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MCQ

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150 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Logic circuit shows the inputs A, Band C. The output Y is '0' (zero) when ______.
Image
  • A
    A = 1, B = 1, C=O
  • A=O, B = 1, C= 1
  • C
    A= 1, B = 0, C = 1
  • D
    A = 0, B = 1, C = 1
Answer
Correct option: B.
A=O, B = 1, C= 1
B
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MCQ 21 Mark
In a transistor, a change of 8.0 mA in the emitter current produces a change of 7.8 mA in the collector current. Then change in the base current is ____________.
  • A
    100 µA
  • B
    50 µA
  • 200 µA
  • D
    150 µA
Answer
Correct option: C.
200 µA
C
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MCQ 31 Mark
Electron in Hydrogen atom first jumps from third excited state to second excited state and then from second excited state to first excited state. The ratio of the wavelengths $\lambda _1 : \lambda _2$ emitted in the two cases respectively is $............$
  • $\frac{27}{5}$
  • B
    $\frac{20}{7}$
  • C
    $\frac{27}{20}$
  • D
    $\frac{7}{5}$
Answer
Correct option: A.
$\frac{27}{5}$
$\frac{27}{5}$
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MCQ 41 Mark
If the mass of the electron is reduced to half, the Rydberg constant ______.
  • A
    remains unchanged.
  • becomes half.
  • C
    becomes double.
  • D
    becomes one fourth.
Answer
Correct option: B.
becomes half.
B
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MCQ 51 Mark
The photon of frequency vis incident on a metal surface whose threshold frequency is $v_0.$ The kinetic energy of the emitted photoelectrons will be$.......$
  • A
    $hv$
  • $h \left( v - v _0\right)$
  • C
    $hv_0$
  • D
    $h \left( v + v _0\right)$
Answer
Correct option: B.
$h \left( v - v _0\right)$
$h \left( v - v _0\right)$
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MCQ 61 Mark
When a light of wavelength 4000 Å falls on a photoelectric emitter, photoelectrons are liberated. For another emitter, light of wavelength 6000 Å is sufficient for photo emission. The work functions of the two emitters are in the ratio of ____________.
  • 3 : 2
  • B
    2 : 3
  • C
    5 : 3
  • D
    3 : 5
Answer
Correct option: A.
3 : 2
A
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MCQ 71 Mark
In a circuit L, C and R are connected in series with an alternating voltage source of f. When current in the circuit leads the voltage by 45°, the value of C ____________.
  • $\frac{1}{2 \pi f(2 \pi f L+R)}$
  • B
    $\frac{1}{2 \pi f ( R + L )}$
  • C
    $\frac{1}{2 \pi f \left( R +\frac{1}{ L }\right)}$
  • D
    $\frac{1}{2 \pi f (2 \pi fR + L )}$
Answer
Correct option: A.
$\frac{1}{2 \pi f(2 \pi f L+R)}$
A
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MCQ 81 Mark
A sound wave has a frequency of 500 Hz and a velocity of 350 m/s. The distance between the two particles having a phase difference of 60° is near ______
  • A
    7 cm
  • B
    70 cm
  • 12 cm
  • D
    120 cm
Answer
Correct option: C.
12 cm
C
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MCQ 91 Mark
The area of a coil is $'A\ '.$ The coil is placed in a magnetic field which changes from $'B_0\ '$ to $4B_0\ '$ in time $'t\ '$. The magnitude of induced e.m.f. in the coil will be $....$
  • A
    $\frac{3 B _0}{ At }$
  • B
    $\frac{4 AB _0}{t}$
  • C
    $\frac{4 B _0}{ At }$
  • $\frac{3 AB _0}{t}$
Answer
Correct option: D.
$\frac{3 AB _0}{t}$
$\frac{3 AB _0}{t}$
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MCQ 101 Mark
Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current which increases with time. ln response, the loop-B ____________.
  • A
    is attracted by the loop-A
  • B
    rotates about its CM, with CM fixed. (CM is the centre of mass)
  • C
    remains stationary
  • is repelled by the loop-A
Answer
Correct option: D.
is repelled by the loop-A
D
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MCQ 111 Mark
The magnetic moment produced in a sample of $2$ gram is $8 \times 10^{-7} A/m^2.$ lf its density is $4g/cm^3,$ then the magnetization of the sample is $.......$
  • A
    $1.2$
  • B
    $1.4$
  • $1.6$
  • D
    $1.8$
Answer
Correct option: C.
$1.6$
$1.6$
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MCQ 121 Mark
The electron in hydrogen atom is moving in an orbit of radius $0.53 \mathring A .$ It takes $1.571 \times 10^{-16} s$ to complete one revolution. The velocity of electron will be $\pi = 3.142.$
  • A
    $5.3 \times 10^6 \frac{ m }{ s }$
  • B
    $4 \times 10^6 \frac{ m }{ s }$
  • $2.12 \times 10^6 \frac{ m }{ s }$
  • D
    $3 \times 10^8 \frac{ m }{ s }$
Answer
Correct option: C.
$2.12 \times 10^6 \frac{ m }{ s }$
$2.12 \times 10^6 \frac{ m }{ s }$
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MCQ 131 Mark
A current loop in a magnetic field ____________.
  • A
    can be in equilibrium in one orientation
  • B
    can be in equilibrium in two orientations, both the equilibrium states are unstable
  • C
    experiences a torque whether the field is uniform or non-uniform in all orientations
  • can be in equilibrium in two orientations, one stable while the other is unstable
Answer
Correct option: D.
can be in equilibrium in two orientations, one stable while the other is unstable
D
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MCQ 141 Mark
A particle of charge $-16 \times 10^{-18} \ C$ moving with velocity $10 m/s$ along the $X-$axis enters a region where a magnetic field of induction $B$ is along $Y-$axis and electric field of magnitude $10^4 V/m$ is along the negative $Z-$axis. If the charged particle continues moving along the $X-$axis, the magnitude of $B$ is $............$.
Image
  • $10^3 \ Wb/m^2$
  • B
    $10^5 \ Wb/m^2$
  • C
    $10^6 \ Wb/m^2$
  • D
    $10^7 \ Wb/m^2$
Answer
Correct option: A.
$10^3 \ Wb/m^2$
$10^3 \ Wb/m^2$
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MCQ 151 Mark
In the measurement of a resistance by the Wheatstone bridge, the known and the unknown resistance are interchanged to eliminate ____________.
  • A
    connection error
  • B
    minor error
  • C
    observational error
  • error due to thermoelectric effect
Answer
Correct option: D.
error due to thermoelectric effect
D
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MCQ 161 Mark
In a metre bridge experiment. the ratio of the left-gap resistance to right gap resistance is 2: 3. The balance point from the left is ______.
  • A
    60 cm
  • 40 cm
  • C
    50 cm
  • D
    20 cm
Answer
Correct option: B.
40 cm
B
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MCQ 171 Mark
Four capacitors of equal capacity have an equivalent capacitance $C_1$ when connected in series and an equivalent capacitance $C_2$ when connected in parallel. The ratio $\frac{c_2}{c_1}$, is $.........$
  • A
    $4$
  • B
    $8$
  • $16$
  • D
    $12$
Answer
Correct option: C.
$16$
$16$
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MCQ 181 Mark
The electrostatic potential inside a charged sphere is given as $V = Ar^2 + B,$ where $r$ is the distance from the centre of the sphere; $A$ and $B$ are constants. Then the charge density in the sphere is$.......$
  • A
    $20 A \varepsilon_0$
  • $-6 A \varepsilon_0$
  • C
    $16 A \varepsilon_0$
  • D
    $-15 A \varepsilon_0$
Answer
Correct option: B.
