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.
| 1. |
Assertion: If the initial and final positions coincide, the displacement is a null vector. Reason: A physical quantity can not be called a vector, if its magnitude is zero.A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.C. If Assertion is True but the Reason is False.D. If both Assertion `&` Reason are false. |
| Answer» Correct Answer - C | |
| 2. |
Assertion: If the rectangular components of a force are 24N and 7N, then the magnitude of the force is 25N. Reason : If `|vecA|=|vecN|=1` then `|vecAxxvecN|^(2)+|vecA.vecN|^(2)=1`A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.C. If Assertion is True but the Reason is False.D. If both Assertion `&` Reason are false. |
| Answer» Correct Answer - B | |
| 3. |
A particle moves along the curve `6y = x^(3)+2`. Find the points on the curve at which the y-coordinate is changing 8 times as fast as the x-coordinate |
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Answer» Correct Answer - `(-4,-(21)/(3)),(4,11)` |
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| 4. |
What is the maximum number of components into which is vector can be split ?A. 2B. 3C. 4D. Infinite |
| Answer» Correct Answer - D | |
| 5. |
`(7^((-1/2))xx5^(2))^(2)+sqrt(25^(3))=`A. `5/7`B. `7/5`C. 35D. `- 5/7` |
| Answer» Correct Answer - A | |
| 6. |
`(2d^(2)e^(-1))^(3)xx(d^(3)/e)^(-2)=`A. `8e^(-2)`B. `8e^(-3)`C. `8e^(-1)`D. `8e^(-4)` |
| Answer» Correct Answer - C | |
| 7. |
`(5(8^(1//3)+27^(1//3))^(3))^(1//4)`=A. 3B. 6C. 5D. 4 |
| Answer» Correct Answer - C | |
| 8. |
`(sqrtx^(3)xx3sqrtx^(5))/(5sqrt(x^(3)))xx30sqrt(x^(77))=`A. `x^(76//15)`B. `x^(78//15)`C. `x^(79//15)`D. `x^(77//15)` |
| Answer» Correct Answer - D | |
| 9. |
If `4sqrt(3sqrt(x^(2)))=x^(k),` then k=A. `2/6`B. 6C. `1/6`D. 7 |
| Answer» Correct Answer - C | |
| 10. |
`(5/6)^(3//4)" when divied by "(5/6)^(7//6)" becomes "(5/6)^(7-x)`, the value of x isA. `7/12`B. `89/12`C. `8/12`D. `10/12` |
| Answer» Correct Answer - B | |
| 11. |
As `theta` increases from `0^(@)` to `90^(@)`, the value of `cos theta` isA. IncreasesB. DecreasesC. Remains constantD. First decrease then increases. |
| Answer» Correct Answer - B | |
| 12. |
The greater value of the function `-5 sin theta +12 cos theta` isA. 12B. 13C. 7D. 17 |
| Answer» Correct Answer - B | |
| 13. |
`(((625)^(-1//2))^(-1//4))^(2)=`A. 4B. 5C. 2D. 3 |
| Answer» Correct Answer - B | |
| 14. |
`(1^(3)+2^(3)+3^(3)+4^(3))^(-3//2)=`A. `10^(-3)`B. `10^(-2)`C. `10^(-4)`D. `10^(-1)` |
| Answer» Correct Answer - A | |
| 15. |
`{4sqrt((1/x)^(-12))}^(-2//3)=`A. `1/x^(2)`B. `1/x^(4)`C. `1/x^(3)`D. `1/x` |
| Answer» Correct Answer - A | |
| 16. |
`(0.000729)^(-3//4)xx(0.09)^(-3//4)=`A. `10^(3)/3^(3)`B. `10^(5)/3^(5)`C. `10^(2)/3^(2)`D. `10^(6)/3^(6)` |
| Answer» Correct Answer - D | |
| 17. |
The slope of graph as shown in figure at points 1,2 and 3 is `m_(1), m_(2)` and `m_(3)` respectively then A. `m_(1)gtm_(2)gtm_(3)`B. `m_(1)ltm_(2)ltm_(3)`C. `m_(1)=m_(2)=m_(3)`D. `m_(1)=m_(3)gtm_(2)` |
| Answer» Correct Answer - B | |
| 18. |
Magnitude of slope of the shown graph. A. First increases then decresesB. First decrease then increasesC. IncreasesD. Decreases |
