MCQ

MCQ 11 Mark

The resultant gate and its Boolean expression for the given circuit is ______.

A
NOR, $\overline{A+B}$
B
OR, A+B
✓
AND, A × B
D
NAND, $\overline{A \cdot B}$

Answer

Correct option: C.

AND, A × B

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MCQ 21 Mark

The current gain $\alpha$ of a transistor is 0.95. The change in collector current corresponding to a change of 0.4 mA in the base current in a common emitter arrangement is ______.

A
0.42 mA
B
0.38 mA
C
2.375 mA
✓
7.6 mA

Answer

Correct option: D.

7.6 mA

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MCQ 31 Mark

When hydrogen atom is in its first excited level, its radius is how many time its ground state radius?

A
half
✓
four times
C
same
D
twice

Answer

Correct option: B.

four times

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MCQ 41 Mark

In Rutherford scattering experiment, the number of particles observed at an angle of 10° is one million per minute. The number of particles/minute at 90° are, ______.

A
63
B
10
✓
231
D
58

Answer

Correct option: C.

231

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MCQ 51 Mark

Two incident radiations having energies two times and ten times of the work function of a metal surface, produce photoelectric effect. The ratio of maximum velocities of emitted photo electrons respectively is ____________.

✓
1 : 3
B
3 : 2
C
1 : 2
D
2 : 3

Answer

Correct option: A.

1 : 3

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MCQ 61 Mark

When light falls on a metal surface, the maximum kinetic energy of the emitted photoelectrons depends upon ______

✓
frequency of the incident light.
B
the time for which light falls on the metal.
C
the intensity of the incident light.
D
the velocity of the incident light.

Answer

Correct option: A.

frequency of the incident light.

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MCQ 71 Mark

In LCR series circuit, an alternating e.m.f. 'e' and current 'i' are given by the equations e = 100 sin (100 t) volt,

$i =100 \sin \left(100 t +\frac{\pi}{3}\right) mA$..

The average power dissipated in the circuit will be ____________.

A
10 W
✓
2.5 W
C
100 W
D
5 W

Answer

Correct option: B.

2.5 W

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MCQ 81 Mark

In half-wave rectifier, the RMS value of A.C. component of the wave is ____________.

A
zero
✓
more than D.C. value
C
less than D.C. value
D
equal to D.C. value

Answer

Correct option: B.

more than D.C. value

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MCQ 91 Mark

The mutual inductance between two coplanar concentric rings $A$ and $B$ of radii $ 'R_1\ ' $ and $'R_2\ '$ placed in air when a current $ 'I\ '$ flows through ring $A$ is $(R_1 >> R_2) (µ_0 =$ permeability of free space$) ........$

✓
$\frac{\mu_0 \pi R _2^2}{2 R _1}$
B
$\frac{\mu_0 \pi R _1}{ R _2}$
C
$\frac{\mu_0 \pi R _1^2}{2 R _2}$
D
$\frac{\mu_0 \pi R _2}{ R _1}$

Answer

Correct option: A.

$\frac{\mu_0 \pi R _2^2}{2 R _1}$

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MCQ 101 Mark

A graph of magnetic ﬂux versus current (I) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor ____________.

A
B
B
C
✓
D
D
A

Answer

Correct option: C.

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MCQ 111 Mark

Above the curie temperature the susceptibility of ferromagnetic substance varies ____________.

✓
inversely as the absolute temperature
B
directly as the absolute temperature
C
directly as the square root of absolute temperature
D
inversely as the square root of absolute temperature

Answer

Correct option: A.

inversely as the absolute temperature

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MCQ 121 Mark

Magnetization of a sample is ______.

A
volume of sample per unit magnetic moment.
✓
net magnetic moment per unit volume.
C
ratio of pole strength to magnetic moment.
D
ratio of magnetic moment and pole strength.

Answer

Correct option: B.

net magnetic moment per unit volume.

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MCQ 131 Mark

The magnetic moment of a circular coil carrying current $(I),$ having radius $(r) $ and number of turns $(n)$ is proportional to $.......$

A
$\frac{1}{ r }$
✓
$r^2$
C
$r$
D
$\frac{1}{ r ^2}$

Answer

Correct option: B.

$r^2$

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MCQ 141 Mark

An electron is projected along the axis of circular conductor carrying current I. Electron will experience ____________.

✓
no force
B
a force at an angle of 30° with the axis
C
a force perpendicular to the axis
D
a force along the axis

Answer

Correct option: A.

no force

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MCQ 151 Mark

In the Wheatstone bridge, (shown in the figure) X = Y and A > B. The direction of the current between a and b will be ____________.

A
from b to a through c
B
from a to b through c
✓
from b to a
D
from a to b

Answer

Correct option: C.

from b to a

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MCQ 161 Mark

In a metre bridge experiment, the null point is obtained at 20 cm from one end of the wire when resistance X is balanced against another resistance Y. If X < Y, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X against Y?

✓
50 cm
B
80 cm
C
40 cm
D
70 cm

Answer

Correct option: A.

50 cm

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MCQ 171 Mark

A capacitor is charged by a battery and energy stored is 'U'. Now the battery is removed and the distance between plates is increased to four times. The energy stored becomes ______.

✓
4U
B
U
C
2U
D
3U

Answer

Correct option: A.

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MCQ 181 Mark

A parallel plate capacitor has a uniform electric field $\overrightarrow{ E }$ in the space between the plates. If the distance between plates is $'d\ '$ and the area of each plate is $'A\ ',$ the energy stored in the capacitor is$......$ $(ε_0 =$ permittivity of free space$)$

A
$\frac{1}{2} \frac{\varepsilon_0 E^2 A}{d}$
B
$\frac{1}{2} \frac{\varepsilon_0 A d}{E^2}$
C
$\frac{1}{2} \frac{\varepsilon_0 E A}{d}$
✓
$\frac{1}{2} \varepsilon_0 E^2 A d$

Answer

Correct option: D.

$\frac{1}{2} \varepsilon_0 E^2 A d$

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MCQ 191 Mark

A parallel combination of two capacitors, 3.6 µF and 7.2 µF, are connected across a 21 V battery. The electric potential energy stored by the capacitors are in the ratio.

A
1 : 1
✓
1 : 2
C
2 : 1
D
4 : 1

Answer

Correct option: B.

1 : 2

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MCQ 201 Mark

If two light waves reaching a point produce destructive interference, then the condition of phase difference is ______

✓
π, 3π, 5π
B
0, 2π, 4π, 6π
C
$\frac{\pi}{2}, \frac{3 \pi}{2}, \frac{5 \pi}{2}$
D
$\frac{\pi}{4}, \frac{\pi}{2}, \frac{3 \pi}{4}$

Answer

Correct option: A.