$-6 A \varepsilon_0$
$-6 A \varepsilon_0$
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MCQ 191 Mark
A metal sphere of radius $1 m$ is charged with $10^{-2} C$ in air. Its bulk modulus is $10^{11}/4\pi ^2.$ The volume strain in the sphere is$............(ε_0 =$ permittivity of free space$)$
  • A
    $\frac{10^{-14}}{8 \varepsilon_0}$
  • $\frac{10^{-15}}{8 \varepsilon_0}$
  • C
    $\frac{10^{-1}}{6 \varepsilon_0}$
  • D
    $\frac{10^{-12}}{4 \varepsilon_0}$
Answer
Correct option: B.
$\frac{10^{-15}}{8 \varepsilon_0}$
$\frac{10^{-15}}{8 \varepsilon_0}$
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MCQ 201 Mark
In Young's experiment for the interference of light, the separation between the silts is d and the distance of the screen from the slits is D. If D is increased by 0.6% and d is decreased by 0.2%, then for the light of a given wavelength, which one of the following is true?

"The fringe width  ____________."

  • A
    increases by 0.2%
  • increases by 0.8%
  • C
    decreases by 0.8%
  • D
    decreases by 0.2%
Answer
Correct option: B.
increases by 0.8%
B
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MCQ 211 Mark
A thin transparent sheet is placed in front of a slit in Young's double slit experiment. The fringe width will ____________.
  • A
    increase
  • remain same
  • C
    decrease
  • D
    becomes non-uniform
Answer
Correct option: B.
remain same
B
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MCQ 221 Mark
A parallel beam of fast-moving electrons is incident perpendicular on a narrow slit. The distance between slit and screen is large. If the speed of the incident electrons is increased then which one of the following statements is correct?
  • A
    The diffraction pattern is not observed on the screen in the case of electrons.
  • B
    The angular width of the central maximum will remain the same.
  • C
    The angular width of the central maximum of the diffraction pattern will increase.
  • The angular width of the central maximum will decrease.
Answer
Correct option: D.
The angular width of the central maximum will decrease.
D
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MCQ 231 Mark
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air colunm in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
  • 6
  • B
    12
  • C
    8
  • D
    4
Answer
Correct option: A.
6
A
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MCQ 241 Mark
For the stationary wave,

y = 8sin(6.25πx) cos(96πt) metre, the distance between a node and the next antinode is ____________.

  • A
    6.25 m
  • 4 cm
  • C
    17. 5 cm
  • D
    1.5 m
Answer
Correct option: B.
4 cm
B
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MCQ 251 Mark
A simple harmonic progressive wave is given by $Y = Y_0 \sin 2\pi \left(n t-\frac{x}{\lambda}\right)$. If the wave velocity is $\left(\frac{1}{8}\right)^{t h}$ of the maximum particle velocity, then the wavelength is$.........$
  • A
    $\pi Y_0/16$
  • B
    $\pi Y_0/2$
  • C
    $\pi Y_0/8$
  • $\pi Y_0/4$
Answer
Correct option: D.
$\pi Y_0/4$
$\pi Y_0/4$
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MCQ 261 Mark
The displacement of a particle performing S.H.M. is given by x = 10 sin $(\omega t +\alpha)$ metre. If the displacement of the particle is 5 m, then the phase of S.H.M. is ____________.
  • $\frac{\pi}{6}$ radian
  • B
    $\frac{\pi}{4}$ radian
  • C
    $\frac{\pi}{3}$ radian
  • D
    $\frac{\pi}{2}$ radian
Answer
Correct option: A.
$\frac{\pi}{6}$ radian
A
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MCQ 271 Mark
A particle executing S.H.M. has amplitude 0.01 m and frequency 60 Hz. The maximum acceleration of the particle is ____________.
  • A
    $88 \pi^2 m / s ^2$
  • $144 \pi^2 m / s ^2$
  • C
    $60 \pi^2 m / s ^2$
  • D
    $140 \pi^2 m / s ^2$
Answer
Correct option: B.
$144 \pi^2 m / s ^2$
B
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MCQ 281 Mark
A vertical spring oscillates with period of $6 s$ with mass $'m \ ' $ suspended from it. When the mass is at rest, the spring is stretched through a distance of$.......($Take $g = \pi ^2)$
  • A
    $5 \ cm$
  • $9 \ cm$
  • C
    $3 \ cm$
  • D
    $7 \ cm$
Answer
Correct option: B.
$9 \ cm$
$9 \ cm$
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MCQ 291 Mark
Ideal gas for which 'ϒ' = 1.5 is suddenly compressed to $\frac{1}{4}$th of its initial volume. The ratio of 4 the final pressure to the initial pressure is ______.
$\left(\Upsilon=\frac{C_{ p }}{ C _{ v }}\right)$
  • A
    1: 18
  • 8: 1
  • C
    1: 16
  • D
    4: 1
Answer
Correct option: B.
8: 1
B
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MCQ 301 Mark
Among the amount of heat absorbed and the amount of work done by a system, ______
  • A
    both depend on only their initial and final states, but not on the path.
  • B
    the first depends on the path but the latter depends only on the initial and final states.
  • both depend on the path.
  • D
    the first only depends on initial and final states but the second, on the path.
Answer
Correct option: C.
both depend on the path.
C
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MCQ 311 Mark
When $1 g$ of water at $0^\circ \ C$ and $1 \times 10^5 N/m^2$ pressure is converted into ice of volume $1.082 \ cm^3,$ the external work done will be $.........$
  • A
    $- 0.0182 J$
  • B
    $0.0182 J$
  • $0.0082 J$
  • D
    $- 0.0082 J$
Answer
Correct option: C.
$0.0082 J$
$0.0082 J$
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MCQ 321 Mark
Two spheres $'S_1\ '$ and $'S_2\ '$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity is in the ratio $1: 4. $ Theo the ratio of $T_1$ to $T_2$ is $.......$
  • A
    $1: \sqrt{2}$
  • $\sqrt{2}: 1$
  • C
    $1: 2$
  • D
    $2: 1$
Answer
Correct option: B.
$\sqrt{2}: 1$
$\sqrt{2}: 1$
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MCQ 331 Mark
Out of 20 J of radiant energy incident on a surface, the energy absorbed by the surface is 4 J and the energy reflected is 8 J. Then, coefficient of transmission of the body is ____________.
  • A
    0.7
  • B
    0. 1
  • C
    zero
  • 0.4
Answer
Correct option: D.
0.4
D
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MCQ 341 Mark
The temperature at which the molecules of nitrogen will have the same r.m.s. velocity as the molecules of oxygen at 327° C is ____________.
  • A
    350° C
  • B
    77° C
  • C
    457° C
  • 252° C
Answer
Correct option: D.
252° C
D
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MCQ 351 Mark
Two rain drops falling through air have radii in the ratio 1 : 2. They will have terminal velocity in the ratio ______.
  • A
    2 : 1
  • B
    1 : 2
  • C
    4 : 1
  • 1 : 4
Answer
Correct option: D.
1 : 4
D
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MCQ 361 Mark
In motors, more viscous oil is used in summer than in winter due to ____________.
  • A
    the decrease in surface tension of oil
  • B
    the rise in temperature in summer, the viscosity of oil increases
  • the rise in temperature in summer, the viscosity of oil decreases
  • D
    the increase in surface tension of oil
Answer
Correct option: C.
the rise in temperature in summer, the viscosity of oil decreases
C
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MCQ 371 Mark
A water barrel stands on a table of height 'h'. A small hole is made on the wall of barrel at its bottom. If the stream of water coming out of the hole strikes the ground at horizontal distance 'R' from the table, the depth 'd' of water in the barrel is ______.
  • A
    $\frac{R^2}{2 h}$
  • $\frac{R^2}{4 h}$
  • C
    $\frac{4 h}{R^2}$
  • D
    $\frac{h}{4 R^2}$
Answer
Correct option: B.
