1. Force of friction and tension in a string in
a) gravitational forces
b) weak forces
c) electromagnetic forces
d) nuclear forces

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2. Role of DNA in heredity is the basis of___________.
a) genetic engineering
b) genetic modification
c) genetic transcription
d) none of these

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1. In the division of two quantities, the maximum value of fractional error is equal to
a) difference of fractional errors in the individual quantities
b) sum of fractional errors in the individual quantities
c) Either (a) or (b)
d) Neither (a) nor(b)

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2. If L and R denote inductance and resistance, respectively then the dimensions of L/R are
a) M¹L⁰T⁰Q^-1
b) M⁰L⁰TQ⁰
c) M⁰L¹T^-1Q⁰
d) M^-1LT⁰Q^-1

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1. A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on . Each step is 1 m long and takes 1s. There is a pit on the road 11m away from the starting point. The drunkard will fall into the pit after
a) 29 s
b) 21 s
c) 37 s
d) 31 s

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2. For motion of an object along the x-axis, the velocity v depends on the displacement x as v = 3x² - 2x, then what is the acceleration at x = 2 m
a) 48 ms^-2
b) 80ms^-2
c) 18 ms^-2
d) 10 ms^-2

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1. A body is moving in a circle of radius 100 cm with a time period of 2 second.The acceleration of the body is
a) 100 π cm/s²
b) 100 π² cm/s²
c) 200 π² cm/s²
d) 200π cm/s²

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2. In the above question, the total distance covered by the body in 8 seconds is
a) 9 m
b) 12 m
c) 18 m
d) 27 m

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1. Friction always _________.
a) Opposes relative motion
b) Opposes motion
c) Both a and b
d) None of these

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2. If the coefficient of friction between all surfaces ( for the shown diagram) is 0.4, then find the minimum force F to have equilibrium of the system

a) 62.5 N
b) 150 N
c) 31.25N
d) 50N

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1. The potential energy function associated with the force $\vec{F}$ = $4xy\hat{i} + 2x^{2}\hat{j}$ is
a) U = -2x²y
b) U = -2x²y + constant
c) U = 2x² y + constant
d) Not defined

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2. The K.E. acquired by a mass m in travelling a certain distance d, starting from rest, under the action of constant force is directly proportional to
a) m
b) √m
c) 1/√m
d) None of these

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1. The rate of_____________of a body about a given axis is___________to__________applied on the body.
a) The external torque ; directly proportional ; change of angular momentum
b) Change of angular momentum ; directly proportional ; the external torque
c) Both a and b
d) None of these

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2. Acceleration of a solid cyclinder rolling without slipping down an incline of inclination θ is
a) (2/3) g sin θ
b) (2/3) g cos θ
c) (2/3) g
d) (2/3) g tan θ

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1. As observed from th eearth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, the acceleration due to gravity
a) be similarly true
b) not be true because the force between earth and mercury is not inverse square law
c) not be true because the major gravitational force on mercury is due to sun
d) not be true because other than gravitational forces

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2. The masses and radii of the earth and the Moon are M₁, R₁ and M₂, R₂, respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is
a) $\sqrt{\frac{2G\left (M_{1} + M_{2} \right )}{d}}$
b) $\sqrt{\frac{4G\left (M_{1} + M_{2} \right )}{d}}$
c) $\sqrt{\frac{4GM_{1}M_{2}}{d}}$
d) $\sqrt{\frac{G\left (M_{1} + M_{2} \right )}{d}}$

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1. The dimensions of four wires of the same material are given below. In which wire the increase in the length will be maximum?
a) Length 100cm, diameter 1mm
b) Length 200 cm, diameter 2 mm
c) Length 300 cm, diameter 3mm
d) Length 50cm, diameter 0.5mm

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2. Two blocks of masses 1kg and 2kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is (40/3π) x 10⁶ N/m² . If g = 10m/s², then what should be the minimum radius of the wire used if it is not to break?
a) 0.5mm
b) 1mm
c) 1.5 mm
d) 2mm