π, 3π, 5π

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MCQ 211 Mark

A thin mica sheet of thickness $4 \times 10^{-6} \ m$ and refractive index $1.5$ is introduced in the path of the first wave. The wavelength of the wave used is $5000 A.$ The central bright maximum will shift $.......$

A
$10$ fringes upward.
✓
$4$ fringes upward.
C
$4$ fringes downward.
D
$10$ fringes downwards.

Answer

Correct option: B.

$4$ fringes upward.

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MCQ 221 Mark

On a rainy day, a small oil film on water shows brilliant colours. This is due to ____________.

✓
interference of light
B
dispersion of light
C
scattering of light
D
absorption of light

Answer

Correct option: A.

interference of light

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MCQ 231 Mark

A sonometer wire of length $'ℓ_1\ '$ is in resonance with a frequency of $250 \ Hz.$ If the length of the wire is increased to $'ℓ_2\ ',$ then $2$ beats per second are heard. The ratio of lengths$\frac{\ell_1}{\ell_2}$of wire will be $.......$

A
$1 : 2$
B
$2 : 1$
✓
$124 : 125$
D
$1 : 250$

Answer

Correct option: C.

$124 : 125$

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MCQ 241 Mark

An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends vibrating in third harmonic. The ratio of lengths of the two pipes is ____________.

A
8 : 3
B
3 : 8
C
4 : 1
✓
1 : 2

Answer

Correct option: D.

1 : 2

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MCQ 251 Mark

Two parallel $ \text{SHMs}$ have equations $y_1 = a_1 \sin(ωt + 2\pi )$ and $y_2 = a_2 \sin(ωt + 4\pi ).$ The amplitude of the resultant is $..........$

A
$\sqrt{a_1^2+a_2^2+a_1 a_2}$
B
$\sqrt{a_1^2+a_2^2}$
✓
$±(a_1 + a_2)$
D
$±(a_1 - a_2)$

Answer

Correct option: C.

$±(a_1 + a_2)$

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MCQ 261 Mark

A body is executing $ \text{S.H.M.}$ Its potential energy is $E_1$ and $E_2$ at displacements $x$ and $y$ respectively. The potential energy at displacement $(x + y)$ is $.......$

✓
$\sqrt{E_1}+\sqrt{E_2}=\sqrt{E}$
B
$E_1 - E_2 = E$
C
$\sqrt{E_1}-\sqrt{E_2}=\sqrt{E}$
D
$E_1 + E_2 = E$

Answer

Correct option: A.

$\sqrt{E_1}+\sqrt{E_2}=\sqrt{E}$

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MCQ 271 Mark

The relation between time and displacement for two particles is given by $Y_1 = 0.06 \sin 27\pi\left(0.04 t+\phi_1\right., y2 = 0.03 \sin 27\pi\left(0.04 t+\phi_2\right).$ The ratio of the intensity of the waves produced by the vibrations of the two particles will be$ ........$

A
$1: 2$
B
$2: 1$
✓
$4: 1$
D
$1 : 4$

Answer

Correct option: C.

$4: 1$

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MCQ 281 Mark

At extreme positions of a particle executing simple harmonic motion, ______

A
both velocity and acceleration are maximum.
B
velocity is maximum but acceleration is zero
C
both velocity and acceleration are zero.
✓
velocity is zero but acceleration is maximum.

Answer

Correct option: D.

velocity is zero but acceleration is maximum.

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MCQ 291 Mark

An ideal gas A and a real gas B have their volumes increased from V to 2V under isothermal conditions. The increase in internal energy ____________.

A
will be zero in both the cases
B
of A will be more than that of B
✓
of B will be more than that of A
D
will be same in both A and B

Answer

Correct option: C.

of B will be more than that of A

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MCQ 301 Mark

An ideal gas is made to go from a state $A$ to stale $B$ in the given two different ways $($see figure$)$
$(i)$ an isobaric and then an isochoric process and
$(ii)$ an isochoric and then an isobaric process. The work done by gas in the two processes are $W_1$ and $W_2$ respectively. Then,

✓
$W_1 > W_2$
B
$W_1 = W_2$
C
$W_1 = W_2/2$
D
$W_1 < W_2$

Answer

Correct option: A.

$W_1 > W_2$

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MCQ 311 Mark

A thermodynamic system goes from states

(i) P, V to 2P, V (ii) P, V to P, 2V

The work done in the two cases is ____________.

A
PV, zero
B
zero, zero
C
PV, PV
✓
zero, PV

Answer

Correct option: D.

zero, PV

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MCQ 321 Mark

About black body radiation, which one of the following is 'WRONG' statement?

A
For shorter wavelengths, intensity is more.
B
For longer wavelengths, intensity is less.
C
All wavelengths are emitted by a black body.
✓
For all wavelengths, intensity is same.

Answer

Correct option: D.

For all wavelengths, intensity is same.

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MCQ 331 Mark

A black body has maximum wavelength $\lambda_{ m }$ at temperature 2200 K. wavelength at temperature 3300 K will be ______.

A
$\frac{9}{4} \lambda_{ m }$
B
$\frac{3}{2} \lambda_{ m }$
✓
$\frac{2}{3} \lambda_{ m }$
D
$\frac{4}{9} \lambda_{ m }$

Answer

Correct option: C.

$\frac{2}{3} \lambda_{ m }$

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MCQ 341 Mark

Which of the substances P, Q, or R has the lowest specific heat? The temperature v/s time graph is shown ______.

A
Q
B
All have equal specific heat
C
R
✓
P

Answer

Correct option: D.

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MCQ 351 Mark

When a capillary tube is immersed in water vertically, water rises to a height $'h\ '$ inside the tube. If the radius of another capillary tube is $1/3^{rd}$ that of the previous, the height to which water will rise in this tube, is $.........$

A
$\frac{h}{3}$
✓
$3h$
C
$h$
D
$h \sqrt{3}$

Answer

Correct option: B.

$3h$

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MCQ 361 Mark

A soap bubble is blown such that its diameter increases from $'d\ '$ to $'D\ '.$ The amount of work done is $.........(T =$ surface tension of soap solution$)$

A
$\pi (D^2 - d^2)T$
✓
$2\pi (D^2 - d^2)T$
C
$8\pi (D^2 - d^2)T$
D
$4\pi (D^2 - d^2)T$

Answer

Correct option: B.

$2\pi (D^2 - d^2)T$

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MCQ 371 Mark

A liquid drop having surface energy 'E' is spread into 216 droplets of same size. The final surface energy of the droplets is ____________.

A
2E
B
4E
C
8E
✓
6E

Answer

Correct option: D.

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MCQ 381 Mark

A solid sphere is rolling on a frictionless surface with translational velocity 'V'. It climbs the inclined plane from 'A' to 'B' and then moves away from Bon the smooth horizontal surface. The value of 'V' should be ______.

✓
$\geq\left[\frac{10 \operatorname{gh}}{7}\right]^{\frac{1}{2}}$
B
$\frac{10 g h}{7}$
C
$\sqrt{2 g h}$
D
$\sqrt{g h}$

Answer

Correct option: A.