$\frac{R^2}{4 h}$
B
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MCQ 381 Mark
The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is $'I\ '.$ It is rotating with angular velocity $'ω\ '.$ Another identical ring is gently placed on it so that their centres coincide. If both the ring are rotating about the same axis, then loss in kinetic energy is$.......$
  • A
    $\frac{I \omega^2}{3}$
  • $\frac{I \omega^2}{4}$
  • C
    $Iω^2$​​​​​​​
  • D
    $\frac{I \omega^2}{2}$
Answer
Correct option: B.
$\frac{I \omega^2}{4}$
$\frac{I \omega^2}{4}$
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MCQ 391 Mark
The moment of inertia of a body initially at rest about a given axis is $1.2 \ kg m^2.$ On applying an acceleration of $25 \ rad/s^2,$ the time it will take to acquire a rotational kinetic energy of $1500 J$ is $.........$
  • A
    $10 s$
  • B
    $8 s$
  • $2 s$
  • D
    $4 s$
Answer
Correct option: C.
$2 s$
$2 s$
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MCQ 401 Mark
A car moves at a speed of $36 \ km \ hr^{-1}$ on a level road. The coefficient of friction between the tyres and the road is $0.8.$ The car negotiates a curve of radius $R.$ If $g = 10 \ ms^{-2} ,$ then the car will skid $($or slip$)$ while negotiating the curve, if the value of $R$ is $........$
  • $12 m$
  • B
    $16 m$
  • C
    $14 m$
  • D
    $6 m$
Answer
Correct option: A.
$12 m$
$12 m$
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MCQ 411 Mark
A donor impurity results in ______.
  • A
    holes as majority carriers and electrons as minority carriers
  • production of n-type semiconductor
  • C
    production of p-type semiconductor
  • D
    conduction band just above the filled valence band
Answer
Correct option: B.
production of n-type semiconductor
B
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MCQ 421 Mark
Infinite charges of magnitude q each are lying at $x = 1, 2, 4, 8 ...$ metre on $X-$axis. The value of the intensity of the electric field at point $x = 0$ due to these charges will be $.........$
  • $12 \times 10^9 q N/C$
  • B
    $4 \times 10^9 q N/C$
  • C
    $6 \times 10^9 q N/C$
  • D
    Zero
Answer
Correct option: A.
$12 \times 10^9 q N/C$
$12 \times 10^9 q N/C$
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MCQ 431 Mark
The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment$\overrightarrow{ p }$ is given by, (r >> separation of two charges forming the dipole, $\varepsilon_0$- permittivity of free space) ____________.
  • A
    $\overrightarrow{ E }=-\frac{\overrightarrow{ p }}{4 \pi \varepsilon_0 r ^2}$
  • B
    $\overrightarrow{ E }=\frac{\overrightarrow{ p }}{4 \pi \varepsilon_0 r ^3}$
  • $\overrightarrow{ E }=-\frac{\overrightarrow{ p }}{4 \pi \varepsilon_0 r ^3}$
  • D
    $\overrightarrow{ E }=\frac{2 \overrightarrow{ p }}{4 \pi \varepsilon_0 r ^3}$
Answer
Correct option: C.
$\overrightarrow{ E }=-\frac{\overrightarrow{ p }}{4 \pi \varepsilon_0 r ^3}$
C
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MCQ 441 Mark
The angle of minimum deviation produced by a thin glass prism in air is $'δ\ '.$ If that prism is immersed in water, the angle of minimum deviation will be $........( _a\mu _g =$ refractive index of glass $w.r.t,$ air $_a\mu _w =$ refractive index of water $w.r.t.$ air$)$
  • $\delta\left[\frac{{ }_a \mu_g-{ }_a \mu_w}{{ }_a \mu_w\left({ }_a \mu_g-1\right)}\right]$
  • B
    $\delta\left[\frac{\left({ }_a \mu_w-{ }_a \mu_g\right)}{{ }_a \mu_w \times{ }_a \mu_g}\right]$
  • C
    $\delta\left[\frac{{ }_a \mu_g-{ }_a \mu_w}{{ }_a \mu_w\left({ }_a \mu_g+1\right)}\right]$
  • D
    $\delta\left[\frac{{ }_a \mu_w-{ }_a \mu_g}{{ }_a \mu_w\left({ }_a \mu_g-1\right)}\right]$
Answer
Correct option: A.
$\delta\left[\frac{{ }_a \mu_g-{ }_a \mu_w}{{ }_a \mu_w\left({ }_a \mu_g-1\right)}\right]$
$\delta\left[\frac{{ }_a \mu_g-{ }_a \mu_w}{{ }_a \mu_w\left({ }_a \mu_g-1\right)}\right]$
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MCQ 451 Mark
For convex mirrors, whatever may be the position of the object, the image formed is always on the ______.
  • A
    same side, real, inverted, magnified
  • B
    opposite side, real, erect, magnified
  • opposite side, virtual, erect, diminished
  • D
    same side, virtual, erect, diminished
Answer
Correct option: C.
opposite side, virtual, erect, diminished
C
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MCQ 461 Mark
A train blowing the whistle moves with a constant velocity 'V' away from an observer standing on the platform. The ratio of the natural frequency of the whistle 'n' to the apparent frequency is 1.2 : 1. If the train is at rest and the observer moves away from it at the same velocity 'V', the ratio of 'n' to the apparent frequency is ______.
  • 1.25 : 1
  • B
    0.51 : 1
  • C
    2.05 : 1
  • D
    1.52 : 1
Answer
Correct option: A.
1.25 : 1
A
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MCQ 471 Mark
A bucket full of hot water cools from $85 ^\circ C$ to $80 ^\circ  C$ in time $T_1,$ from $80 ^\circ  C$ to $75 ^\circ  C$ in time $T_2$ and from $75 ^\circ C$ to $70 ^\circ  C$ in time $T_3,$ then$........$
  • $T_123$
  • B
    $T_1>T_2>T_3$​​​​​​​
  • C
    $T_1>T_23$
  • D
    $T_1=T_2=T_3$​​​​​​​
Answer
Correct option: A.
$T_123$
$T_123$
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MCQ 481 Mark
A satellite is to revolve round the earth in a circle of radius 9600 km. The speed with which this satellite be projected into an orbit, will be ______.
  • 6.532 km/s 
  • B
    64 km/s
  • C
    9.8 km/s
  • D
    8.325 km/s
Answer
Correct option: A.
6.532 km/s 
A
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MCQ 491 Mark
Three equal masses each of 50 g, are placed at the corners of a right angled isosceles triangle whose two equal sides are 5 cm each. The position of the centre of mass of the system is ____________.
  • $x =\frac{5}{3} cm , y =\frac{5}{3} cm$
  • B
    $x =\frac{5}{3} cm , y =\frac{5}{2} cm$
  • C
    x = 5 cm, y = 5 cm
  • D
    $x =\frac{5}{3} cm , y =5 cm$
Answer
Correct option: A.
$x =\frac{5}{3} cm , y =\frac{5}{3} cm$
A
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MCQ 501 Mark
The v-t graph of an athlete is shown below. The distance travelled by him between t = 0 and t = 18 s is
Image
  • 49.5 m
  • B
    78 m
  • C
    36 m
  • D
    56 m
Answer
Correct option: A.
49.5 m
A
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MCQ 511 Mark
A random variable X has the following probability distribution:
X = x–101234
P(X = x)0.252k0.1k0.152k
Then, the expected value of X is ______.
  • A
    1.5
  • B
    0.7
  • 1.3
  • D
    0.5
Answer
Correct option: C.
1.3
C
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MCQ 521 Mark
The c.d.f. of a discrete r.v. x is
x012345
F(x)0.160.410.560.700.911.00
Then P(1 < x ≤ 4) = ______
  • A
    0.36
  • 0.50
  • C
    0.75
  • D
    0.25 
Answer
Correct option: B.
