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1.

Displacement-time equation of a particle executing SHM is `x=A sin (omega t+(pi)/6)` Time taken by the particle to go directly from `x=-A/2"to"x=+A/2`A. `(pi)/(3omega)`B. `(pi)/(2omega)`C. `(pi)/(omega)`D. `(pi)/(omega)`

Answer» Correct Answer - A
2.

Assertion : The graph of `PE` and `KE` of a particle is `SHM` with respect to position is a parabola Reason : This because `PE` and `KE` not vary linearly with positionA. If both statement -I and Statement -II are true , and statement-II is the correct explanation of statement -IB. If both statemenrt-I and Statement-II are true but statement-II is not the correct explanation of statement -IC. If statement -I is true but statement -II is false.D. If statement -I is true but statement -II is true

Answer» Correct Answer - B
3.

Two drops of same radius are falling through air with steady speed v. If the two drops coalesce, what would be the terminal speed –A. 4VB. 2VC. 3VD. `2^(2//3)`V

Answer» Correct Answer - D
4.

A solid cube of side a and density `rho_(0)` floats on the surface of a liquid of density `rho`. If the cube is slightly pushed downward, then it oscillates simple harmonically with a period ofA. `2pi(rhoL//sigmag)^(1//2)`B. `2pi(sigmaL//rhog)^(1//2)`C. `1//2pi(rhoL//sigmag)^(1//2)`D. `1//2pi(sigmaL//rhog)^(1//2)`

Answer» Correct Answer - B
5.

Assertion : If ice on the pole melts, length of the day will shorten. Reason: Ice will flow towards equator and will result in the decrease in moment of inertia of earth resulting in decrease in frequency of rotation of earth.A. If both statement -I and Statement -II are true , and statement-II is the correct explanation of statement -IB. If both statemenrt-I and Statement-II are true but statement-II is not the correct explanation of statement -IC. If statement -I is true but statement -II is false.D. If statement -I is true but statement -II is true

Answer» Correct Answer - C
6.

A standing tuning fork of frequency `f` is used to find the velocity of sound in air by resonance column appartus. The difference two resonating lengths is `1.0 m`. Then the velocity of sound in air isA. `fm//s`B. `2fm//s`C. `f//2m//s`D. `3fm//s`

Answer» Correct Answer - B
7.

One end of a glass capillary tube with a radius `r=0.05cm` is immersed into water to a depth of `h=2cm`.Excess pressure required to blow an air bubble out of the lower end of the tube will be `(S.T` of water `=70"dyne"//cm`).Take `g=980cm//s^(2)`.A. `480 N//m^(2)`B. `680 N//m^(2)`C. `120 N//m^(2)`D. `820//m^(2)`

Answer» Correct Answer - A
8.

Vibrating tuning fork of frequency `n` is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through `8.75 cm`, the intensity of sound changes from a maximum to minimum. If the speed of sound is `350 m//s`. Then `n` is A. 500HzB. 1000HzC. 2000HzD. 4000Hz

Answer» Correct Answer - B
9.

A whistle emitting a sound of frequency `440 H`z is tied to string of `1.5 m` length and rotated with an angular velocity of `20 rad//sec` in the horizontal plane. Then the range of frequencies heard by an observer stationed at a large distance from the whistle will `(v=330 m//s)`A. 400.0Hz to 484.0 HzB. 403.3 Hz to 480.0 HzC. 400.0 Hz to 480.0 HzD. 403.3Hz to 484.0Hz

Answer» Correct Answer - D
10.

The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by `y=2cm` `sin[(0.6cm^-1)x]cos[(500pis^-1)t]`. The length of the string isA. 24.6cmB. 12.5cmC. 20.6cmD. 15.7cm

Answer» Correct Answer - D
11.

