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.
| 101. |
Suppose the sun expands so that its radius becomes `100` times its present radius and its surface temperature becomes half of its present value. The total energy emited by it then will increase by a factor of :A. `10^(4)`B. 625C. 256D. 16 |
| Answer» Correct Answer - B | |
| 102. |
A satellite is to be geo-stationary, which of the following are essential conditions?A. a & bB. a, b & cC. c & dD. a, b, c & d |
| Answer» Correct Answer - D | |
| 103. |
Let `P(x) = x^(7) - 3x^(5) +x^(3) - 7x^(2) +5` and `q(x) = x- 2`. The remainder if `p(x)` is divided by `q(x)` isA. `(5)/(2)`B. 5C. 17D. `-3` |
| Answer» Correct Answer - C | |
| 104. |
The sum of the solutions of the equations `9^(x) - 6.3^(x) +8 = 0` isA. `log_(3)2`B. `log_(3)6`C. `log_(3)8`D. `log_(3)4` |
| Answer» Correct Answer - B | |
| 105. |
If `x +y =a` and `x^(2) +y^(2)=b`, then the value of `(x^(3)+y^(3))`, isA. abB. `a^(2)+b`C. `a+b^(2)`D. `(3ab-a^(3))/(2)` |
| Answer» Correct Answer - D | |
| 106. |
The expression `3(a^2+1)^2+(2(a-1)(a^2+1)-5(a-1)^2-4(0.75a^4+3a-1)` when sinplified redues toA. `2a^(3)-a^(2)`B. `2a^(2)-a^(3)`C. `2a^(3)`D. `2a^(2)` |
| Answer» Correct Answer - A | |
| 107. |
In the following figure, if `PQ = R` (P is the centre of the bigger circle) and the shaded area is equal to A, then the radius of the inner circle is equal to - A. `(pi R-A)`B. `sqrt((piR-(A)/(pi)))`C. `sqrt(R-(A)/(pi))`D. `sqrt(R^(2)-(A)/(pi))` |
| Answer» Correct Answer - D | |
| 108. |
If `(a^(2)+b^(2))^(3) = (a^(3)+b^(3))^(2)` and `ab ne 0` then the numerical value of `(a)/(b)+ (b)/(a)` is equal to-A. `(3)/(2)`B. `(2)/(3)`C. 1D. `(4)/(9)` |
| Answer» Correct Answer - B | |
| 109. |
The ratio to total are of the rectangle to the total shaded area A. `(2)/(pi)`B. `(4)/(4-pi)`C. `(4-pi)/(pi)`D. `(pi)/(4)` |
| Answer» Correct Answer - B | |
| 110. |
If x,y are real numbers such that `3^((x)/(y)+1) -3^((x)/(y)-1) = 24`, then the value of `(X+y)//(x-y)` is:- |
| Answer» Correct Answer - D | |
| 111. |
The value of y which will satisfy the equations `2x^(2)+6x +5y +1 = 0` and `2x +y +3 = 0` may be found by solving:-A. `y^(2)+14y - 7= 0`B. `y^(2)+8y +1 = 0`C. `y^(2)+10y - 7 = 0`D. `y^(2)+y-12 = 0` |
| Answer» Correct Answer - C | |
| 112. |
How many real numbers x satisfy the equation `3^(2x+2)-3^(x+3)-3^(x)+3 = 0`? |
| Answer» Correct Answer - C | |
| 113. |
The angles of a triangle are in the ratio of 2:3:4, the measurement of greatest angle is-A. `30^(@)`B. `60^(@)`C. `100^(@)`D. `80^(@)` |
| Answer» Correct Answer - B | |
| 114. |
Let `T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(1)/(sqrt(6)-sqrt(5))+(1)/(sqrt(5)+2)` then-A. `T lt 1`B. `T = 1`C. `1 lt T lt 2`D. `T lt 2` |
| Answer» Correct Answer - B | |
| 115. |
The ratio of the areas of the incircle and the circumcircle of a square is-A. `1:sqrt(2)`B. `1:sqrt(3)`C. `1:4`D. `1:2` |
| Answer» Correct Answer - D | |
| 116. |