0.50
B
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MCQ 531 Mark
A coin is tossed $10$ times. The probability of getting exactly six heads is$.....$
  • A
    $^{10}C_6$​​​​​​​
  • $\frac{105}{512}$
  • C
    $\frac{512}{513}$
  • D
    $\frac{105}{512}$
Answer
Correct option: B.
$\frac{105}{512}$
$\frac{105}{512}$
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MCQ 541 Mark
Solution of the differential equation $\frac{d y}{d x}=\frac{(\tan x-y)}{\cos ^2 x}$ is ______.
  • A
    $y e^{\tan x}=\tan x-1+c$
  • B
    $y^2=\tan x-1+c e^{\tan x}$
  • $y=\tan x-1+c e^{-\tan x}$
  • D
    $y e^{-\tan x}=\tan x-1+c$
Answer
Correct option: C.
$y=\tan x-1+c e^{-\tan x}$
C
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MCQ 551 Mark
The order and degree of the differential equation$\frac{ d ^2 y }{ dx ^2}+\left(\frac{ d ^3 y }{ dx ^3}\right)+x^{\frac{1}{5}}=0$ are respectively.
  • 3, 1
  • B
    3, 2
  • C
    2, 5
  • D
    2, 3
Answer
Correct option: A.
3, 1
A
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MCQ 561 Mark
Degree of the given differential equation

$\left(\frac{ d ^3 y }{ dx ^2}\right)^2=\left(1+\frac{ dy }{ dx }\right)^{\frac{1}{3}}$ is
  • 6
  • B
    3
  • C
    $\frac{1}{2}$
  • D
    2
Answer
Correct option: A.
6
A
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MCQ 571 Mark
The area $($in sq. units$)$ enclosed between the curves $y = x^2$ and $y = |x|$ is $.......$
  • A
    $1$
  • B
    $\frac{1}{6}$
  • C
    $\frac{2}{3}$
  • $\frac{1}{3}$
Answer
Correct option: D.
$\frac{1}{3}$
$\frac{1}{3}$
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MCQ 581 Mark
Area bounded by the curve xy = 4, X-axis between x = 1, x = 5 is ______.
  • A
    4 log 3 sq. units
  • B
    8 log 2 sq. units
  • C
    2 log 5 sq. units
  • 4 log 5 sq. units
Answer
Correct option: D.
4 log 5 sq. units
D
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MCQ 591 Mark
$\int_0^{\frac{1}{\sqrt{2}}} \frac{\sin ^{-1} x}{\left(1-x^2\right)^{\frac{3}{2}}} d x$ = ______.
  • A
    $\frac{\pi}{2}-\log 2$
  • B
    $\frac{\pi}{4}+\frac{1}{2} \log 2$
  • C
    $\frac{\pi}{2}+\log 2$
  • $\frac{\pi}{4}-\frac{1}{2} \log 2$
Answer
Correct option: D.
$\frac{\pi}{4}-\frac{1}{2} \log 2$
D
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MCQ 601 Mark
$\int_0^{\frac{\pi}{2}}\left(\frac{3 \sqrt{\sec x}}{3 \sqrt{\sec x}+3 \sqrt{\operatorname{cosec} x}}\right) d x$ = ______.
  • $\frac{\pi}{4}$
  • B
    $\frac{\pi}{3}$
  • C
    $\frac{\pi}{6}$
  • D
    $\frac{\pi}{2}$
Answer
Correct option: A.
$\frac{\pi}{4}$
A
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MCQ 611 Mark
$\int_0^{\frac{\pi}{2}} \frac{\cos x}{(4+\sin x)(3+\sin x)}$dx = ?
  • A
    $\log \left(\frac{4}{3}\right)$
  • B
    $\log \left(\frac{11}{15}\right)$
  • C
    $\log \left(\frac{4}{5}\right)$
  • $\log \left(\frac{16}{15}\right)$
Answer
Correct option: D.
$\log \left(\frac{16}{15}\right)$
D
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MCQ 621 Mark
If $\frac{d y}{d x}=y+3$ and y(0) = 2, then y(log 2) is equal to ______.
  • A
    13
  • B
    -2
  • C
    5

Answer
Correct option: D.

D
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MCQ 631 Mark
$\int x^x(1+\log x) d x$ = ______.
  • $x^x+c$
  • B
    $x^x \log x+c$
  • C
    $x^{2 x}+c$
  • D
    $\frac{1}{2}(1+\log x)^2+c$
Answer
Correct option: A.
$x^x+c$
A
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MCQ 641 Mark
$\int( I -\cos x) \operatorname{cosec}^2 x d x$ = ______.
  • $\tan \left(\frac{x}{2}\right)+ c$
  • B
    $-\cot \left(\frac{x}{2}\right)+ c$
  • C
    $-2 \cot \left(\frac{x}{2}\right)+ c$
  • D
    $2 \tan \left(\frac{x}{2}\right)+ c$
Answer
Correct option: A.
$\tan \left(\frac{x}{2}\right)+ c$
A
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MCQ 651 Mark
The minimum value of the function $f(x) = 13 - 14x + 9x^2$ is $........$
  • A
    $-\frac{68}{9}$
  • $\frac{68}{9}$
  • C
    $\frac{59}{9}$
  • D
    $-\frac{59}{9}$
Answer
Correct option: B.
$\frac{68}{9}$
$\frac{68}{9}$
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MCQ 661 Mark
If the tangent to $y^2 = 4ax$ at the point $($at$^2, 2$at$),$ where $| t | > 1$ is a normal to $x^2 – y^2 = a^2$ at the point $(a \sec \theta \ ' a \tan \theta ),$ then $.......$
  • A
    $t = 2 \tan \theta$
  • $t = – cosec \ \theta$
  • C
    $t = 2 \cot \theta$
  • D
    $t = – \sec \ \theta$
Answer
Correct option: B.
$t = – cosec \ \theta$
$t = – cosec \ \theta$
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MCQ 671 Mark
If f(x) = $\frac{\sin ^2 x}{1+\cot x}+\frac{\cos ^2 x}{1+\tan x}$, then $f ^{\prime}\left(\frac{\pi}{4}\right)$ is ______.
  • A
    $\frac{1}{\sqrt{3}}$
  • B
    $\sqrt{3}$
  • 0
  • D
    $-\sqrt{3}$
Answer
Correct option: C.
0
C
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MCQ 681 Mark
If x = p sin θ, y = q cos θ, then $\frac{d y}{d x}$ = _____.
  • A
    $\left(\frac{q}{p}\right) \tan \theta$
  • B
    $\left(-\frac{p}{q}\right) \tan \theta$
  • C
    tan θ
  • $\left(-\frac{q}{p}\right) \tan \theta$
Answer
Correct option: D.
$\left(-\frac{q}{p}\right) \tan \theta$
D
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MCQ 691 Mark
If $\frac{v^2}{3}$, then $\left(-\frac{v}{2} \frac{d f}{d t}\right)$ is equal to, $($where $f$ is acceleration$) .......$
  • $f^2$
  • B
    $-f^3$​​​​​​​
  • C
    $-f^2$​​​​​​​
  • D
    $f^3$​​​​​​​
Answer
Correct option: A.
$f^2$
$f^2$
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MCQ 701 Mark
The minimum value of z = 7x + 9y subject to 3x + y ≤ 6, 5x + 8y ≤ 40, x ≥ 0, y ≥ 2 is ______.
  • 18
  • B
    45
  • C
    $\frac{82}{3}$
  • D
    9
Answer
Correct option: A.
18
A
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MCQ 711 Mark
The constraints of an LPP are 7 ≤ x ≤ 12, 8 ≤ y ≤ 13. Determine the vertices of the feasible region formed by them.
  • A
    (8, 7), (8, 12), (12, 13), (7, 13)
  • (7, 8), (12, 8), (12, 13), (7, 13)
  • C
    (7, 8), (12, 8), (13, 12), (13, 7)
  • D
    (8, 7), (8, 12), (13, 12), (13, 7)
Answer
Correct option: B.