$\geq\left[\frac{10 \operatorname{gh}}{7}\right]^{\frac{1}{2}}$

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MCQ 391 Mark

Let $I_1$ and $I_2$ be the moments of inertia of two bodies of identical geometrical shape. If the first body is made of aluminium and the second of iron, then $............$

A
$I_1 = I_2$
B
$I _1=\frac{ I _2}{2}$
✓
$I_1 < I_2$
D
$I_1 > I_2$

Answer

Correct option: C.

$I_1 < I_2$

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MCQ 401 Mark

For a body moving with constant speed in a horizontal circle, which of the following remains constant?

A
Acceleration
B
Centripetal force
C
Velocity
✓
Kinetic energy

Answer

Correct option: D.

Kinetic energy

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MCQ 411 Mark

In the following figures, the diodes are either forward biased or reversed biased. Choose the CORRECT statement:

✓
(i) and (iii) are forward biased and (ii) and (iv) reverse biased.
B
(ii) and (iii) are forward biased and (i) and (iv) reverse biased.
C
(i) and (iv) are forward biased and (ii) and (iii) reverse biased
D
(i) and (ii) are forward biased and (iii) and (iv) reverse biased.

Answer

Correct option: A.

(i) and (iii) are forward biased and (ii) and (iv) reverse biased.

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MCQ 421 Mark

Electric field on the axis of a small electric dipole at a distance $r$ is $E_1$ and at a distance of $2r$ on its perpendicular bisector, the electric field is $E_2.$ Then the ratio $E_2: E_1$ is$ .......$

A
$1: 4$
✓
$1: 16$
C
$1: 8$
D
$1: 2$

Answer

Correct option: B.

$1: 16$

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MCQ 431 Mark

Critical angle of light passing from glass to air is maximum for ____________.

A
green
B
violet
✓
red
D
yellow

Answer

Correct option: C.

red

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MCQ 441 Mark

A car sounding a horn of frequency 1000 Hz passes au observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is 11 : 9. If the speed of sound is 'V', the speed of the car is ______.

A
$\frac{ V }{100}$
✓
$\frac{ V }{10}$
C
$\frac{ V }{5}$
D
V

Answer

Correct option: B.

$\frac{ V }{10}$

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MCQ 451 Mark

The temperature of a body is 37°C on a Celsius scale, what is its temperature on the Kelvin scale?

A
300 K
B
137 K
✓
310 K
D
37 K

Answer

Correct option: C.

310 K

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MCQ 461 Mark

A body is projected vertically upwards from earth's surface with velocity $2v_e$ where $v_e$ is escape velocity from earth's surface. The velocity when body escapes the gravitational pull is $.......$

A
$\sqrt{7} V_e$
B
$\sqrt{5} V_e$
C
$2V_e$
✓
$\sqrt{3} V_e$

Answer

Correct option: D.

$\sqrt{3} V_e$

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MCQ 471 Mark

The centre of mass of a system of two particles divides the distance between them ______.

A
in direct ratio of masses of pruticles.
B
in direct ratio of square of masses of particles.
C
in inverse ratio of square of masses of particles.
✓
in inverse ratio of masses of particles.

Answer

Correct option: D.

in inverse ratio of masses of particles.

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MCQ 481 Mark

A body of mass $5 \ kg$ is moving in a straight line. The relation between its displacement and time is $x = (t^3 - 2t - 10)m.$ What is the force acting on it at the end of $5$ second?

A
$100 N$
B
$80 N$
C
$120 N$
✓
$150 N$

Answer

Correct option: D.

$150 N$

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MCQ 491 Mark

A ball of mass 'm' is attached to the free end of an inextensible string of length 'l'. Let 'T' be the tension in the string. The ball is moving in horizontal circular path about the vertical axis. The angular velocity of the ball at any particular instant will be ______.

A
$\sqrt{\frac{m l}{T}}$
B
$\sqrt{\frac{T m}{l}}$
✓
$\sqrt{\frac{T}{m l}}$
D
$\sqrt{\frac{T l}{m}}$

Answer

Correct option: C.

$\sqrt{\frac{T}{m l}}$

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MCQ 501 Mark

A mass m is attached to the end of a rod of length l. The mass goes along a vertical circular path with the other end hinged at its centre. What should be the minimum velocity of the mass at the bottom of the circle so that the mass completes the circle?

A
$\sqrt{5 gl}$
✓
$\sqrt{4 g l}$
C
$\sqrt{3 g l}$
D
$\sqrt{2 g l}$

Answer

Correct option: B.

$\sqrt{4 g l}$

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MCQ 511 Mark

If the mean and variance of a binomial variate X are 14 and 10 respectively, then the probability that X takes a value greater than or equal to 1 is ______

A
$\frac{1}{2^{49}}$
B
$\frac{2^{47}-1}{2^{47}}$
✓
$\frac{2^{49}-1}{2^{49}}$
D
$\frac{1}{2^{47}}$

Answer

Correct option: C.

$\frac{2^{49}-1}{2^{49}}$

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MCQ 521 Mark

If the p.d.f of a c.r.v. X is f(x) =$\begin{array}{ll} K . e ^{-\theta x} ; & \theta>0,0 \leq x<\infty \\ 0 ; & \text { otherwise }\end{array}$ Then, K = ______

✓
θ
B
2θ
C
$\frac{\theta}{2}$
D
$\frac{\theta}{3}$

Answer

Correct option: A.

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MCQ 531 Mark

The c.d.f. of a discrete r.v. X is

X = x	-4	-2	-1	0	2	4	6	8
F(x)	0.2	0.4	0.55	0.6	0.75	0.80	0.95	1

Then P(X ≤ 4|X > -1) = ?

✓
$\frac{5}{9}$
B
$\frac{1}{5}$
C
$\frac{4}{9}$
D
$\frac{1}{4}$

Answer

Correct option: A.

$\frac{5}{9}$

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MCQ 541 Mark

The p.m.f. of a random variable X is

P(x) = $\frac{5-x}{10}$, x = 1, 2, 3, 4
= 0, otherwise

The value of E(X) is ______.

A
3
✓
2
C
1
D
0

Answer

Correct option: B.

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MCQ 551 Mark

lf y = $a e^{\cos ^{-1} x}$, then corresponding to this the differential equation is ______.

A
$\frac{d y}{d x}=\frac{x}{\sqrt{1-x^2}}$
✓
$\frac{d y}{d x}=\frac{-y}{\sqrt{1-x^2}}$
C
$\frac{d y}{d x}=\frac{\sqrt{1-x^2}}{y}$
D
$\frac{d y}{d x}=\frac{-x}{\sqrt{1-x^2}}$

Answer

Correct option: B.