The vibrations of string of length `60 cm` fixed at both ends are presented by the equations ` y = 4 sin ( pi x//15) cos ( 96 pi t)` where `x and y` are in cm and t in `s`. The maximum displacement at `x = 5 cm` isA. `2sqrt3cm`B. `3sqrt2cm`C. `sqrt2cm`D. `sqrt3cm`

Answer» Correct Answer - A
12.

Two rods of the same length and areas of cross-section `A_1` and `A_2` have their ends at the same temperature. `K_1` and `K_2` are the thermal conductivities of the two rods. The rate of flow of heat is same in both the rods if-A. `A_(1)/A_(2)=L_(1)/K_(2)`B. `A_(1)/A_(2)=K_(2)/K_(1)`C. `A_(1)A_(2)=K_(1)K_(2)`D. placed in hot oil

Answer» Correct Answer - B
13.

Two sound sources are moving in opposite directions with velocities `v_1` and `v_2(v_1gtv_2)`. Both are moving away from a stationary observer. The frequency of both the sources is 900 Hz. What is the value of `v_1-v_2` so that the beat frequency observed by the observer is 6 Hz? Speed of sound `v=300(m)/(s)`. Given that `v_1` and `v_2ltltltv`.A. 1m/sB. 2m/sC. 3m/sD. 4m/s

Answer» Correct Answer - B
14.

The frequency changes by `10%` as the source approaches a stationary observer with constant speed `v_S`, What sould be the percentage change in ferquency as the source recedes from the observer with the same speed? Given that `v_Sltltv` (v speed of sound in air).A. 0.143B. 0.2C. 0.167D. 0.1

Answer» Correct Answer - D
15.

For a certain organ pipe , three successive resonance observed are `425 , 595 and 765 Hz`. Taking the speed of sound to be `340 ms^(-1)` , find the length of the pipe , in meter .A. 2.0mB. 0.4mC. 1.0mD. 0.2m

Answer» Correct Answer - C
16.

It is said that a liquid rises or is depressed in a capillary due to the surface tension. If a liquid neither rises nor depresses in a capillary, can we conclude that the surface tension of the liquid is zero ?A. Angle of contact is `0^(0)`B. Angle of contact may be `90^(@)`C. Surface tension of the liquid must be zeroD. None of these

Answer» Correct Answer - B
17.

Mass `M` is split into two parts `m` and `(M-m)`, which are then separated by a certain distance. What is the ratio of `(m//M)` which maximises the gravitational force between the parts ?A. `m = M/4`B. `m = 2/3 M`C. `m = M/3`D. m = M/2`

Answer» Correct Answer - D
18.

`x_(1)=A sin (omegat-0.1x)` and `x_(2)=A sin (omegat-0.1 x-(phi)/2)` Resultant amplitude of combined wave isA. `2A cos (phi)/4`B. `Asqrt(2cosphi//2)`C. `2A (phi)/2`D. `Asqrt(2(1+cos(phi)/4))`

Answer» Correct Answer - A
19.

A body of weight 30N hangs from one end of a long, vertical spring whose other end is attached to a rigid support. The spring extends by 5cm when a force of 10N is applied to it. The time period of the vertical oscillations of the body isA. `2sqrt((15pi))s`B. `(pi//5)sqrt((3//2))sec`C. `(pi//10)sqrt((3//2))sec`D. `20)sqrt((2//3))sec`

Answer» Correct Answer - B
20.

In the bottom of a vessel with mercury there is a round hole of diameter `d=70mum`. At what maximum thickness of the mercury Layer will the liquid still not flow out through this hole ? `[rho_("mercury")=13600(kg)/(m^(3))]`A. `T/(r rhog)`B. `T/(2r rho g)`C. `(2T)/(r rhog)`D. `(4T)/(r rho g)`

Answer» Correct Answer - C
21.

A stationary wave is given by `y = 5 sin (pi x)/( 3) cos 40 pi t` where `x and y` are in `cm and t` is in second. a. What are the amplitude and velocity of the component wave whose superposition can give rise to this vibration ? b. What is the distance between the nodes ? c. What is the velocity of a particle of the string at the position ` x = 1.5 cm when t = 9//8 s`?A. 1.5cmB. 3cmC. 6cmD. 4cm

Answer» Correct Answer - B
22.