| Answer» Correct Answer - B | |
| 19. |
If `x^(y)=y^(x)" and "x=2y`, then the values of x and y are (x, y gt 0)A. `x=4, y=2`B. `x=3, y=2`C. `x=1, y=1`D. None of these |
| Answer» Correct Answer - A | |
| 20. |
If `sqrt(9^(x))=3sqrt(9^(2))`, then x =A. `2/3`B. `4/3`C. `1/3`D. `5/3` |
| Answer» Correct Answer - B | |
| 21. |
The graph shows a linear relation between variable y and x. Consider two quantities p and q defined by the equations. `p=y/x` `q=(y-b)/x` As x changes from zero to a, which of the following statements are correct according to the graph?A. Quantity p increases and 1 decrease.B. Quantity p decrease and q increases.C. Quantitity p decreases and q remain constant.D. Quantity p increase and q remain constant. |
| Answer» Correct Answer - C | |
| 22. |
If `a=x+1/x, " then "x^(3)+x^(-3)=`A. `a^(3)+3a`B. `a^(3)-3a`C. `a^(3)+3`D. `a^(3)-3` |
| Answer» Correct Answer - B | |
| 23. |
`(x^(1/(a-b)))^(1/(a-c))xx(x^(1/(b-c)))^(1/(b-a))xx(x^(1/(c-a)))^(1/(c-b))`A. 1B. 8C. 0D. None |
| Answer» Correct Answer - A | |
| 24. |
A vector perpendicular to `(4hati-3hatj)` may be :A. `4hati+3hatj`B. `7veck`C. `6hati`D. `3hati-4hatj` |
| Answer» Correct Answer - B | |
| 25. |
Two vectors `vecA` and `vecB` are such that `vecA+vecB=vecC` and `A^(2)+B^(2)=C^(2)`. Which of the following statements, is correct:-A. `vecA` ais parallel to `vecB`B. `vecA` is anti-parallel to `vecB`C. `vecA` is perpendiuclar to `vecB`D. `vecA` and `vecB` are equal in magnitude |
| Answer» Correct Answer - C | |
| 26. |
If `(3sqrt4)^(2x+1/2)=1/32`, then x =A. -2B. 4C. -6D. -4 |
| Answer» Correct Answer - D | |
| 27. |
Two positive numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find the numbers. |
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Answer» here a = 4, b = 5 and x = 24. `:." The first number"=(ax)/(b-a)=(4xx24)/(5-4)=96`. and the second number `=(bx)/(b-a)=(5xx24)/(5-4)=120`. |
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| 28. |
The sum of two numbers is c and their quotient is `p/q`. Find the numbers. |
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Answer» Let the numbers be x, y. Given `" "x+y=c …(1)` and, `x/y=p/q …(2)` `:. x/(x+y)=p/(p+q)` `rArr x/c=p/(p+q)["Using (1)"]` `rArr x=(pc)/(p+q)" and "y=(qc)/(p+q)` |
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| 29. |
If `a/b=c/d=e/f,` then show that `(a^(3)b+2c^(2)e-3ae^(2)f)/(b^(4)+2d^(2)f-3bf^(3))=(ace)/(bdf)`(wherever defined) |
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Answer» `a/b=c/d=e/f=krArra=bk, c=dk, e=fk` `:.(a^(3)b+2c^(2)e-3ae^(2)f)/(b^(4)+2d^(2)f-3bf^(3))=(k^(3)(b^(4)+2d^(2)f-3df^(3)))/(b^(4)+2d^(2)f-3bf^(3))=k^(3)=(ace)/(bdf)` |
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| 30. |
If `x=3-2sqrt2," find "x^(2)+1/x^(2)` |
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Answer» We have, `x=3-2sqrt2` `:. 1/x=1/(3-2sqrt2)xx(3+2sqrt2)/(3+2sqrt2)` `=(3+2sqrt2)/((3)^(2)+(2sqrt2)^(2))=(3+2sqrt2)/(9-8)=3+2sqrt2` Thus,`x^(2)+1/x^(2)=(3-2sqrt2)^(2)+(3+2sqrt2)^(2)` `=(3)^(2)+(2sqrt2)^(2)-2xx3xx2sqrt2+(3)^(2)+(2sqrt2)^(2)+2xx3xx2sqrt2` `=9+8-12sqrt2+9+8+12sqrt2=34` |