$\frac{d y}{d x}=\frac{-y}{\sqrt{1-x^2}}$

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MCQ 561 Mark

The differential equation of all circles which passes through the origin and whose centre lies on the X-axis is ______

A
$\left(x^2-y^2\right)-x y \frac{d y}{d x}=0$
✓
$\left(x^2-y^2\right)+2 x y \frac{d y}{d x}=0$
C
$\left(x^2-y^2\right)-2 x y \frac{d y}{d x}=0$
D
$\left(x^2-y^2\right)+x y \frac{d y}{d x}=0$

Answer

Correct option: B.

$\left(x^2-y^2\right)+2 x y \frac{d y}{d x}=0$

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MCQ 571 Mark

The order and degree of the differential equation $\left(\frac{d y}{d x}\right)^3+\left(\frac{d^3 y}{d x^3}\right)+x y=0$ are respectively ______.

A
2 and 3
B
3 and 2
C
1 and 3
✓
3 and 1

Answer

Correct option: D.

3 and 1

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MCQ 581 Mark

The area of the curve $xy^2 = 4(2 – x)$ bounded by $Y-$axis is $.......$

A
$12\pi$
B
$16\pi$
C
$8\pi$
✓
$4\pi$

Answer

Correct option: D.

$4\pi$

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MCQ 591 Mark

If $\int_0^{\frac{\pi}{2}} \log (\cos x) dx =-\frac{\pi}{2} \log 2$, then $\int_0^{\frac{\pi}{2}} \log (\cos e c x) dx =$ ?

✓
$\frac{\pi}{2} \log 2$
B
$-\frac{\pi}{2} \log 2$
C
$\frac{\pi}{2}+\frac{\pi}{2} \log 2$
D
$\frac{\pi}{2}-\frac{\pi}{2} \log 2 $

Answer

Correct option: A.

$\frac{\pi}{2} \log 2$

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MCQ 601 Mark

If $\int_0^{ k } \frac{ dx }{2+32 x^2}=\frac{\pi}{32}$, then the value of $k$ is ______.

A
4
✓
$\frac{1}{4}$
C
3
D
$\frac{1}{3}$

Answer

Correct option: B.

$\frac{1}{4}$

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MCQ 611 Mark

$\int_0^{\frac{\pi}{4}} \frac{\sin 2 x}{\sin ^4 x+\cos ^4 x} d x$ = ____________.

A
π
B
$\frac{\pi}{2}$
C
2π
✓
$\frac{\pi}{4}$

Answer

Correct option: D.

$\frac{\pi}{4}$

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MCQ 621 Mark

$\int \frac{x}{x+2} dx$ = ______.

A
x - log |x + 2| + c
B
x + 2log |x + 2| + c
C
x + log |x + 2| + c
✓
x - 2log |x + 2| + c

Answer

Correct option: D.

x - 2log |x + 2| + c

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MCQ 631 Mark

$\int e ^{2 x }\left(\frac{2 x \log x+1}{x}\right) dx =........$

A
$e ^{2 x }+c$
✓
$e^{2x} \log x + c$
C
$e^x \log 2x + c$
D
$2e^{2x} + c$

Answer

Correct option: B.

$e^{2x} \log x + c$

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MCQ 641 Mark

$\int \frac{\sin x}{1+\sin x}$ dx = ______.

A
sec x - tan x - x + c
B
sec x + tan x + x + c
✓
sec x - tan x + x + c
D
sec x + tan x - x + c

Answer

Correct option: C.

sec x - tan x + x + c

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MCQ 651 Mark

If $f(x) = x^2$ and $g(x) =\sin x,$ then $ f(x).g(x)dx = $ ?

✓
$2x \sin x + 2cos \ x - x^2 \cos x + c$
B
$x \cos x + \sin \ x + c$
C
$2x \sin x - 2cos \ x - x^2 \cos x + c$
D
$- x \cos x + \sin x + c$

Answer

Correct option: A.

$2x \sin x + 2cos \ x - x^2 \cos x + c$

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MCQ 661 Mark

The sides of a square are increasing at the rate of $0.2 \ cm/sec$. When the side is $25\ cm$ long, its area is increasing at the rate of $........$

A
$0.10 \ cm^2/sec$
✓
$10 \ cm^2/sec$
C
$1 \ cm^2/sec$
D
$100 \ cm^2/sec$

Answer

Correct option: B.

$10 \ cm^2/sec$

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MCQ 671 Mark

The total number of points on the curve $x^2 - 4y^2 = 1$ at which the tangents to the curve are parallel to the line $x = 2y$ is $............$

✓
$0$
B
$1$
C
$4$
D
$2$

Answer

Correct option: A.

$0$

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MCQ 681 Mark

If y = $(\cos x)^{(\cos x)^{(\cos x)}}$, then $\frac{ d }{ d x}$ = ______.

✓
$\frac{-y^2 \tan x}{1-y \log \cos x}$
B
$\frac{-y^2 \tan x}{1+y \log \cos x}$
C
$\frac{y \tan x}{1+y \log \cos x}$
D
$\frac{y \tan x}{1-y \log \cos x}$

Answer

Correct option: A.

$\frac{-y^2 \tan x}{1-y \log \cos x}$

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MCQ 691 Mark

If x = cos t sin 2t and y = sin t cos 2t, then at t =$\frac{\pi}{4}$, the value of $\frac{d y}{d x}$ is equal to ______.

A
$\frac{1}{2}$
B
-2
C
$-\frac{1}{2}$
✓
2

Answer

Correct option: D.

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MCQ 701 Mark

The differential equation of the family of curves y =$ae ^{2(x+ b )}$ is ______.

A
$\frac{d y}{d x}+y=0$
✓
$\frac{d y}{d x}-2 y=0$
C
$\frac{d y}{d x}+2 y=0$
D
$\frac{d y}{d x}-y=0$

Answer

Correct option: B.

$\frac{d y}{d x}-2 y=0$

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MCQ 711 Mark

The minimum value of z = 5x + 13y subject to constraints 2x + 3y ≤ 18, x + y ≥ 10, x ≥ 0, y ≥ 2 is ______

A
34
B
36
C
35
✓
No optimum value

Answer

Correct option: D.

No optimum value

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MCQ 721 Mark

The maximum value of z = 7x + 6y.
Subject to the constraints x ≤ 45, y ≤ 55 and x ≥ 0, y ≥ 0 is ______.

A
315
B
654
C
330
✓
645

Answer

Correct option: D.

645

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MCQ 731 Mark

If the line $\frac{x+1}{2}=\frac{y-5}{3}=\frac{z- p }{6}$ lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is ______.

A
–4
B
2
✓
4
D
3

Answer

Correct option: C.

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MCQ 741 Mark

The equation of the plane through the point (2, -1, -3) and parallel to the lines $\frac{x-1}{3}=\frac{y+2}{2}=\frac{z}{-4}$ and $\frac{x}{2}=\frac{y-1}{-3}=\frac{z-2}{2}$ is ______.

A
8x + 14y - 13z + 37 = 0
✓
8x + 14y + 13z + 37 = 0
C
8x - 14y + 13z + 37 = 0
D
8x + 14y + 13z - 37 = 0

Answer

Correct option: B.