A body starts from rest from a point distant `r_(0)` from the centre of the earth. It reaches the surface of the earth whose radius is `R`. The velocity acquired by the body isA. `GM_(e)(1/R_(0)-1/R_(0))`B. `2GM_(2)(1/R_(e)-1/R_(e))`C. `GM_(e)sqrt(1/R_(e)-1/R_(0))`D. `sqrt(2gM_(e)(1/R_(e)-1/R_(0)))`

Answer» Correct Answer - D
23.

The mass of planet mars is `1/10` th of the mass of earth and radius is `1/2` of the radius of earth. If the scape velocity at the earth is 11.2km/s, then the scape velocity at Mars will beA. 10 km/sB. 5 km/sC. 20 km/sD. 40 km/s

Answer» Correct Answer - B
24.

A disc of radius `R` is pivoted at its rim. The period for small oscillations about an axis perpendicular to the plane of disc isA. `2pisqrt(R/g)`B. `2pisqrt((2R)/(3g))`C. `2pisqrt((2R)/(g))`D. `2pisqrt((3R)/(2g))`

Answer» Correct Answer - D
25.

There is a howizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius `R`. If the surface tension of the loop be `T`, then what will be the tension in the thread?A. `piR^(2)//T`B. `piR^(2)T`C. `2piRT`D. `RT`

Answer» Correct Answer - D
26.

The value of `g` at a particular point is `10 m s^(-2)`. Suppose the earth shrinks uniformly to half of its present size without losing any mass. The value of `g` at the same point (assuming that the distance of the point from the centre of the earth does not change) will now beA. `4.9 m//s^2`B. `3/1 m//s^(2)`C. `9.8m//s^(2)`D. `1/9.6 m//s^(2)`

Answer» Correct Answer - C
27.

A number of particles each of mass 0.75kg are placed at distances 1m, 2m, 4m, 8m etc. from origin along positive X axis. the intensity of gravitational field at the origin will be -A. GB. `3/4 G`C. `1/2 G`D. zero

Answer» Correct Answer - A
28.

If two balls of same metal weighing 5 gm and 10 gm strike with a target with the same velocity. The heat energy so developed is used for raising their temperature alone, then the temperature will be higherA. For bigger will be higherB. For smaller ballC. Eqyal for both the ballsD. None is correct form the above three

Answer» Correct Answer - C
29.

A student takes 50 g wax (specific heat `=0.6 kcal//kg^(@)C`) and heats it till it boils. The graph between temperature and time is as follows. Heat supplied to the wax per minute and boiling point are respectively.A. 500cal,50^(@)C`B. `1000cal,100^(@)`C. `1500cal,200^(@)CD. 3000cal,200^(@)C`

Answer» Correct Answer - C
30.

The temperature of a body is increased from `–73°C` to 327°C. Then the ratio of emissive power is –A. `1//9`B. `1//27`C. `27`D. `1//81`

Answer» Correct Answer - D
31.

A bucket full of hot water is kept in a room and it cools from 75°C to 70°C in T1 minutes, from 70°C to 65°C in `T_2` minutes and from 65°C to 60°C in `T_3` minutes. Then –A. `T_(1)=T_(2)=T_(3)~B. `T_(1) lt T_(2) lt T_(3)`C. `T_(1) gt T_(2) gt T_(3)`D. `T_(1) lt T_(2) gt T_(3)`

Answer» Correct Answer - B
32.

The rectangular surface of area `8 cm xx 4 cm` of a black body at temperature `127^(@)C` emits energy `E` per section if length and breadth are reduced to half of the initial value and the temperature is raised to `327^(@)C`, the ratio of emission of energy becomesA. `(3//8)E`B. `(9//16)E`C. `(81//16)E`D. `(81//64)E`

Answer» Correct Answer - D