InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 351. |
Integrate the following (1)`intx^(-3/2)dx` (2)`intsin60^(@)dx` (3)`int(1)/(10x)dx`(4)`int(2x^(3)-x^(2)+1)dx` |
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Answer» Correct Answer - (i)`-2x^(-3//2)+C` (ii)`(sqrt(3))/(2)x+C` (iii)`(1)/(10)logx+C` (iv)`(x^(4))/(2)-(x^(3))/(3)+x+C` |
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| 352. |
The radius of spherical bubble is changing with time. The rate of change of its volume is given by :A. `4pir^(2)(dr)/(dt)`B. `(4)/(3)pir^(2)`C. `(8)/(3)pir^(2)`D. `(8)/(3)pir(dr)/(dt)` |
| Answer» Correct Answer - A | |
| 353. |
Evaluate the following definite integrals. (a)`int_(0)^(3)(x^(2)+1)dx` (b)`int_(2)^(3)(x^(3)-4x^(2)+5x-10)dx` (c)`int_(0)^(pi//4)(cosx-sinx)dx` |
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Answer» Correct Answer - (a) 12 (b)`-(79)/(12)` (c)`sqrt(2)-1` |
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| 354. |
The pressure P and volume V of a gas are related as `PV^(3//2)=K` where K is a constant. The percentage increase in the pressure for a diminution of `0.5%` of the volume isA. `0.25%`B. `0.75%`C. `1.50%`D. `0.50%` |
| Answer» Correct Answer - B | |
| 355. |
A soap film in formed on a frame of area `4xx10^(-3)m^(2)`. If the area of the film in reduced to half, then the change in the potential energy of the film is (surface tension of soap solution`=40xx10^(-3)N//m)`A. `32xx10^(-5)` JB. `16xx10^(-5)` JC. `8xx10^(-5)` JD. `16xx10^(-5)` J |
| Answer» Correct Answer - A | |
| 356. |
An ideal gas is subjected to a thermodynamic process `PV^(2//5)=0.40` where P is in Pa and V is in `m^(3)`. What is the slope of the P-V curve with volume plotted against x-axis at V=1 `m^(3)`?A. -1B. -3.5C. -2.5D. None of these |
| Answer» Correct Answer - A | |
| 357. |
Given that `y=(10)/(sinx+sqrt(3)cosx)`.Minimum value of y isA. zeroB. 2C. 5D. `10//(1+sqrt()3)` |
| Answer» Correct Answer - C | |
| 358. |
(5)Value of `int_(0)^(2)3x^(2)dx+int_(0)^(pi//2)sinxdx`is |
| Answer» Correct Answer - 9 | |
| 359. |
The value of integral `int_(2)^(4)(dx)/(x)` is :-A. `3 log_(e)2`B. `log_(e)2`C. `log_(e)4`D. `2log_(e)8` |
| Answer» Correct Answer - B | |
| 360. |
Evaluate the following indefinite integrals. (a)`int(dx)/(sqrt(x))` (b)`int(dx)/((2x+3))` (c)`intsin(2pix+30^(@))dx` (d)`intsinxcosxdx` (e)`int(3x^(3)-5x^(2)+2)dx` (f)`int(2e^(-x//3)dx` |
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Answer» Correct Answer - (a)`2sqrt(x)+C` (b)`(1)/(2)l n(2x+3)+C` (c)`-(1)/(2pi)cos(2pix+30^(@))+C` (d)`-(1)/(4)cos2x+C` (e)`3(x^(4))/(4)-(5x^(3))/(5)+2x+C` (f)`-6e^(-x//3)+C` |
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| 361. |
Find the value of `x_(1)`, so that `int_(0)^(x_(1))ydx=5` |
| Answer» Correct Answer - 3 | |
| 362. |
Givne `(x)/(y)=(5)/(6)` now x is reduced by 62 and the ratio of x and y becomes `(2)/(3)` then find x and y respectively :-A. 310, 372B. 392, 330C. 500, 600D. 250, 300 |
| Answer» Correct Answer - A | |
| 363. |
The pressure (P) and absolute temperature (T) of an ideal gas are related to each other as `Pprop(1)/(T^(2))`. If temperature of gas is 300 K and its volume changes from V to 8 V, then find the final temperature of gas.A. 600 KB. 300 KC. 373 KD. 273 K |
| Answer» Correct Answer - A | |
| 364. |
If `yx^(2)/(3)="constant"` when x=x_(1)`, then y=300, then find the y when `x=(8x_(1))/(27)`A. 450B. 375C. 675D. 405 |
| Answer» Correct Answer - C | |
| 365. |
If `y=propx^(4)` When`x=1000, y=y_(1)` then find the value of x so that value of y can be `2y_(1)` ,A. 2000B. 1190C. 1410D. 4000 |