8x + 14y + 13z + 37 = 0

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MCQ 751 Mark

If the line $\frac{x}{-3}=\frac{y}{2}=\frac{z}{5}$ is perpendicular to the line$\frac{x-2}{2}=\frac{ y -1}{ k }=\frac{ z -3}{ k +11}$, then the value of k is ______.

A
$\frac{1}{5}$
B
7
C
- 5
✓
- 7

Answer

Correct option: D.

- 7

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MCQ 761 Mark

The lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendicular to each other, if ______

A
ac + a'c' = 1
✓
aa' + cc' = -1
C
aa' + cc' = 1
D
ac + a'c' = -1

Answer

Correct option: B.

aa' + cc' = -1

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MCQ 771 Mark

Direction cosines of the line $\frac{x+2}{2}=\frac{2 y-5}{3}$, z = -1 are ______.

A
$\frac{4}{5},-\frac{2}{5}, \frac{1}{5}$
B
$-\frac{3}{5}, \frac{4}{5}, 0$
C
$\frac{3}{5}, \frac{4}{5}, \frac{1}{5}$
✓
$\frac{4}{5}, \frac{3}{5}, 0$

Answer

Correct option: D.

$\frac{4}{5}, \frac{3}{5}, 0$

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MCQ 781 Mark

If $\vec{a}, \vec{b}, \vec{c}$ are mutually perpendicular vectors having magnitudes 1, 2, 3 respectively, then $\left[\begin{array}{lll}\vec{a}+\vec{b}+\vec{c} & \vec{b}-\vec{a} & \vec{c}\end{array}\right]$ = ______.

A
6
B
0
✓
12
D
18

Answer

Correct option: C.

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MCQ 791 Mark

If $|\overline{ a }|=|\overline{ b }|=1, \overline{ a } \cdot \overline{ b }=0$ and $\overline{ a }+\overline{ b }+\overline{ c }=\overline{0}$, then $|\overline{ c }|$ is equal to ______.

A
$\sqrt{3}$
B
$\sqrt{5}$
C
1
✓
$\sqrt{2}$

Answer

Correct option: D.

$\sqrt{2}$

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MCQ 801 Mark

The equation of the plane through (-1, 1, 2), whose normal makes equal acute angles with co-ordinate axes is ______

A
$\bar{r} \cdot(\hat{i}+\hat{j}+\widehat{k})=6$
B
$\bar{r} \cdot(\hat{i}-\hat{j}+\widehat{k})=3$
C
$\bar{r} \cdot(3 \hat{i}-3 \hat{j}+3 \hat{k})=2$
✓
$\bar{r} \cdot(\hat{i}+\hat{j}+\widehat{k})=2$

Answer

Correct option: D.

$\bar{r} \cdot(\hat{i}+\hat{j}+\widehat{k})=2$

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MCQ 811 Mark

The combined equation of the pair of lines through origin such that one is parallel to $3x + 2y = 3$ and the other is perpendicular to 6x + $3y + 17 = 0$ is ...............

A
$3x^2 - 4xy + 4y^2 = 0$
B
$3x^2 - 8xy + 4y^2 = 0$
✓
$3x^2 - 4xy - 4y^2 = 0$
D
$3x^2 + 4xy + 4y^2 = 0$

Answer

Correct option: C.

$3x^2 - 4xy - 4y^2 = 0$

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MCQ 821 Mark

If $(a + 3b)(3a + b) = 4h^2,$ then the angle between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is $..........$

A
$45^\circ$
✓
$60^\circ$
C
$30^\circ$
D
$\frac{\tan ^{-1} 1}{2}$

Answer

Correct option: B.

$60^\circ$

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MCQ 831 Mark

If $2tan^{-1} (\cos x) = \tan^{-1} (cosec^2 x),$ then $x = ...............$

A
$\frac{\pi}{2}$
B
$\frac{\pi}{6}$
C
$\pi $
✓
$\frac{\pi}{3}$

Answer

Correct option: D.

$\frac{\pi}{3}$

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MCQ 841 Mark

If polar co-ordinates of a point are $\left(\frac{1}{2}, \frac{\pi}{2}\right)$, then its cartesian co-ordinates are ______.

A
$\left(\frac{1}{2}, 2\right)$
✓
$\left(0, \frac{1}{2}\right)$
C
$\left(\frac{1}{2}, 4\right)$
D
$\left(4, \frac{1}{2}\right)$

Answer

Correct option: B.

$\left(0, \frac{1}{2}\right)$

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MCQ 851 Mark

The equation $3\sin^2x + 10$ \cos $x – 6 = 0$ is satisfied, if ............

A
$x =2 n \pi \pm \cos ^{-1}\left(\frac{1}{6}\right)$
✓
$2 n \pi \pm \cos ^{-1}\left(\frac{1}{3}\right)$
C
$x = n \pi \pm \cos ^{-1}\left(\frac{1}{3}\right)$
D
$x = n \pi \pm \cos ^{-1}\left(\frac{1}{6}\right)$

Answer

Correct option: B.

$2 n \pi \pm \cos ^{-1}\left(\frac{1}{3}\right)$

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MCQ 861 Mark

The matrix $\left[\begin{array}{ccc}\lambda & 1 & 0 \\ 0 & 3 & 5 \\ 0 & -3 & \lambda\end{array}\right]$ is invertible ______.

A
for all real values of λ
B
only for λ ≠ 0
✓
when λ ≠ 0 and λ ≠ –5
D
only when λ ≠ –5

Answer

Correct option: C.

when λ ≠ 0 and λ ≠ –5

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MCQ 871 Mark

If $\left[\begin{array}{ccc}1 & 0 & -1 \\ 0 & 2 & 1 \\ 1 & -2 & 0\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then the values of $x, y, z$ respectively are $......$

✓
$3, 0, 2$
B
$2, 0, 3$
C
$3, 0, –2$
D
$–2, 0, 3$

Answer

Correct option: A.

$3, 0, 2$

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MCQ 881 Mark

The logical statement [∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p) is equivalent to: ______

✓
p
B
∼p
C
∼r
D
∼q

Answer

Correct option: A.

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MCQ 891 Mark

The negation of the statement "If you don't work bard you will not become successful." is ______.

✓
You don't work hard and you will become successful.
B
You don't work hard or you will become successful.
C
You work hard and you will become successful.
D
You work hard and you will not become successful.

Answer

Correct option: A.

You don't work hard and you will become successful.

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MCQ 901 Mark

The only statement among the following i.e., a tautology is ______.

A
A ∨ (A ∧ B)
B
A ∧ (A ∨ B)
✓
[A ∧ (A → B)] → B
D
B → [A ∧ (A → B)]

Answer

Correct option: C.

[A ∧ (A → B)] → B

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MCQ 911 Mark

If f(x) = $\frac{\sin \left(x^2-x\right)}{x}$, x ≠ 0, is continuous at x = 0, then f(0) is ______.

