Fluorescent screen
• (C) Focusing anode
• (D) Time base generator

The instrument used to measure power factor directly is

• (A) Wattmeter
• (B) Ammeter
• (C) Voltmeter
• (D) Power factor meter

The scale of a PMMC instrument is

• (A) Non-uniform
• (B) Uniform
• (C) Logarithmic
• (D) Exponential

An oscillator circuit is used to

• (A) Convert AC into DC
• (B) Generate sustained AC signal
• (C) Measure resistance
• (D) Store charge

Which of the following is not a typical application of an oscillator?

• (A) Signal generator
• (B) Radio transmitter
• (C) Rectifier
• (D) Digital clock

The basic function of an oscillator is to

• (A) Amplify DC signal
• (B) Generate alternating waveform
• (C) Convert DC to fixed resistance
• (D) Measure voltage only

Which oscillator gives very high frequency stability?

• (A) RC phase shift oscillator
• (B) Hartley oscillator
• (C) Wien bridge oscillator
• (D) Crystal oscillator

In an RC phase shift oscillator, the feedback network provides a phase shift of

• (A) \(90^\circ\)
• (B) \(180^\circ\)
• (C) \(270^\circ\)
• (D) \(360^\circ\)

Wien bridge oscillator is commonly used for

• (A) RF signal generation
• (B) Audio frequency generation
• (C) Rectification
• (D) Voltage regulation

Crystal oscillator is preferred because it offers

• (A) Low efficiency
• (B) High frequency stability
• (C) High noise
• (D) Poor selectivity

In Boolean algebra, \(A+AB\) is equal to

• (A) \(A\)
• (B) \(B\)
• (C) \(AB\)
• (D) \(A+B\)

According to De Morgan's theorem, \(\overline{A+B}\) is equal to

• (A) \(\overline{A}+\overline{B}\)
• (B) \(\overline{A}\,\overline{B}\)
• (C) \(AB\)
• (D) \(A+B\)

For a half adder, the Sum and Carry outputs are respectively

• (A) \(A+B,\ AB\)
• (B) \(A\oplus B,\ AB\)
• (C) \(AB,\ A+B\)
• (D) \(A\oplus B,\ A+B\)

A flip-flop is used to store

• (A) One bit of data
• (B) One byte of data
• (C) One word of data
• (D) Analog signal only

The BCD representation of decimal number \(9\) is

• (A) \(1000\)
• (B) \(1001\)
• (C) \(1010\)
• (D) \(1111\)

The output of a NAND gate is zero when

• (A) All inputs are zero
• (B) Any one input is zero
• (C) All inputs are one
• (D) Inputs are unequal

A PN junction diode conducts current when it is

• (A) Reverse biased
• (B) Forward biased
• (C) Unbiased
• (D) Open circuited

A Zener diode is mainly used as a

• (A) Rectifier
• (B) Voltage regulator
• (C) Amplifier
• (D) Oscillator

A rectifier converts

• (A) DC into AC
• (B) AC into DC
• (C) AC into AC only
• (D) DC into DC only

A bridge rectifier uses how many diodes?

• (A) \(1\)
• (B) \(2\)
• (C) \(3\)
• (D) \(4\)

The ripple factor of a full-wave rectifier is approximately

• (A) \(1.21\)
• (B) \(0.482\)
• (C) \(0.707\)
• (D) \(1.11\)

When a transistor is used as a switch, it operates in

• (A) Active region only
• (B) Cut-off and saturation regions
• (C) Breakdown region only
• (D) Inverse active region only

The input impedance of an ideal operational amplifier is

• (A) Zero
• (B) Very low
• (C) Infinite
• (D) Equal to output impedance

The IC \(555\) is commonly used as a

• (A) Timer
• (B) Transformer
• (C) Rectifier diode
• (D) Inductor