in the figure given below , if the areas of the regions are equal then which of the following is true ? A. `x = y`B. `x = 2y`C. `2x = y`D. `x^(2) = y^(2)` |
| Answer» Correct Answer - A::B::D | |
| 117. |
In the following figure `AC = 10 & BD = 14`, then area of quadrilateral ABCD- A. `70 sqrt(3)`B. `140 sqrt(3)`C. `35 sqrt(3)`D. 70 |
| Answer» Correct Answer - C | |
| 118. |
Value of `((x^(4)+x^(2)+1))/((x^(2)-x+1))-(x+1)^(2)` isA. xB. `-x`C. 2xD. 3x |
| Answer» Correct Answer - B | |
| 119. |
If `tan^(4)theta +tan^(2) theta = 2`, then the value of `cos^(4)theta +cos^(2)theta` is-A. `(3)/(4)`B. `(3)/(2)`C. `(1)/(2)`D. 1 |
| Answer» Correct Answer - C | |
| 120. |
Depending on in which quadrant an angle `theta` lies, functions `costheta` and `sintheta` may be positive or negative. In the second column of the given lable are specified whether these functions are positive or negative and in the first column are specified quadrants. `{:("Column-I","Column-II"),((A)" First",(P)sintheta" is positive"),((B)" Second",(Q)sintheta" is negative"),((C)" Third",(R)costheta" is negative"),((D)" Fourth",(S)tantheta" and "sintheta"both are negative"),(,(T)sectheta" is negative and "sintheta" is positive"):}` |
| Answer» Correct Answer - `(A) to (P) ; (B) to (P,R,T); (C ) to (Q,R); (D) to (Q,S)` | |
| 121. |
Suggest suitable match between fuction given in the first column and its description given in the second column. `{:("Column-I","Column-II"),((A) sin""(390^(@)),(P)" Positive"),((B)sin""(-30^(@)),(Q)" Negative"),((C)cos""120^(@),(R)" Zero"),((D) tan""(-120^(@)),(S)" Modulus is greater"):}` |
| Answer» Correct Answer - `(A) to (P,T); (B) to (Q,T) ; ( C) to (Q,T) ; (D) to (P,S)` | |
| 122. |
If `tantheta=(24)/(7)` and `sintheta` is negative then value of `costheta` will beA. `(7)/(25)`B. `-(7)/(25)`C. `(24)/(25)`D. `-(24)/(25)` |
| Answer» Correct Answer - B | |
| 123. |
If `vpropt^(5//2)` thenA. `vpropt^(3//2)`B. `a prop sqrt(t)`C. Both aboveD. `v prop sqrt(t) |
|
Answer» Correct Answer - C `"(""Hint".v=(dx)/(dt),a=(dv)/(dt)")"` |
|
| 124. |
How many solid spherical balls of radius 2cm and b are constants. If `f(2)=1" and "f(-3)=11`,A. 4B. 16C. 32D. 64 |
| Answer» Correct Answer - D | |
| 125. |
If m and n are the two natural number such that `m^(n)=25`, then find the value of `n^(m)`:- |
| Answer» Correct Answer - 4 | |
| 126. |
Which of the following conditions imply that the real number x is rational ? `(i) x^(1//2)"is rational"" "(ii) x^(2)and x^(5) "are rational"" "(iii) x^(2)and x^(4)"are rational"`A. I and II onlyB. I and II onlyC. II and III onlyD. I,II and III |
| Answer» Correct Answer - A | |
| 127. |
If `x = sqrt(7)+(1)/(sqrt(7))`, then the value of `(128)^(x^(2))` is-A. `2^(40)`B. `2^(64)`C. `2^(56)`D. `2^(24)` |
| Answer» Correct Answer - B | |
| 128. |
Given that `y=sin3x+(4)/(3)cos3x`. What is the maximum rate of change in y with respect to x ? |
| Answer» Correct Answer - 7.5 | |
| 129. |
Differentiation of cos `(sqrt(x))` with respect to x isA. `-sinsqrt(x)`B. `-(1)/(2sqrt(x))sinsqrt(x)`C. `-sqrt(x)sinsqrt(x)`D. `-(1)/(sqrt(x))sinsqrt(x)` |