A
2
B
0
✓
-1
D
1

Answer

Correct option: C.

-1

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MCQ 921 Mark

$\lim _{x \rightarrow \infty} \frac{(3 x+3)^{40}(9 x-3)^5}{(3 x+1)^{45}}$ = ______.

A
9
B
27
✓
243
D
81

Answer

Correct option: C.

243

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MCQ 931 Mark

Let $f : R \rightarrow R $ be defined by $f(x) =\left\{\begin{array}{l}3 x ; \quad x>2 \\ 2 x^2 ; \quad 1 \leq x \leq 2 \\ 4 x ; \quad x<1\end{array}\right.$ Then $ f(-2) + f(1) + f(3)$ is $.......$

A
$5$
✓
$3$
C
$10$
D
$19$

Answer

Correct option: B.

$3$

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MCQ 941 Mark

The number of ways in which 51 books can be distributed among three students, each receiving 17 books, is ______

A
$\frac{51 !}{(17 !)^2 \times 3}$
✓
$\frac{51 !}{(17 !)^3}$
C
$\frac{51 !}{(17 !)^3 \times 3}$
D
51!

Answer

Correct option: B.

$\frac{51 !}{(17 !)^3}$

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MCQ 951 Mark

The argument of the complex number $\frac{4+9 i}{13+5 i}$ is ______.

✓
$\frac{\pi}{4}$
B
$\frac{\pi}{6}$
C
$\frac{\pi}{5}$
D
$\frac{\pi}{3}$

Answer

Correct option: A.

$\frac{\pi}{4}$

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MCQ 961 Mark

Let A and B be two events such that P(A) $\neq$ 1 and P(B) $\neq$ 0, then $P \left(\frac{\overline{ B }}{\overline{\bar{A}}}\right)$ = ______.

A
$1- P \left(\frac{\overline{ B }}{ A }\right)$
✓
$\frac{1- P ( A \cup B )}{ P (\overline{ A })}$
C
$1- P \left(\frac{ B }{ A }\right)$
D
$\frac{ P (\overline{ B })}{ p (\overline{ A })}$

Answer

Correct option: B.

$\frac{1- P ( A \cup B )}{ P (\overline{ A })}$

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MCQ 971 Mark

For certain data, the following information is available. Obtain the combined standard deviation.

	X	Y
Mean	13	17
S.D.	3	2
Size	20	30

A
15.4
✓
3.14
C
9.84
D
1.54

Answer

Correct option: B.

3.14

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MCQ 981 Mark

The equation of circle whose diameter lies on $3x + 5y = -7$ and $2x - y = 4$ which passes through$\left(-5, \frac{1}{2}\right)$ is

✓
$x 2+y 2-2 x+4 y=\frac{149}{4}$
B
$x^2+y^2+2 x-4 y=\frac{149}{4}$
C
$x^2 + y^2 + 2x - 4y = 149$
D
$x^2 + y^2 - 2x + 4y = 149$

Answer

Correct option: A.

$x 2+y 2-2 x+4 y=\frac{149}{4}$

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MCQ 991 Mark

If one of the lines given by $kx^2 + 2xy – 3y^2 = 0$ is perpendicular to the line $3x + 5y+ 1 = 0,$ then the value of k is .......

A
$3$
✓
$5$
C
$-\frac{3}{5}$
D
$-\frac{7}{2}$

Answer

Correct option: B.

$5$

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MCQ 1001 Mark

$\sin^2(5^\circ ) + \sin^2(10^\circ ) + \sin^2(15^\circ ) + ... + \sin^2(85^\circ ) + \sin^2(90^\circ ) =...........$

A
$\frac{9}{2}$
B
$\frac{39}{2}$
✓
$\frac{19}{2}$
D
$\frac{49}{2}$

Answer

Correct option: C.

$\frac{19}{2}$

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MCQ 1011 Mark

Which among the following amino acids has the lowest molecular mass?

A
Proline
B
Aspartic acid
✓
Glycine
D
Serine

Answer

Correct option: C.

Glycine

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MCQ 1021 Mark

Which of the following monosaccharide is a ketohexose?

A
Ribose
B
Ribulose
✓
Fructose
D
Glucose

Answer

Correct option: C.

Fructose

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MCQ 1031 Mark

Which of the following compounds is obtained when quaternary ammonium hydroxide is strongly heated?

✓
Alkene
B
Alkyne
C
Alkane
D
Amide

Answer

Correct option: A.

Alkene

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MCQ 1041 Mark

What is the molar mass of the amine formed when acetamide undergoes Hofmann bromamide degradation?

A
35 g/mol
B
59 g/mol
✓
31 g/mol
D
45 g/mol

Answer

Correct option: C.

31 g/mol

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MCQ 1051 Mark

Which of the following will give positive iodoform test?

A
B
✓
D
All of these

Answer

Correct option: C.

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MCQ 1061 Mark

The IUPAC nomenclature for ethyl isobutyl ketone is ____________.

A
4-ethylhexan-3-one
B
2, 2-dimethylpentan-3-one
C
1, 2-dimethylpentan-4-one
✓
5-methylhexan-3-one

Answer

Correct option: D.

5-methylhexan-3-one

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MCQ 1071 Mark

Choose the $\text{INCORRECT}$ statement about
$C _2 H _5- O - C _2 H _5$
from the following.

A
Earlier it was used as a general anaesthetic in surgical operations.
B
It is used as a solvent for Grignard reagents.
✓
It is more toxic than $CHCI_3.$
D
It is more soluble in fatty acids than in water.

Answer

Correct option: C.

It is more toxic than $CHCI_3.$

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MCQ 1081 Mark

Methyl alcohol reacts with acetyl chloride to give ____________.

A
ethyl acetate
B
acetaldehyde
✓
methyl acetate
D
chloromethane

Answer

Correct option: C.

methyl acetate

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MCQ 1091 Mark

Identify 'B' in the following reaction.
$
\text { 2-Bromobutane } \xrightarrow[\Delta]{ KOH \text { alc } \cdot} A \xrightarrow{ HI } B
$

✓
2-Iodobutane
B
Butan-2-ol
C
But-1-ene
D
1-Iodobutane

Answer

Correct option: A.

2-Iodobutane

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MCQ 1101 Mark

An alkyl iodide on refluxing with aqueous KOH solution gave isopropyl alcohol. The structure of alkyl iodide could be:

✓
B
C
$CH _3- CH _2- CH _2- I$
D
$CH _3- CH _2- CH _2- CH _2- I$

Answer

Correct option: A.

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MCQ 1111 Mark

Which one of the following complexes can exhibit geometrical isomerism?

✓
$[Pt(NH_3)_2Cl_2] ($ square planar $)$
B
$[Zn(NH_3)_2Cl_2] ($ tetrahedral $)$
C
$[Cu(NH_3)_4]^{2+} ($square planar $)$
D
$[Co(NH_3)_5Cl]^{2+} ($ octahedral $)$

Answer

Correct option: A.

