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2021 43 questions

Q312021 · 26 Aug 2021 · Shift 2
The temperature of equal masses of three different liquids x, y and z are $1 0^{\circ} C$ , $2 0^{\circ} C$ and $3 0^{\circ} C$ respectively. The temperature of mixture when x is mixed with y is $1 6^{\circ} C$ and that when y is mixed with z is $2 6^{\circ} C$ . The temperature of mixture when x and z are mixed will be :
1. A. $28.3 2^{\circ} C$
2. B. $25.6 2^{\circ} C$
3. C. $23.8 4^{\circ} C$
4. D. $20.2 8^{\circ} C$
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Answer: C
Q352021 · 26 Aug 2021 · Shift 2
1. A. $tan^{- 1} (\frac{- \frac{B}{2}}{A - B \frac{3}{2}})$
2. B. $tan^{- 1} (\frac{A}{0.7 B})$
3. C. $tan^{- 1} (\frac{3 B}{2 A - B})$
4. D. $tan^{- 1} (\frac{B c o s θ}{A - B s i n θ})$
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Answer: C
Q412021 · 26 Aug 2021 · Shift 2
A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :
1. A.hyperbola
2. B.parabola in the direction of motion of plane
3. C.straight line vertically down the plane
4. D.parabola in a direction opposite to the motion of plane
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Answer: C
Q402021 · 27 Jul 2021 · Shift 2
1. A.
2. B.
3. C.
4. D.
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Answer: B
Q452021 · 27 Jul 2021 · Shift 2
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :
1. A. $(\frac{9 P}{8 m})^{\frac{1}{2}} t^{\frac{3}{2}}$
2. B. $(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{2}{3}}$
3. C. $(\frac{9 m}{8 P})^{\frac{1}{2}} t^{\frac{3}{2}}$
4. D. $(\frac{8 P}{9 m})^{\frac{1}{2}} t^{\frac{3}{2}}$
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Answer: D
Q472021 · 27 Jul 2021 · Shift 2
A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_{0} [1 - (\frac{t - T}{T})^{2}]$ Where $F_{0}$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :
1. A. $2 F_{0} T/M$
2. B. $F_{0} T/2M$
3. C. $4 F_{0} T/3M$
4. D. $F_{0} T/3M$
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Answer: C
Q342021 · 25 Jul 2021 · Shift 1
1. A.OR
2. B.AND
3. C.NOR
4. D.NAND
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Answer: B
Q362021 · 25 Jul 2021 · Shift 1
1. A.(a) $\to$ (iv), (b) $\to$ (i), (c) $\to$ (iii), (d) $\to$ (ii)
2. B.(a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (i), (d) $\to$ (ii)
3. C.(a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
4. D.(a) $\to$ (i), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (iii)
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Answer: B
Q452021 · 25 Jul 2021 · Shift 1
Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = $9.8 m/ s^{2}$ )
1. A.3 drops / 2 seconds
2. B.2 drops / second
3. C.1 drop / second
4. D.1 drop / 7 seconds
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Answer: C
Q312021 · 25 Jul 2021 · Shift 2
The relation between time t and distance x for a moving body is given as $t = m x^{2} + n x$ , where m and n are constants. The retardation of the motion is : (When v stands for velocity)
1. A. $2 m v^{3}$
2. B. $2 mn v^{3}$
3. C. $2 n v^{3}$
4. D. $2 n^{2} v^{3}$
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Answer: A
Q372021 · 25 Jul 2021 · Shift 2
A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around : (take the value of g as $10 m/ s^{2}$ )
1. A.300 m
2. B.200 m
3. C.125 m
4. D.250 m
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Answer: C
Q472021 · 25 Jul 2021 · Shift 2
Two vectors $X$ and $Y$ have equal magnitude. The magnitude of $(X - Y)$ is n times the magnitude of $(X + Y)$ . The angle between $X$ and $Y$ is :
1. A. $cos^{- 1} (\frac{- n ^{2} - 1}{n ^{2} - 1})$
2. B. $cos^{- 1} (\frac{n ^{2} - 1}{- n ^{2} - 1})$
3. C. $cos^{- 1} (\frac{n ^{2} + 1}{- n ^{2} - 1})$
4. D. $cos^{- 1} (\frac{n ^{2} + 1}{n ^{2} - 1})$
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Answer: B
Q312021 · 22 Jul 2021 · Shift 2
What will be the projection of vector $A = \hat{i} + \hat{j} + \hat{k}$ on vector $B = \hat{i} + \hat{j}$ ?