(7, 8), (12, 8), (12, 13), (7, 13)
B
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MCQ 721 Mark
If the origin and the points P(2, -7, 5), Q(2, 3, - 5) and R(x, y, z) are co-planar, then ______ 
  • A
    x - y + z = 0
  • B
    x - y + 2z = 0
  • x + y + z = 0
  • D
    x - 2y + z = 0
Answer
Correct option: C.
x + y + z = 0
C
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MCQ 731 Mark
The distance of the point (1, 0, 2) from the point of intersection of the line $\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}$ and the plane x - y + z = 16, is _____.
  • 13
  • B
    $3 \sqrt{21}$
  • C
    8
  • D
    $2 \sqrt{14}$
Answer
Correct option: A.
13
A
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MCQ 741 Mark
The shortest distance between A (1, 0, 2) and the line $\frac{x+1}{3}=\frac{y-2}{-2}=\frac{z+1}{-1}$ is given by line joining A and B, then B in the line is ______.
  • A
    (1, -2, -1)
  • B
    $\left(\frac{2}{3}, 1,-1\right)$
  • C
    $\left(\frac{2}{3}, \frac{-1}{2},-2\right)$
  • $\left(\frac{1}{2}, 1, \frac{-3}{2}\right)$
Answer
Correct option: D.
$\left(\frac{1}{2}, 1, \frac{-3}{2}\right)$
D
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MCQ 751 Mark
The direction cosines of a line which is perpendicular to both the lines whose direction ratios are -2, 1, -1 and -3, -4, 1 are ______ 
  • A
    $\frac{3}{\sqrt{155}}, \frac{5}{\sqrt{155}}, \frac{11}{\sqrt{155}}$
  • B
    $\frac{3}{\sqrt{155}}, \frac{-5}{\sqrt{155}}, \frac{11}{\sqrt{155}}$
  • $\frac{-3}{\sqrt{155}}, \frac{5}{\sqrt{155}}, \frac{11}{\sqrt{155}}$
  • D
    $\frac{3}{\sqrt{155}}, \frac{5}{\sqrt{155}}, \frac{-11}{\sqrt{155}}$
Answer
Correct option: C.
$\frac{-3}{\sqrt{155}}, \frac{5}{\sqrt{155}}, \frac{11}{\sqrt{155}}$
C
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MCQ 761 Mark
If the volume of tetrahedron whose vertices are A(0, 1, 2), B(2, -3, 0), C(1, 0, 2) and D(-2,-3,lambda) is $\frac{7}{3}$ cu.units, then the value of λ is ______.
  • A
    - 2
  • B
    4
  • C
    1
  • 3
Answer
Correct option: D.
3
D
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MCQ 771 Mark
If G$(\bar{g})$ is the centroid, $H(\bar{h})$ is the orthocentre and P$(\bar{p})$ is the circumcentre of a triangle and $x \bar{p}+y \bar{h}+z \bar{g}=0$, then ______.
  • A
    x = 2,y = -3, z = 5
  • x = 2, y = 1, z = -3
  • C
    x = -2, y = 5, z = 1
  • D
    x = 1, y = 2, z = -3
Answer
Correct option: B.
x = 2, y = 1, z = -3
B
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MCQ 781 Mark
If $\overline{ a }, \overline{ b }, \overline{ c }$ are the three non-coplanar vectors and $\overline{ p }, \overline{ q }, \overline{ r }$ are defined by the relations $\overline{ p }=\frac{\overline{ b } \times \overline{ c }}{\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]}, \overline{ q }=\frac{\overline{ c } \times \overline{ a }}{\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]}, \overline{ r }=\frac{\overline{ a } \times \overline{ b }}{\left[\begin{array}{lll}\overline{ a } & \overline{ b } & \overline{ c }\end{array}\right]}$ then $(\overline{ a }+\overline{ b }) \cdot \overline{ p }+(\overline{ b }+\overline{ c }) \cdot \overline{ q }+(\overline{ c }+\overline{ a }) \cdot \overline{ r }$ = ______.
  • A
    0
  • B
    2
  • C
    1
  • 3
Answer
Correct option: D.
3
D
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MCQ 791 Mark
If $(\overline{ a }+2 \overline{ b }-\overline{ c }) \cdot[(\overline{ a }-\overline{ b }) \times(\overline{ a }-\overline{ b }-\overline{ c })]= k [\overline{ a } \overline{ b } \overline{ c }]$, then the value of k is
  • A
    1
  • B
    4
  • C
    2
  • 3
Answer
Correct option: D.
3
D
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MCQ 801 Mark
If $m_1, m_2$ are slopes of lines represented by $3x^2 – 10xy – 8y^2 = 0,$ then equation of lines passing through origin with slopes $\frac{1}{m_1}, \frac{1}{m_2}$ will be $.........$
  • A
    $3y^2 – 10xy + 8x^2 = 0$
  • $3y^2 – 10xy – 8x^2 = 0$
  • C
    $3x^2 – 10xy + 8y^2 = 0$
  • D
    $3x^2 – 10xy – 8y^2 = 0$
Answer
Correct option: B.
$3y^2 – 10xy – 8x^2 = 0$
$3y^2 – 10xy – 8x^2 = 0$
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MCQ 811 Mark
Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three vectors having magnitudes 1, 1, and 2 respectively. If If $\bar{a} \times(\bar{a} \times \bar{c})+\bar{b}=\overline{0}$, then the acute angle between $\bar{a}$ and $\bar{c}$ is _____.
  • A
    $\frac{\pi}{4}$
  • $\frac{\pi}{6}$
  • C
    $\frac{\pi}{3}$
  • D
    none of these
Answer
Correct option: B.
$\frac{\pi}{6}$
B
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MCQ 821 Mark
The joint equation of bisectors of angles between lines $x = 5$ and $y = 3$ is $.......$
  • A
    $(x - 5) (y - 3) = 0$
  • B
    $xy = 0$
  • C
    $xy - 5x - 3y + 15 = 0$
  • $x^2 - y^2- 10x + 6y + 16 = 0$
Answer
Correct option: D.
$x^2 - y^2- 10x + 6y + 16 = 0$
$x^2 - y^2- 10x + 6y + 16 = 0$
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MCQ 831 Mark
In a triangle ABC, ∠C = 90°, then the value of $-^{-1}\left(\frac{a}{b+c}\right)+\tan ^{-1}\left(\frac{b}{c+a}\right)$ is ______.
  • $\frac{\pi}{4}$
  • B
    $\frac{\pi}{2}$
  • C
    $\pi$
  • D
    $\frac{\pi}{3}$
Answer
Correct option: A.
$\frac{\pi}{4}$
A
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MCQ 841 Mark
If in ΔABC, $\sin \frac{B}{2} \sin \frac{C}{2}=\sin \frac{A}{2}$ and 2s is the perimeter of the triangle, then s is ______.
  • A
    a
  • 2a
  • C
    4a
  • D
    3a
Answer
Correct option: B.
2a
B
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MCQ 851 Mark
$\int \frac{(\sin (\log x))^2}{x} \log \times dx = $?
  • $-\frac{1}{2} \cos (\log x)^2+ c$
  • B
    $-\frac{1}{2} \sin (\log x)^2+c$
  • C
    $\sin (\log x)^2 + c$
  • D
    $\cos (\log x)^2 + c$
Answer
Correct option: A.
$-\frac{1}{2} \cos (\log x)^2+ c$
$-\frac{1}{2} \cos (\log x)^2+ c$
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MCQ 861 Mark
If A =$\left[\begin{array}{ccc}2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & p & 2\end{array}\right]$ and $A ^{-1}=\left[\begin{array}{ccc}-\frac{2}{5} & 0 & \frac{3}{5} \\ -\frac{1}{5} & \frac{1}{5} & q \\ \frac{2}{5} & \frac{1}{5} & -\frac{2}{5}\end{array}\right]$, then ______.