$[Pt(NH_3)_2Cl_2] ($ square planar $)$

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MCQ 1121 Mark

$\text{EAN}$ of Fe in $[Fe(CN)_6]^{4−}$ is equal to..........

A
$35$
B
$34$
✓
$36$
D
$37$

Answer

Correct option: C.

$36$

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MCQ 1131 Mark

Which element from following forms colourless compounds in +2 oxidation state?

A
Cu (Z = 29)
✓
Zn (Z = 30)
C
Co (Z = 27)
D
Mn (Z = 25)

Answer

Correct option: B.

Zn (Z = 30)

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MCQ 1141 Mark

Which of the following is a mineral of zinc?

A
Cuprite
B
Limonite
✓
Calamine
D
Siderite

Answer

Correct option: C.

Calamine

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MCQ 1151 Mark

The spin only magnetic moment of $Mn^{3+} (Z = 25)$ in aqueous solution is ...........

A
$\sqrt{6} BM$
B
$\sqrt{3} BM$
C
$3 \sqrt{6} BM$
✓
$2 \sqrt{6} BM$

Answer

Correct option: D.

$2 \sqrt{6} BM$

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MCQ 1161 Mark

Which transition metal is used as a catalyst in the conversion of inedible oils into solid fat?

A
Mo
✓
Ni
C
Fe
D
Zn

Answer

Correct option: B.

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MCQ 1171 Mark

Which among the following is NOT a mineral of chlorine?

A
Carnallite
✓
Cryolite
C
Sylvine
D
Horn silver

Answer

Correct option: B.

Cryolite

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MCQ 1181 Mark

In the following reaction, chlorine acts as a/an
$2 FeSO _4+ H _2 SO _4+ Cl _2 \longrightarrow Fe _2\left( SO _4\right)_3+2 HCl$

A
dehydrating agent
B
bleaching agent
✓
oxidizing agent
D
reducing agent

Answer

Correct option: C.

oxidizing agent

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MCQ 1191 Mark

What is the colour of gaseous ozone?

A
Blue black
✓
Blue
C
Violet black
D
Yellowish white

Answer

Correct option: B.

Blue

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MCQ 1201 Mark

The formula of chlorous acid is $...........$

A
$HOCl$
B
$HCIO_3$
✓
$HClO_2$
D
$HCIO_4$

Answer

Correct option: C.

$HClO_2$

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MCQ 1211 Mark

A certain zero order reaction has rate constant $0.025\ M \ s^{-1}$. What will be the concentration of reactant $'A\ '$ after $15$ seconds, if initial concentration is $0.50 M$?

✓
$0.125 M$
B
$0.060 M$
C
$0.375 M$
D
$0.50 M$

Answer

Correct option: A.

$0.125 M$

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MCQ 1221 Mark

A first order reaction takes 40 minutes for 30% decomposition. What is the half-life of reaction?

A
67.8 min
B
82.2 min
C
59.5 min
✓
77.8 min

Answer

Correct option: D.

77.8 min

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MCQ 1231 Mark

In a first order reaction, the concentration of the reactant, decreases from $0.8 \ mol \ dm^{−3}$ to $0.4 \ mol \ dm^{−3}$ in $15$ minutes. The time taken for the concentration to change from $0.1 \ mol \ dm^{−3}$ to $0.025 \ mol \ dm^{−3}$ is $........$

A
$7.5$ minutes
B
$60$ minutes
✓
$30$ minutes
D
$15$ minutes

Answer

Correct option: C.

$30$ minutes

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MCQ 1241 Mark

A certain quantity of electricity is passed through aqueous $Al_2(SO_4)_3$ and $CuSO_4$ solutions connected in series. $0.09 g$ of $Al$ is deposited on cathode during electrolysis. The amount of copper deposited on cathode in grams is : $($Atomic mass of $Al = 27 u, Cu = 63.5 u)$

A
$31.8$
✓
$0.318$
C
$3.18$
D
$0.636$

Answer

Correct option: B.

$0.318$

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MCQ 1251 Mark

What is the cell constant of $\frac{ N }{10} \text{KCl}$ solution at $25^\circ C,$ if conductivity and resistance of a solution is $0.0112\ \Omega ^{−1} \ cm^{−1}$ and $55.0\ \Omega$ respectively?

A
$0.2 \ cm^{−1}$
B
$2.0 \ cm^{−1}$
C
$0.491 \ cm^{−1}$
✓
$0.616 \ cm^{−1}$

Answer

Correct option: D.

$0.616 \ cm^{−1}$

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MCQ 1261 Mark

Molar conductance of $BaCl_2, H2SO_4 $and $HCl$ at infinite dilution are $X_1, X_2$ and $X_3$ respectively. Molar conductance of $BaSO_4 $at infinite dilution is $...........$

A
$X_1 + X_2 − X_3$
✓
$X_1 + X_2 − 2X_3$
C
$\frac{\left( X _1+ X _2-2 X _3\right)}{2}$
D
$\frac{\left( X _1+ X _2- X _3\right)}{2}$

Answer

Correct option: B.

$X_1 + X_2 − 2X_3$

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MCQ 1271 Mark

Given that, $C _{( s )}+ O _{2( g )} \longrightarrow CO _{2( g )}$ $\Delta H ^{\circ}=- XkJ
$
$
2 CO _{( g )}+ O _{2( g )} \longrightarrow 2 CO _{2( g )}$
$\Delta H^{\circ}=-Y kJ$, then standard enthalpy of formation of carbon monoxide is ________.

A
2X - Y kJ
✓
$\frac{Y-2 X}{2} k J$
C
$\frac{2 X - Y }{2} kJ$
D
Y - 2X kJ

Answer

Correct option: B.

$\frac{Y-2 X}{2} k J$

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MCQ 1281 Mark

The standard heats of formation for $CCl _{4( g )}, H _2 O _{( g )}, CO _{2( g )}$, and $HCl _{( g )}$ are $-25.5,-57.8,-94.1$ and $-22.1 kcal mol ^{-1}$, respectively.
$\Delta H$ for the reaction
$
CCl _{4( g )}+2 H _2 O _{( g )} \longrightarrow CO _{2( g )}+4 HCl _{( g )}$ at $298 K$

A
−265.8 kcal
✓
−41.4 kcal
C
−199.5 kcal
D
−32.9 kcal

Answer

Correct option: B.

−41.4 kcal

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MCQ 1291 Mark

Given the bond energies $N \equiv N , H - H$ and $N - H$ bonds are 945 , 436 and $391 kJ / mol$ respectively. The enthalpy of the reaction;
$
N _{2( g )}+3 H _{2( g )} \longrightarrow 2 NH _{3( g )}
$

✓
−93 kJ
B
−102 kJ
C
+93 kJ
D
+102 kJ

Answer

Correct option: A.