1. A. $2 (\hat{i} + \hat{j} + \hat{k})$
2. B. $(\hat{i} + \hat{j})$
3. C. $2 (\hat{i} + \hat{j})$
4. D. $2 (\hat{i} + \hat{j} + \hat{k})$
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Answer: B
Q372021 · 22 Jul 2021 · Shift 2
A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ________ s.
1. A. $\frac{2 R _{e}}{g} [(1 + \frac{h}{R _{e}})^{\frac{3}{2}} - 1]$
2. B. $\frac{1}{3} \frac{R _{e}}{2 g} [(1 + \frac{h}{R _{e}})^{\frac{3}{2}} - 1]$
3. C. $\frac{R _{e}}{2 g} [(1 + \frac{h}{R _{e}})^{\frac{3}{2}} - 1]$
4. D. $\frac{1}{3} \frac{2 R _{e}}{g} [(1 + \frac{h}{R _{e}})^{\frac{3}{2}} - 1]$
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Answer: D
Q452021 · 22 Jul 2021 · Shift 2
What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?
1. A. $\frac{3}{2} k_{B} T$
2. B. $k_{B} T$
3. C. $\frac{2}{3} k_{B} T$
4. D. $\frac{1}{2} k_{B} T$
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Answer: A
Q492021 · 22 Jul 2021 · Shift 2
Choose the correct option
1. A.True dip is always equal to apparent dip.
2. B.True dip is not mathematically related to apparent dip.
3. C.True dip is less than the apparent dip.
4. D.True dip is always greater than the apparent dip.
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Answer: C
Q602021 · 22 Jul 2021 · Shift 2· Numerical answer
In 5 minutes, a body cools from $7 5^{\circ} C$ to $6 5^{\circ} C$ at room temperature of $2 5^{\circ} C$ . The temperature of body at the end of next 5 minutes is ________ $^{\circ} C$ .
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Answer: 57
Q442021 · 20 Jul 2021 · Shift 1
If $A$ and $B$ are two vectors satisfying the relation $A \cdot B = A \times B$ . Then the value of $A - B$ will be :
1. A. $A^{2} + B^{2} + 2 A B$
2. B. $A^{2} + B^{2}$
3. C. $A^{2} + B^{2} - 2 A B$
4. D. $A^{2} + B^{2} + 2 A B$
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Answer: C
Q452021 · 20 Jul 2021 · Shift 1
The entropy of any system is given by $S = α^{2} β ln [\frac{μ k R}{J β ^{2}} + 3]$ where $α$ and $β$ are the constants. $μ$ , J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take $S = \frac{d Q}{T}$ ] Choose the incorrect option from the following :
1. A. $α$ and J have the same dimensions.
2. B.S and $α$ have different dimensions
3. C.S, $β$ , k and $μ R$ have the same dimensions
4. D. $α$ and k have the same dimensions
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Answer: D
Q472021 · 20 Jul 2021 · Shift 1
1. A. $55.44 cm$
2. B. $18.23 cm$
3. C. $9.52 cm$
4. D. $37.58 cm$
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Answer: D
Q482021 · 20 Jul 2021 · Shift 1
1. A.(b)
2. B.(c)
3. C.(d)
4. D.(a)
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Answer: B
Q492021 · 20 Jul 2021 · Shift 1
The value of tension in a long thin metal wire has been changed from $T_{1}$ to $T_{2}$ . The lengths of the metal wire at two different values of tension $T_{1}$ and $T_{2}$ are $l_{1}$ and $l_{2}$ respectively. The actual length of the metal wire is :
1. A. $\frac{l _{1} + l _{2}}{2}$
2. B. $T_{1} T_{2} l_{1} l_{2}$
3. C. $\frac{T _{1} l _{2} - T _{2} l _{1}}{T _{1} - T _{2}}$
4. D. $\frac{T _{1} l _{1} - T _{2} l _{2}}{T _{1} - T _{2}}$
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Answer: C
Q552021 · 20 Jul 2021 · Shift 1· Numerical answer
The amplitude of wave disturbance propagating in the positive x-direction is given by $y = \frac{1}{1 + x ^{2}}$ at time $t = 0$ and $y = \frac{1}{1 + ( x - 2 ) ^{2}}$ at $t = 1 s$ , where x and y are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be ________ m/s.
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Answer: 2
Q582021 · 20 Jul 2021 · Shift 1· Numerical answer
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Answer: 100
Q392021 · 18 Mar 2021 · Shift 1
1. A.
2. B.
3. C.
4. D.
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Answer: B