  • A
    p = – 3, q = 2
  • p = – 2, q = 0
  • C
    p = 1, q = – 2
  • D
    p = 1, q = 2
Answer
Correct option: B.
p = – 2, q = 0
B
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MCQ 871 Mark
If $AB = I$ and $B = A^T,$ then $.......$
  • A
    $A^{-1} = A$
  • B
    $A^{-1} = A^2$​​​​​​​
  • $A^{-1} = A^T$​​​​​​​
  • D
    $A = A^T$​​​​​​​
Answer
Correct option: C.
$A^{-1} = A^T$​​​​​​​
$A^{-1} = A^T$​​​​​​​
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MCQ 881 Mark
(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.
  • A
    Tautology
  • Contradiction
  • C
    Tautology and contradiction
  • D
    Contingency
Answer
Correct option: B.
Contradiction
B
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MCQ 891 Mark
The contrapositive of (p ∧ r) → q is ______.
  • A
    ∼p ∨ ∼r → ∼q
  • ∼q → ∼p ∨ ∼r 
  • C
    ∼q → (p ∧ r) 
  • D
    q → (p ∧ r) 
Answer
Correct option: B.
∼q → ∼p ∨ ∼r 
B
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MCQ 901 Mark
Determine which of the following quantified statement is false$....$
  • $\forall x \in N, x^2 > x$
  • B
    $\forall x \in N,$ such that $x^3 > 0$
  • C
    $∃ x \in N$ such that $x^2 < 0$
  • D
    $∃ x \in N, x^2 = x$
Answer
Correct option: A.
$\forall x \in N, x^2 > x$
$\forall x \in N, x^2 > x$
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MCQ 911 Mark
Domain of the function f(x) = $\sqrt{1+4 x-x^2}$ is ______.
  • A
    $-\sqrt{5} \leq x \leq \sqrt{5}$
  • B
    $-2+\sqrt{5} \leq x \leq-2-\sqrt{5}$
  • $2-\sqrt{5} \leq x \leq 2+\sqrt{5}$
  • D
    -2 ≤ x ≤ 2
Answer
Correct option: C.
$2-\sqrt{5} \leq x \leq 2+\sqrt{5}$
C
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MCQ 921 Mark
The value of $\lim _{x \rightarrow 0} \frac{1+\sin x-\cos x+\log _e(1-x)}{x^3}$ is ______.
  • $-\frac{1}{2}$
  • B
    1
  • C
    -1
  • D
    $\frac{1}{2}$
Answer
Correct option: A.
$-\frac{1}{2}$
A
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MCQ 931 Mark
If a function $f(x)$ is given as $f(x) = x^2 – 6x + 4$ for all $x \in R,$ then $f(–3) =.......$
  • A
    $18$
  • $31$
  • C
    $12$
  • D
    $13$
Answer
Correct option: B.
$31$
$31$
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MCQ 941 Mark
If $\frac{1}{8 !}+\frac{1}{7 !}=\frac{x}{9 !}$, than x is equal to ______.
  • A
    170
  • B
    90
  • C
    50
  • 81
Answer
Correct option: D.
81
D
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MCQ 951 Mark
If A = {x, y, z}, B = {1, 2}, then the total number of relations from set A to set B are ______.
  • A
    32
  • 64
  • C
    16
  • D
    8
Answer
Correct option: B.
64
B
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MCQ 961 Mark
A die is thrown nine times. If getting an odd number is considered as a success, then the probability of three successes is ______
  • A
    ${ }^9 C _3\left(\frac{1}{2}\right)^7$
  • B
    ${ }^9 C _3\left(\frac{1}{2}\right)^8$
  • C
    None of these
  • ${ }^9 C _6\left(\frac{1}{2}\right)^9$
Answer
Correct option: D.
${ }^9 C _6\left(\frac{1}{2}\right)^9$
D
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MCQ 971 Mark
In a series of observations, coefficient of variation is 25 and mean is 20, then the variance is ______.
  • A
    49
  • B
    8
  • 25
  • D
    16
Answer
Correct option: C.
25
C
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MCQ 981 Mark
The equation of the tangent to the curve $x = 2 \cos^3 \theta $ and $y = 3 \sin^3 \theta $ at the point $\theta =\frac{\pi}{4}$ is $...........$
  • A
    $2 x+3 y=3 \sqrt{2}$
  • B
    $2 x-3 y=3 \sqrt{2}$
  • $3 x+2 y=3 \sqrt{2}$
  • D
    $3 x-2 y=3 \sqrt{2}$
Answer
Correct option: C.
$3 x+2 y=3 \sqrt{2}$
$3 x+2 y=3 \sqrt{2}$
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MCQ 991 Mark
The angle between the lines x sin 60° + y cos 60° = 5 and x sin 30° + y cos 30° = 7 is ______ 
  • A
    90°
  • B
    45°
  • C
    60°
  • 30°
Answer
Correct option: D.
30°
D
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MCQ 1001 Mark
$\frac{\sin 20^{\circ}+2 \sin 40^{\circ}}{\sin 70^{\circ}=}$ ______.
  • A
    $2 \sqrt{3}$
  • B
    1
  • C
    $\frac{1}{\sqrt{3}}$
  • $\sqrt{3}$
Answer
Correct option: D.
$\sqrt{3}$
D
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MCQ 1011 Mark
Which among the following monomers is used to prepare Teflon?
  • A
    Image
  • $CF_2 = CF_2$
  • C
    $CH_3 – CH = CH_2$
  • D
    $CH_2 = CH – Cl$
Answer
Correct option: B.
$CF_2 = CF_2$
$CF_2 = CF_2$
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MCQ 1021 Mark
Which of the following is used as a substitute for wool?

  • Image
  • B

    Image
  • C
    $\left[- NH -\left( CH _2\right)_5- CO -\right]_{ n }$
  • D
    $\left[- CF _2- CF _2-\right]_{ n }$
Answer
Correct option: A.

Image
A
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MCQ 1031 Mark
Which of the following amino acid is an essential amino acid?
  • A
    Proline
  • B
    Alanine
  • Threonine
  • D
    Serine
Answer
Correct option: C.
Threonine
C
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MCQ 1041 Mark
Which among the following reagents is used to confirm the presence of carbonyl group in glucose?
  • A
    hot HI
  • B
    $Br_2 $ water
  • C
    dilute $HNO_3$​​​​​​​
  • $NH_2OH$
Answer
Correct option: D.
$NH_2OH$
$NH_2OH$
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MCQ 1051 Mark
The following compound is a/an ____________.
Image
  • A
    unsymmetrical, aromatic 3° amine
  • symmetrical, aromatic 3° amine
  • C
    symmetrical, aromatic 2° amine
  • D
    unsymmetrical, aromatjc 2° amine
Answer
Correct option: B.
symmetrical, aromatic 3° amine
B
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MCQ 1061 Mark
Nitrogen atom in amines is $.......$
  • A
    sp hybridised
  • $sp^3$​​​​​​​ hybridised
  • C
    $dsp^2 $ hybridised
  • D
    $sp^2 $ hybridised
Answer
Correct option: B.
$sp^3$​​​​​​​ hybridised
$sp^3$​​​​​​​ hybridised
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MCQ 1081 Mark
Which of the following compounds does NOT undergo aldol condensation?
  • A
    3-Methylbutanal
  • B
    Acetophenone
  • Benzaldehyde
  • D
    Cyclopentanone
Answer
Correct option: C.
Benzaldehyde
C
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MCQ 1101 Mark
The number of isomeric alcohols possible with the formula $C_4H_{10}O$ is $........$
  • A
    $3$
  • $4$
  • C
    $5$
  • D
    $6$
Answer
Correct option: B.