−93 kJ

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MCQ 1301 Mark

A sample of gas absorbs 4000 kJ of heat and surrounding does 2000 J of work on sample, what is the value of ΔU?

A
2000 kJ
✓
4002 kJ
C
4000 kJ
D
6000 kJ

Answer

Correct option: B.

4002 kJ

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MCQ 1311 Mark

$3$ moles of an ideal gas is compressed from $50 dm^3 $ to $30 dm^3 $ against a constant external pressure of $3.039 \times 10^5 N m^{−2}. $The work done in calories is $.........(1 J = 0.239 cal)$

A
$+72.63 cal$
✓
$+1452.6 cal$
C
$+2905.2 cal$
D
$+30.39 cal$

Answer

Correct option: B.

$+1452.6 cal$

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MCQ 1321 Mark

Which is true for heat and temperature?

A
Both are extensive properties
✓
Extensive and Intensive properties respectively
C
Both are intensive properties
D
Intensive and extensive properties respectively

Answer

Correct option: B.

Extensive and Intensive properties respectively

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MCQ 1331 Mark

Van't Hoff factor for $K_3[Fe(CN)_6]$ is $3.333$. What is it's percentage dissociation in water?

A
$58 \%$
✓
$77.7 \%$
C
$83 \%$
D
$70 \%$

Answer

Correct option: B.

$77.7 \%$

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MCQ 1341 Mark

The osmotic pressure of blood is 7.65 atm at 310 K. An aqueous solution of glucose isotonic with blood contains ____________ g of glucose in 1 L of solution.

A
53.4
B
3.54
✓
54.1
D
4.53

Answer

Correct option: C.

54.1

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MCQ 1351 Mark

Given $K_b$ and $K_f$ of water are $0.52$ and $1.86 K \ kg \ mol^{-1}$ respectively. An aqueous solution freezes at $- 0.186^\circ C,$ what is the boiling point of solution?

A
$0.52^\circ C$
B
$0.052^\circ C$
✓
$100.052^\circ C$
D
$100.52^\circ C$

Answer

Correct option: C.

$100.052^\circ C$

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MCQ 1361 Mark

Calculate molal elevation constant of water if $0.154$ molal solution of a substance boils at $373.23 K.$
$($Given: Boiling point of water $= 373.15 K)$

A
$2.53 K \ kg\ mol^{−1}$
✓
$0.52 K \ kg\ mol^{−1}$
C
$0.66 K \ kg \ mol^{−1}$
D
$1.86 K \ kg\ mol^{−1}$

Answer

Correct option: B.

$0.52 K \ kg\ mol^{−1}$

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MCQ 1371 Mark

If $1$ mole of$........$is added to $1 \ dm^3$ of water, the boiling point of water will decrease.

A
glucose
✓
methyl alcohol
C
sucrose
D
$NaCl$

Answer

Correct option: B.

methyl alcohol

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MCQ 1381 Mark

Which of the following ion is diamagnetic?

A
$Co^{2+}$
B
$Ni^{2+}$
✓
$Sc^{3+}$
D
$Mn^{2+}$

Answer

Correct option: C.

$Sc^{3+}$

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MCQ 1391 Mark

Which of the following is an example of substitutional impurity defect?

✓
Brass
B
Zinc sulphide
C
Sodium chloride
D
Stainless steel

Answer

Correct option: A.

Brass

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MCQ 1401 Mark

Zinc forms hcp structure. What is the number of octahedral voids formed in $0.2 \ mol$ of it?

A
$2.4 \times 10^{23}$
✓
$1.2 \times 10^{23}$
C
$1.2 \times 10^{24}$
D
$2.4 \times 10^{24}$

Answer

Correct option: B.

$1.2 \times 10^{23}$

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MCQ 1411 Mark

When HCl is treated with propene in presence of sodium peroxide, the major product obtained is ____________.

A
1-Chloropropane
B
2, 2-dichloropropane
✓
2-Chloropropane
D
1, 2-dichloropropane

Answer

Correct option: C.

2-Chloropropane

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MCQ 1421 Mark

Which of the following yields only one type of monosubstituted chloroalkane upon chlorination?

A
Isobutane
B
n-Butane
C
Propane
✓
Cyclopentane

Answer

Correct option: D.

Cyclopentane

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MCQ 1431 Mark

Select the CORRECT statement regarding adsorption of gases on solids.

A
The amount of gas adsorbed is directly proportional to temperature.
✓
At very high pressures, the extent of adsorption becomes independent of the pressure.
C
Gases having low critical temperature liquefy easily and can readily be adsorbed.
D
The extent of adsorption decreases with increase in surface area of adsorbent.

Answer

Correct option: B.

At very high pressures, the extent of adsorption becomes independent of the pressure.

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MCQ 1441 Mark

At a constant pressure, the density of a certain amount of an ideal gas is ____________.

A
directly proportional to the square of the temperature
✓
inversely proportional to the temperature
C
directly proportional to the temperature
D
independent of a temperature

Answer

Correct option: B.

inversely proportional to the temperature

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MCQ 1451 Mark

In ____________, hydrogen bonding is stronger than corresponding alcohols.

A
Ethers
✓
Carboxylic acids
C
Aldehydes
D
Phenols

Answer

Correct option: B.

Carboxylic acids

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MCQ 1461 Mark

Calculate the strength of $10$ volume solution of hydrogen peroxide?

A
$45.51 \ g L^{-1}$
✓
$30.35 \ g L^{-1}$
C
$15.175 \ g L^{-1}$
D
$60.71 \ g L^{-1}$

Answer

Correct option: B.

$30.35 \ g L^{-1}$

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MCQ 1471 Mark

Carbon is present in highest oxidation number in $......$

✓
$CO _3^{2-}$
B
$CaC_2$
C
$C _2 O _4^{2-}$
D
$CO$

Answer

Correct option: A.

$CO _3^{2-}$

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MCQ 1481 Mark

Which of the following is $ \text{INCORRECTLY}$ matched?

A
$H_2S -$ polar molecule with polar bonds
B
$CO_2 -$ non$-$polar molecule with polar bonds
C
$CHCl_3 -$ polar molecule with polar bonds
✓
$CCl_4 -$ non$-$polar molecule with non$-$polar bonds

Answer

Correct option: D.

$CCl_4 -$ non$-$polar molecule with non$-$polar bonds

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MCQ 1491 Mark

In hydrogen atom, the de Broglie wavelength of an electron in the first Bohr's orbit is $.........[$Given that Bohr radius, $a_0 = 52.9 \ pm]$

A
$211.6 \ \pi pm$
B
$52.9 \ \pi pm$
✓
$105.8 \ \pi pm$
D
$26.45 \ \pi pm$

Answer

Correct option: C.

$105.8 \ \pi pm$

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MCQ 1501 Mark

Mole is the SI unit of ____________.

A
pressure
✓
amount of substance
C
volume
D
density

Answer

Correct option: B.

amount of substance

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