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1. For a ball falling in a liquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is
a) 1
b) (2 α² ρ g/ 9η²)
c) (2 α² (ρ - σ)g/ 9η)
d) none of these

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2. A sphere of relative density σ and diamter D has concentric cavity of diameter d. When the sphere just floats on water in a tank, the ratio of D/d is ( σ-1 /σ)^1/3.
a) True
b) False

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1. A sphere, a cube and a thin circular plate, all of same material and same mass are initially heated to same high temperature.
a) Plate will cool fastest and cube the slowest
b) Sphere will cool fastest and cube the slowest
c) Plate will cool fastest and sphere the slowest
d) Cube will cool fastest and plate the slowest

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2. A sphere, a cube and a thin circular plate are made of same substance and all have mass . These are heated to 200⁰C and then placed in a room. Then the
a) Temperature of sphere drops to room temperature at last
b) Temperature of cube drops to room temperature at last
c) Temperature of thin circular plate drop to room temperature at last
d) Temperatures of all the three drop to room temperature at the same time

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1. Specific heat of a gas during an isothermal change is
a) zero
b) positive
c) negative
d) infinity

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2. A reversible engine converts one-sixth of the heat input into work. When the temp. of the sink is reduced by 62⁰C, the efficiency of the engine is doubled. The temp. source and sink are
a) 95⁰C , 37⁰C
b) 80⁰C , 37⁰C
c) 99⁰C, 37⁰C
d) 90⁰C, 37⁰

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1. A sample of an ideal gas is taken through the cyclic process ABCA shown in fig. It rejects 50J of heat during the part AB, does not absorb or reject the heat during BC, and accepts 70J of heat during CA, Forty joules of work is done on the gas during the part BC. The internal energies at B and C, respectively, will be

a) 1450 J and 1410J
b) 1550J and 1590 J
c) 1450J and 1490J
d) 1550J and 1510J

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2. A container of volume 1m is divided into two equal compartments by a partition. One of these compartments contains an ideal gas at 300K. The other compartment is vacuum. The whole system is thermally isolated from its surrounding. The partition is removed and the gas expands to occupy the whole volume of the container . Its temperature now would be
a) 300 K
b) 250 K
c) 200K
d) 10K

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1. A block of mass m is suspended from a spring and executes vertical SHM of time period T as shown in fig. The amplitude of the SHM is A and spring is never in compressed state during the oscillation. The magnitude of minimum force exerted by spring on the block is

a) $mg - \frac{4\pi^{2}}{T^{2}}mA$
b) $mg + \frac{4\pi^{2}}{T^{2}}mA$
c) $mg - \frac{\pi^{2}}{T^{2}}mA$
d) $mg + \frac{\pi^{2}}{T^{2}}mA$

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2. A particle executes simple harmonic motion between x- -A and x= +A. The time taken for it to go from 0 to A/2 is T₁, and to go from A/2 to A is T₂ . Then
a) T₁ < T₂
b) T₁ > T₂
c) T₁ = T₂
d) T₁ = 2T₂

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1. The equation of a wave on a string of linear mass density 0.04 kg m^-1 is given by
y = 0.02(m)sin[2π(t/0.04(s)-(x/0.50(m)))]
The tension in the string is
a) 12.5 N
b) 0.5 N
c) 6.25 N
d) 4.0 N

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2. Two waves are passing through a region in the same direction at the same time. If the equation of these waves are
y₁ = $asin\frac{2\pi}{\lambda}\left (vt - x \right )$
and y₂ = $bsin\frac{2\pi}{\lambda}\left [\left (vt - x \right ) + x_{0} \right ]$
then the amplitude of the resulting wave for x₀ = (λ/2) is
a) |a - b|
b) a + b
c) $\sqrt{a^{2} + b^{2}}$
d) $\sqrt{a^{2} + b^{2} + 2ab cos x}$

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1. Which of the following pairs of forces cannot be added to give a resultant force of 4N?
a) 2N and 8N
b) 2N and 2N
c) 2N and 6N
d) 2N and 4N