$4$
$4$
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MCQ 1111 Mark
What is the major product obtained in the sulphonation of chlorobenzene with concentrated sulphuric acid?
  • 4-Chlorobenzene sulphonic acid
  • B
    Benzene sulphonic acid
  • C
    3-Chlorobenzene sulphonic acid
  • D
    2-Chlorobenzene sulphonic acid
Answer
Correct option: A.
4-Chlorobenzene sulphonic acid
A
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MCQ 1121 Mark
What is the correct order of $C-X$ bond strength in $CH_3X?$
  • $CH_3F > CH_3CI > CH_3Br > CH_3I$
  • B
    $CH_3F > CH_3Br > CH_3CI > CH_3I$
  • C
    $CH_3I > CH_3Br > CH_3Cl > CH_3F$
  • D
    $CH_3CI > CH_3Br > CH_3I > CH_3F$
Answer
Correct option: A.
$CH_3F > CH_3CI > CH_3Br > CH_3I$
$CH_3F > CH_3CI > CH_3Br > CH_3I$
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MCQ 1131 Mark
The number of unpaired electrons in the complex ion $[NiCl_4]^{2−}$^ is $..........$
  • A
    $1$
  • B
    $4$
  • $2$
  • D
    $0$
Answer
Correct option: C.
$2$
$2$
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MCQ 1141 Mark
The compound(s) that exhibit(s) geometrical isomerism is $($are$)$ :
$(I) \ [Pt(en)Cl_2]$
$(II) \ [Pt(en)_2]Cl_2$
$(III) \ [Pt(en)_2Cl_2]$
$(IV)\  [Pt(NH_3)_2Cl_2]$
  • $(III)$ and $(IV)$
  • B
    $(II)$ and $(III)$
  • C
    $(I)$ and $(IV)$
  • D
    $(I)$ and $(II)$
Answer
Correct option: A.
$(III)$ and $(IV)$
$(III)$ and $(IV)$
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MCQ 1151 Mark
Elements from atomic number 104 to 118 are called as ____________.
  • postactinoid elements
  • B
    lanthanoids
  • C
    transuranium elements
  • D
    actinoids
Answer
Correct option: A.
postactinoid elements
A
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MCQ 1161 Mark
Which element among the following lanthanoids has the smallest atomic radius?
  • Erbium
  • B
    Europium
  • C
    Gadolinium
  • D
    Cerium
Answer
Correct option: A.
Erbium
A
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MCQ 1171 Mark
Which of the following has completely filled d orbital in its ground state?
  • A
    Cr
  • Zn
  • C
    Fe
  • D
    Ti
Answer
Correct option: B.
Zn
B
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MCQ 1181 Mark
The bent $T-$shaped interhalogen is $......$
  • $ClF_3$
  • B
    $CIF_5$
  • C
    $Icl$
  • D
    $BrF_5$
Answer
Correct option: A.
$ClF_3$
$ClF_3$
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MCQ 1191 Mark
Which among the following catalysts is used in manufacture of sulphuric acid by contact process?
  • A
    $MnO_2$
  • B
    $Fe$ with $Mo$
  • $V_2O_5$
  • D
    $Ni$
Answer
Correct option: C.
$V_2O_5$
$V_2O_5$
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MCQ 1201 Mark
Identify the correct decreasing order of oxidizing power.
  • A
    $HClO_2 > HClO_3 > HClO$
  • B
    $HClO > HClO_3 > HClO_2$
  • $HClO > HClO_2 > HClO_3$
  • D
    $HClO_2 > HCIO > HClO_3$
Answer
Correct option: C.
$HClO > HClO_2 > HClO_3$
$HClO > HClO_2 > HClO_3$
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MCQ 1211 Mark
The potential energy of the transition state is ____________.
  • A
    less than the potential energy of reactants but more than the potential energy of products
  • B
    less than the potential energy of either reactants or products
  • greater than the potential energy of either reactants or products
  • D
    greater than the potential energy of reactants but less than the potential energy of products
Answer
Correct option: C.
greater than the potential energy of either reactants or products
C
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MCQ 1221 Mark
The initial concentration of reactant $(A)$ is $2 mol dm ^{-3}$ for a zero order reaction $A \longrightarrow B$ The rate constant $( k )$ is related to its half-life $\left(t_{1 / 2}\right)$ by the equation:
  • A
    $k =\left( t _{1 / 2}\right)^0$
  • B
    $k=\sqrt{t_{1 / 2}}$
  • $k =\left( t _{1 / 2}\right)^{-1}$
  • D
    $k =\left( t _{1 / 2}\right)^{-2}$
Answer
Correct option: C.
$k =\left( t _{1 / 2}\right)^{-1}$
C
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MCQ 1231 Mark
If time required to decrease concentration of reactant from 0.8 M to 0.2 M is 12 hours, the half life of this first order reaction is ____________.
  • A
    4 hr
  • 6 hr
  • C
    8 hr
  • D
    12 hr
Answer
Correct option: B.
6 hr
B
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MCQ 1241 Mark
Which of the following metals does NOT displace zinc from it's solution?
  • Fe
  • B
    Na
  • C
    K
  • D
    Al
Answer
Correct option: A.
Fe
A
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MCQ 1251 Mark
Find INCORRECT statement with reference to NICAD cell.
  • A
    It is a secondary dry cell.
  • B
    Anode is made by cadmium metal.
  • C
    It can be recharged.
  • Cathode is made by nickel metal.
Answer
Correct option: D.
Cathode is made by nickel metal.
D
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MCQ 1261 Mark
Identify the correct decreasing of relative tendency of metals to undergo oxidation from following.
  • A
    Fe > Cr > Al > Mg
  • Mg > Al > Cr > Fe
  • C
    Cr > Al > Mg > Fe
  • D
    Al > Fe > Cr > Mg
Answer
Correct option: B.
Mg > Al > Cr > Fe
B
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MCQ 1271 Mark
How many Faradays of electricity are required to deposit $20 g$ of calcium from molten calcium chloride using inert electrodes?
$($ Molar mass of calcium $= 40 g mol^{−1})$
  • A
    $0.5 F$
  • B
    $2 F$
  • C
    $0.25 F$
  • $1 F$
Answer
Correct option: D.
$1 F$
$1 F$
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MCQ 1281 Mark
The resistance of a conductivity cell containing $0.001 \ M \ \text{KCl}$ solution at $298 K$ is $1500 \Omega $. What is the cell constant if conductivity of $0.001 \ M \ \text{KCl}$ solution at $298 K$ is $0.146 \times 10^{−3}S \ cm^{−1}$?
  • A
    $1.02 \ cm^{−1}$
  • B
    $0.25 \ cm^{−1}$
  • $0.219 \ cm^{−1}$
  • D
    $0.973 \ cm^{−1}$
Answer
Correct option: C.
$0.219 \ cm^{−1}$
$0.219 \ cm^{−1}$
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MCQ 1291 Mark
For the reaction: $ 2 Cl _{( g )} \longrightarrow Cl _{2( g )}$
  • A
    ∆H is positive, ∆S is negative
  • B
    ∆H is positive, ∆S is positive
  • C
    ∆H is negative, ∆S is positive
  • ∆H is negative, ∆S is negative
Answer
Correct option: D.
∆H is negative, ∆S is negative
D
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MCQ 1301 Mark
Calculate the enthalpy of hydrogenation of $C_2H_{4(g)},$ given that the enthalpy of formation of ethane and ethylene are $−30.2 \ kcal$ and $+12.5 \ kcal$ respectively.
  • A
    $−4.8 \ kcal$
  • B
    $−7.7\  kcal$
  • C
    $+7.7\  kcal$
  • $−42.7\  kcal$
Answer
Correct option: D.
$−42.7\  kcal$
$−42.7\  kcal$
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MCQ 1311 Mark
For the reaction,
$
A _{( s )}+2 B _{( g )} \longrightarrow 5 C _{( s )}+ D _{( l )}
$
, $\Delta H$ and $\Delta U$ are related as __________.