| Answer» Correct Answer - B | |
| 130. |
Two waves are given by `y_(1)=asin(omegat-kx)` and `y_(2)=a cos(omegat-kx)`. The phase difference between the two waves is -A. `(lambda//2pi)phi`B. `((phi+(pi//2))/(2pi))lambda`C. `(2pi)/(lambda)(phi-(pi)/(2))`D. `(2pi)/(lambda)phi` |
| Answer» Correct Answer - B | |
| 131. |
Ice at `-20^(@)C` mixed with 200g water at `25^(@)C`. If temperature of mixture is `10^(@)C` then mass of ice is -A. 30 gmB. 20 gmC. 15 gmD. 40 gm |
| Answer» Correct Answer - A | |
| 132. |
The ratio of number of collisions per second at the walls of containers by He and `O_(2)` gas molecules kept at same volume and temperature is (assume normal incidence on walls)A. `2 : 1`B. `1 : 2`C. `2sqrt(2) : 1`D. `1 : 2sqrt(2)` |
| Answer» Correct Answer - C | |
| 133. |
Calculate the time required to heat 20 kg of water from `10^(@)C` to `35^(@)C` using an immersion heater rated 1000 W. Assume that `80%` of the power input is used to heat the water. Specific heat capacity of water`=4200 J//kg-k`A. 40 minB. 44 minC. 36 minD. 48 min |
| Answer» Correct Answer - B | |
| 134. |
The sum of all value of x so that `16^((x^(2)+_3x-1))=8^((x^(2)+3x+2))`, isA. 2B. 3C. `-3`D. `-5` |
| Answer» Correct Answer - C | |
| 135. |
If `(21.4)^(a) = (0.00214)_(b) = 100`, then the value of `(1)/(a)-(1)/(b)` isA. is a rational numberB. primeC. irrationalD. composite |
| Answer» Correct Answer - D | |
| 136. |
Which of the following force is not conservative :-A. `bar(F)=3hati+4hatj`B. `bar(F)=3xhati+4yhatj`C. `bar(F)=3yhati+4xhatj`D. `bar(F)=3x^(2)hati+4y^(2)hatj` |
| Answer» Correct Answer - C | |
| 137. |
The potential energy of a particle of mass 1 kg moving along x-axis given by `U(x)=[(x^(2))/(2)-x]J`. If total mechanical speed (in m/s):-A. `sqrt(5)`B. `sqrt(7)`C. `sqrt(3)`D. None |
| Answer» Correct Answer - A | |
| 138. |
The potential energy of an object of mass m moving in xy plane in a conservative field is given by U = ax + by , where x and y are position coordinates of the object. Find magnitude of its acceleration :-A. `(sqrt(a^(2)+b^(2)))/(m)`B. `(a^(2)+b^(2))/(m)`C. `sqrt(a^(2)+b^(2))`D. None |
| Answer» Correct Answer - A | |
| 139. |
A particle executes simple harmonic motion according to equation `4(d^(2)x)/(dt^(2))+320x=0`. Its time period of oscillation is :-A. `(2pi)/(5sqrt(3))s`B. `(pi)/(3sqrt(2))s`C. `(pi)/(2sqrt(5))s`D. `(2pi)/(sqrt(3))s` |
| Answer» Correct Answer - C | |
| 140. |
`alpha` and `beta` are the angle made by a vector from positive x & positive y-axes redpectively. Which set of `alpha` and `beta` is not possibleA. `60^(@),60^(@)`B. `45^(@), 60^(@)`C. `60^(@), 45^(@)`D. `30^(@), 45^(@)` |
| Answer» Correct Answer - D | |
| 141. |
A particle located in one dimensional potential field has potential energy function`U(x)=(a)/(x^(2))-(b)/(x^(3))`, where a and b are positive constants. The position of equilibrium corresponds to x equal toA. `(3a)/(2b)`B. `(2b)/(3a)`C. `(2a)/(3b)`D. `(3b)/(2a)` |