| Answer» Correct Answer - B | |
| 366. |
`4sqrt(6)xx3sqrt(24)`= :-A. (1) 124B. (2)134C. (3) 144D. (4) 154 |
| Answer» Correct Answer - C | |
| 367. |
Choose the correct statement :-A. Time period of a simple pendulum depends on amplitude.B. Time shown by a spring watch varies with acceleration due to gravity g.C. In a simple pendulum, time period varies linearly with the length of the pendulum.D. The graph between length of the pendulum and time period is a parabola. |
| Answer» Correct Answer - D | |
| 368. |
A simple pendulum has a time period T in vacuum. Its time period when it is completely immersed in a liquid of density one-eight of the density of material of the bob isA. `sqrt((7)/(8))T`B. `sqrt((5)/(8))T`C. `sqrt((3)/(8))T`D. `sqrt((8)/(7))T` |
| Answer» Correct Answer - D | |
| 369. |
The time period of a simple pendulum in a stationary train is T. The time period of a mass attached to a spring is also T. The train accelerates at the rate `5 m//s^(2)`. If the new time periods of the pendulum and spring be `T_(P)` and `T_(S)` respectively, then :-A. `T_(P)=T_(S)`B. `T_(P)gtT_(S)`C. `T_(P)ltT_(S)`D. Cannot be predicted |
| Answer» Correct Answer - C | |
| 370. |
The amplitude of damped oscillator becomes `1/3` in `2s`. Its amplitude after `6s` is `1//n` times the original. The value of `n` isA. `3^(2)`B. `root(3)(2)`C. `root(3)(3)`D. `3^(3)` |
| Answer» Correct Answer - D | |
| 371. |
A simple pendulm has a length L and a bob of mass M. The bob is vibrating with amplitude a .What is the maximum tension in the string?A. mgB. `mg[1+((a)/(L))^(2)]`C. `mg[1+((a)/(2L))]^(2)`D. `mg[1+((a)/(L))]^(2)` |
| Answer» Correct Answer - B | |
| 372. |
There are two bodies A & B of same mass body A is at rest while body B is under going uniform motion, which is correct statements ?A. Inertia of `Agt`inertia of B.B. Inertia of `Bgt` inertia of A.C. Inertia of A = inertia of B.D. Either `1^(st), 2^(nd)" or "3^(rd)` depending upon the shape of body. |
| Answer» Correct Answer - C | |
| 373. |
Two cars A and B are moving in same direction with velocities 30 m/s and 20 m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of `2m//s^(2)`. There will be no collision when :-A. `dlt2.5`mB. `dlt125`mC. `dgt25`mD. `dgt125`m |
| Answer» Correct Answer - C | |
| 374. |
Two turning forks of frequencies `n_(1)` and `n_(2)` produces n beats per second. If `n_(2)` and n are known, `n_(1)` may be given byA. `(n_(2))/(n)+n_(2)`B. `n_(2)n`C. `n_(2)+-n`D. `(n_(2))/(n)-n_(2)` |
| Answer» Correct Answer - C | |
| 375. |
In the figure , the intensity of waves arriving at D from two coherent soucrces `s_(1) and s_(2) is I_(0)`. The wavelength of the wave is ` lambda = 4 m` . Resultant intensity at D will be A. `4I_(0)`B. `I_(0)`C. `2I_(0)`D. zero |
| Answer» Correct Answer - C | |
| 376. |
When a guitar is sounded with a 440 Hz tuning fork, a beat frequency of 5 Hz is heard. If the experiment is repeated with a tuning fork of 437 Hz, the beat frequency is 8 Hz. The string frequency (in Hz) is :-A. 445B. 435C. 429D. 448 |
| Answer» Correct Answer - A | |
| 377. |
Find interaction force between 3Kg and 4Kg block. |
| Answer» Correct Answer - 25 N | |
| 378. |
The dot product of two vectors of magnitudes 3 units and 5 units cannot be :- (i) -20 (ii) 16 (iii) -10 (br) 14A. (i,iii)B. (i,ii)C. (i, iv)D. (ii, iii, iv) |
| Answer» Correct Answer - B | |
| 379. |
If `vecP=vec(KQ)` (Here K is constant) them :-A. `vecP||vecQ`B. `vecP||vecQ`C. `vecP_|_vecQ`D. Both (1) and (2) |
| Answer» Correct Answer - D | |