  • A
    ∆H = ∆U + RT
  • B
    ∆H = ∆U
  • C
    ∆H = ∆U + 2 RT
  • ∆H = ∆U − 2 RT
Answer
Correct option: D.
∆H = ∆U − 2 RT
D
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MCQ 1321 Mark
For a particular reaction, the system absorbs 8 kJ of heat and does 2.5 kJ of work on its surrounding. What will be the change in internal energy of the system?
  • A
    −5.5 kJ
  • B
    −10.5 kJ
  • +5.5 kJ
  • D
    +10.5 kJ
Answer
Correct option: C.
+5.5 kJ
C
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MCQ 1331 Mark
A system absorbs 900 J of heat and does work. The change in internal energy (∆U) for the process is +460 J. The work done by the system is ____________.
  • A
    440 J
  • −440 J
  • C
    1360 J
  • D
    −1360 J
Answer
Correct option: B.
−440 J
B
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MCQ 1341 Mark
Which one of the following is NOT an intensive property?
  • Heat capacity
  • B
    Melting point
  • C
    Temperature
  • D
    Surface tension
Answer
Correct option: A.
Heat capacity
A
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MCQ 1351 Mark
Which of the following equations is NOT correct for van't Hoff factor?
  • A
    i = $\frac{ n (\text { Observed })}{ n (\text { Theortical })}$
  • $i =\frac{\text { Observed molar mass }}{\text { Theoretical molar mass }}$
  • C
    $i=\frac{\text { Theoretical molar mass }}{\text { Observed molar mass }}$
  • D
    $i =\frac{\pi(\text { Observed })}{\pi(\text { Theortical })}$
Answer
Correct option: B.
$i =\frac{\text { Observed molar mass }}{\text { Theoretical molar mass }}$
B
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MCQ 1361 Mark
If $10 g$ each of glucose, urea and sucrose is dissolved in $250\  mL$ of water having osmotic pressure $\pi _1, \pi _2$ and $\pi _3$respectively, the decreasing order of osmotic pressure of these solutions is $.........$
  • A
    $\pi _3> \pi _1> \pi _2$
  • $\pi _2> \pi _1> \pi _3$
  • C
    $\pi _{1 }> \pi _{2 }> \pi _3$
  • D
    $\pi _2> \pi _3> \pi _1$
Answer
Correct option: B.
$\pi _2> \pi _1> \pi _3$
$\pi _2> \pi _1> \pi _3$
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MCQ 1371 Mark
What happens when isotonic solution of A (molecular weight 342) and B (molecular weight 60) are separated through semipermeable membrane?
  • A
    Transfer of solvent from solution of A to that of B takes place.
  • No transfer of solvent from solution of A to that of B takes place.
  • C
    Change in temperature of the solutions takes place.
  • D
    Transfer of solvent from solution of B to that of A takes place.
Answer
Correct option: B.
No transfer of solvent from solution of A to that of B takes place.
B
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MCQ 1381 Mark
The coordination number of each sphere in bcc lattice is ____________.
  • A
    12
  • 8
  • C
    6
  • D
    14
Answer
Correct option: B.
8
B
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MCQ 1391 Mark
How many lithium atoms are present in a unit cell with edge length $3.5 \mathring A $ and density $0.53 g \ cm^{-3} ($ At. mass of $Li= 6.94).$
  • two atoms
  • B
    six atoms
  • C
    four atoms
  • D
    one atom
Answer
Correct option: A.
two atoms
two atoms
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MCQ 1401 Mark
Calcite and ____________ are two forms of calcium carbonate.
  • aragonite
  • B
    cristobalite
  • C
    α-quartz
  • D
    β-quartz
Answer
Correct option: A.
aragonite
A
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MCQ 1421 Mark
As per $\text{IUPAC}$ nomenclature, the name of the complex $[Fe(H_2O)_5(NCS)]^{2+}$ is $......$
  • A
    pentaaquathiocyanatoiron $(III)$ ion
  • B
    pentaaquaisothiocyanatoiron $(II)$ ion
  • C
    isothiocyanatopentaaquairon $(III)$ ion
  • pentaaquaisothiocyanatoiron $(III)$ ion
Answer
Correct option: D.
pentaaquaisothiocyanatoiron $(III)$ ion
pentaaquaisothiocyanatoiron $(III)$ ion
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MCQ 1431 Mark
Which of the following is the INCORRECT match?
  • Compound: Mercury
  • B
    Element: Gold
  • C
    Heterogeneous mixture: Suspension
  • D
    Homogeneous mixture: An aqueous solution of sugar
Answer
Correct option: A.
Compound: Mercury
A
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MCQ 1441 Mark
The critical temperature of a substance is the temperature ____________.
  • A
    above which the substance melts
  • B
    above which the substance can exist only as a liquid
  • above which the substance cannot be liquefied
  • D
    above which the substance undergoes thermal decomposition
Answer
Correct option: C.
above which the substance cannot be liquefied
C
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MCQ 1451 Mark
Castner-Kellner cell is used in the preparation of ____________.
  • A
    sodium bicarbonate
  • B
    sodium carbonate
  • C
    sodium chloride
  • sodium hydroxide
Answer
Correct option: D.
sodium hydroxide
D
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MCQ 1461 Mark
Identify the strongest oxidising agent.
$
\left[\begin{array}{ll}
& Na ^{+}+ e ^{-} \longrightarrow Na \\
E ^0=-2.714 V & \\
E ^0=+1.200 V & Pt ^{2+}+2 e ^{-} \longrightarrow Pt \\
; E ^0=+0.535 V & \\
& I _2+2 e ^{-} \longrightarrow 2 I ^{-} \\
;{ }^0=-0.280 V & Co ^{2+}+2 e ^{-} \longrightarrow Co
\end{array}\right.
$
  • A
    $Na$
  • B
    $I_2$
  • C
    $Sn^{2+}$
  • $Pt^{2+}$
Answer
Correct option: D.
$Pt^{2+}$
$Pt^{2+}$
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MCQ 1471 Mark
Energy required to dissociate $6 g$ of gaseous hydrogen into free gaseous atoms is $208$ kcal at $25^\circ C$. Bond energy of $H-H$ bond will be $............$
  • A
    $52 \ kcal \ mol^{−1}$
  • B
    $\frac{52}{6.023} \times 10^{23} kcal \ mol -1$
  • C
    $10.4 \ kcal \ mol^{−1}$
  • $69.33 \ kcal \ mol^{−1}$
Answer
Correct option: D.
$69.33 \ kcal \ mol^{−1}$
$69.33 \ kcal \ mol^{−1}$
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MCQ 1481 Mark
Identify the $\text{CORRECT}$ option according to $\text{MOT}$.
  • A
    $O_2$ molecule is diamagnetic with bond order equal to $2$.
  • B
    $F_2$ molecule is paramagnetic with bond order equal to $2$.
  • $H_2$ molecule is diamagnetic with bond order equal to $1$.
  • D
    $Li_2$ molecule is diamagnetic with bond order equal to $2$.
Answer
Correct option: C.
$H_2$ molecule is diamagnetic with bond order equal to $1$.
$H_2$ molecule is diamagnetic with bond order equal to $1$.
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MCQ 1491 Mark
A particle has a mass of $0.002 \ kg$ and uncertainty in its velocity is $9.2 \times 10^{−6} m/s,$ then uncertainty in position is $\geq ........(h = 6.6 \times 10^{−34} J s)$
  • A
    $2.86 \times 10^{−30} m$
  • B
    $2.86 \times 10^{−28} m$
  • C
    $2.86 \times 10^{−34} m$
  • $2.86 \times 10^{−29} m$
Answer
Correct option: D.
$2.86 \times 10^{−29} m$
$2.86 \times 10^{−29} m$
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