| Answer» Correct Answer - D | |
| 142. |
A particle of mass m in a unidirectional potential field have potential energy `U(x)=alpha+2betax^(2)`, where `alpha` and `beta` are positive constants. Find its time period of oscillations.A. `2pisqrt((2beta)/(m))`B. `2pisqrt((m)/(2beta))`C. `pisqrt((m)/(beta))`D. `pisqrt((beta)/(m))` |
| Answer» Correct Answer - C | |
| 143. |
When a block of mass m is suspended separately by two different springs have time period `t_(1)" and "t_(2)`. If same mass is connected to parallel combination of both springs, then its time period is given by :-A. `(t_(1)t_(2))/(t_(1)+t_(2))`B. `(t_(1)t_(2))/(sqrt(t_(1)^(2)+t_(2)^(2)))`C. `sqrt((t_(1)t_(2))/(t_(1)+t_(2)))`D. `t_(1)+t_(2)` |
| Answer» Correct Answer - B | |
| 144. |
A particle moving on x - axis has potential energy `U = 2 - 20x + 5x^(2)` joule along x - axis. The particle is relesed at `x = -3`. The maximum value of `x` will be (`x` is in metre)A. 5 mB. 3 mC. 7 mD. 8 m |
| Answer» Correct Answer - C | |
| 145. |
A particle executing S.H.M. has angular frequency `6.28 s^(-1)` and amplitude 10 cm find (a) the time period (b) the maximum speed ( c ) the maximum acceleration (d) the speed when the displacement is 6 cm from the mean postiton ( e ) the speed at `t=1//6`s assuming that the motion starts from rest at t=0 |
| Answer» Correct Answer - `"["1s,0.628(m)/(s),4(m)/(s^(2)),50.2(cm)/(s),-54.4(cm)/(s)"]"` | |
| 146. |
In forced oscillations , a particle oscillates simple harmonically with a frequency equal toA. Frequency of driving forceB. Natural frequency of bodyC. Difference of frequency of driving force and natural frequencyD. Mean of frequency of driving force and natural frequency |
| Answer» Correct Answer - A | |
| 147. |
A 100 g mass stretches a particular spring by 9.8 cm, when suspended vertically from it. How large a mass must be attached to the spring if the period of vibration is to be 6.28 s?A. 1000gB. `10^(5)g`C. `10^(7)g`D. `10^(4)g` |
| Answer» Correct Answer - D | |
| 148. |
Railway tracks are banked at the curves so that :A. the train may not fall down inwardsB. the weight of the train may be reducedC. the necessary centripetal force to train may be obtained from the horizontal compoinent of the reaction force of railway tracksD. no frictional force may be produced between the wheel and the track |
| Answer» Correct Answer - C | |
| 149. |
A liquid flows in a tube from left to right as shown in figure. `A_(1)` and `A_(2)` are the cross-section of the portions of the tube as shown. Then the ratio of speeds `v_(1)//v_(2)` will be A. `A_(1)//A_(2)`B. `A_(2)//A_(1)`C. `sqrt(A_(2))//sqrt(A_(1))`D. `sqrt(A_(1))//sqrt(A_(2))` |
| Answer» Correct Answer - B | |
| 150. |
A vessel contains a mixture of nitrogen of mass 7 g and carbon dioxide of mass 11 g at temperature 290 K and perssure 1 atm.Find the density of the mixture.A. 1.1 g/LB. 1.2 g/LC. 1.51 g/LD. 1.6 g/L |
| Answer» Correct Answer - C | |