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2. Two point masses 1 and 2 move with uniform velocities $\vec{v}_{1}$ and $\vec{v}_{2}$, respectively. Their initial position vectors are $\vec{r}_{1}$ and $\vec{r}_{2}$, respectively . Which of the following should be satisfied for the collision of the point masses?
a) $ \frac{\vec{r}_{1} - \vec{r}_{2}}{\left | \vec{r}_{2} - \vec{r}_{1} \right |}$ = $\frac{\vec{v}_{2} - \vec{v}_{1}}{\left | \vec{v}_{2} - \vec{v}_{1} \right |}$
b) $ \frac{\vec{r}_{2} - \vec{r}_{1}}{\left | \vec{r}_{2} - \vec{r}_{1} \right |}$ = $\frac{\vec{v}_{2} - \vec{v}_{1}}{\left | \vec{v}_{2} - \vec{v}_{1} \right |}$
c) $ \frac{\vec{r}_{2} - \vec{r}_{1}}{\left | \vec{r}_{2} + \vec{r}_{1} \right |}$ = $\frac{\vec{v}_{2} - \vec{v}_{1}}{\left | \vec{v}_{2} + \vec{v}_{1} \right |}$
d) $ \frac{\vec{r}_{2} + \vec{r}_{1}}{\left | \vec{r}_{2} + \vec{r}_{1} \right |}$ = $\frac{\vec{v}_{2} - \vec{v}_{1}}{\left | \vec{v}_{2} + \vec{v}_{1} \right |}$

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1. A body of mass 3 kg moving with a velocity of 4 m/s towards left collides head on with body of mass 4 kg moving in opposite direction with a velocity of 3 m/s. After collision the two bodies stick together and move with a common velocity which is
a) zero
b) 12 m/s towards left
c) 12 m/s towards right
d) $\frac{12}{7}$ m/s towards left

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2. A heavy chain of length 1 m and weight 20 kg hangs vertically with one end attached to a peg and carries a block of mass 10 kg at the other end. Find the height by which the centre of mass of the system of chain + block rises.
a) 0.417 m
b) 0.437 m
c) 0.365 m
d) 0.405 m

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1. A uniform sphere of mass m, radius r and moment of inertia I about its centre moves along the x-axis as shows in Figure. Its centre of mass moves with velocity = v₀ and it rotates about its centre of mass with angular velocity = ω₀. Let $\vec{L}$ = (Iω₀ + mv₀r)(-k). THe angular momentum of the body about the origin O is

a) $\vec{L}$, only if v₀ = ω₀r
b) greater than $\vec{L}$, if v₀ ω₀r
c) less than $\vec{L}$, if v₀ > ωr
d) $\vec{L}$, for all values of ω₀ and v₀

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2. A yo-yo is placed on a rough horizontal surface and a constant force F, which is less than its weight, pulls it vertically. Due to this

a) friction force acts towards left, so it will move towards left
b) friction force acts towards right, so it will move towards right
c) it will move towards left, so friction force acts towards left
d) it will move towards right so friction acts towards right

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1. A tank is filled with water of density 10³ kg/m³ and oil of density 9 × 10³ kg/m³. The height of water layer is 1 m and that of the oil layer is 4 m. The velocity of efflux from an opening in the bottom of the tank is
a) $\sqrt{85}m/s$
b) $\sqrt{88}m/s$
c) $\sqrt{92}m/s$
d) $\sqrt{98}m/s$

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2. A square box of water has a small hole located in one of the bottom corners. When the box is full and sitting on a level surface, complete opening of the hole results in a flow of water with speed v₀, as shown in figure (a) . When the box is still half empty, it is tilted by 45⁰ so that the hole is at the lowest point. Now the water will flow out with a speed of

a) v₀
b) v₀/2
c) $\frac{v_{0}}{\sqrt{2}}$
d) $\frac{v_{0}}{\sqrt[4]{2}}$

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