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| 31. |
`a^(6)-b^(6)` |
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Answer» `a^(6)-b^(6)=(a^(2))^(3)-(b^(2))^(3)` `=(a^(2)-b^(2))(a^(4)+a^(2)b^(2)+b^(4))` `=(a-b)(a+b)(a^(2)-ab+b^(2))(a^(2)+ab+b^(2))` |
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| 32. |
`9x^(4)-10x^(2)+1` |
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Answer» `9x^(4)-10x^(2)+1=(9x^(2)-1)(x^(2)-1)` `=(3x-1)(3x+1)(x-1)(x+1)` |
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| 33. |
Rationalise the denominator of `1/(sqrt3-sqrt2-1)` |
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Answer» `1/(sqrt3-sqrt2-1)=1/(sqrt3-sqrt2-1)xx(sqrt3-sqrt2+1)/(sqrt3-sqrt2+1)=(sqrt3-sqrt2+1)/((sqrt3-sqrt2-1)(sqrt3-sqrt2-1))` `(sqrt3-sqrt2+1)/((sqrt3-sqrt2)^(2)-1^(2))` `=(sqrt3-sqrt2+1)/(3+2-2sqrt3xxsqrt2-1)=(sqrt3-sqrt2+1)/(4-2sqrt6)` `=(sqrt3-sqrt2+1)/(2(2-sqrt6))=(sqrt3-sqrt2+1)/(2(2-sqrt6))xx(2+sqrt6)/(2+sqrt6)` `((sqrt3-sqrt2+1)(2+sqrt6))/(2(2^(2)-(sqrt6)^(2)))` `(2sqrt3-2sqrt2+2+sqrt3xxsqrt6-sqrt2xxsqrt6+sqrt6)/(2(4-6))` `=(2sqrt3-2sqrt2+2+sqrt(3xx6)-sqrt(2xx6)+sqrt6)/-4` `=(2sqrt3-2sqrt2+2+sqrt(3^(2)xx2)-sqrt(2^(2)xx3)+sqrt6)/-4` `=(2sqrt3-2sqrt2+2+3sqrt2-2sqrt3+sqrt6)/-4` `=(sqrt2+sqrt6+2)-4=-((sqrt2+sqrt6+2)/4)` |
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| 34. |
Evaluate the following (i) `(3sqrt64)^((-1)/2)" "(ii) (121/169)^(-3//2)` |
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Answer» (i) `(3sqrt64)^((-1)/2)=[(64)^(1/3)]^((-1)/2)=(64)^(1/3xx(-1)/2)=(64)^((-1)/6)` `=(2^(6))^((-1)/6)=2^(6xx((-1)/6))=2^(-1)=1/2` (ii) `((11xx11)/(13xx13))^(-3//2)=(11^(2)/13^(2))^(-3//2)=(11/13)^(2xx(-3)/2)=(11/13)^(-3)=(11/13)^(3)=2197/1331` |
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| 35. |
`x^(2)+6x-187` |
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Answer» `x^(2)+6x-187=x^(2)+17x-11x-187` `=x(x+17)-11(x+17)` `=(x-17)(x-11)` |
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| 36. |
Find the remainder when `x^(3)-ax^(2)+6x-a` is divided by x - a |
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Answer» `" Let "p(x) =x^(3)-ax^(2)+6x-a` `p(a) =a^(3)-a(a)^(2)+6(a) -a` `=a^(3)-a^(3)+6a-a=5a` So, by the Remainder theorem, remainder =5a |
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| 37. |
`(3x-Yy)^(2)-(2x-3y)^(2)` |
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Answer» Use `a^(2)-b^(2)=(a-b)(a+b)` `(3y-y)^(2)-(2x-3y)^(2)=(3x-y+2x-3y)(3x-y-2x+3y)` `=(5x-4y)(x+2y)` |
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| 38. |
Use the factor theorem tio determine whether (x-1) is a factor of f(x) `=2sqrt2x^(3)+5sqrt2x^(2)-7sqrt2` |
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Answer» By using factor theorem,(x-1) is a factor of f(x), only when f(1) = 0 `f(1)=2sqrt2(1)^(3)+5sqrt2(1)^(2)-7sqrt2=2sqrt2+5sqrt2-7sqrt2=0` `" Hence",(x-1)` is a factor of f(x). |
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| 39. |
What happens, when we multiply a vector by (-2) ?A. direction reverses and unit changesB. direction reverses and magnitude is doubledC. direction remains unchanged and unit changesD. none of these |
| Answer» Correct Answer - B | |
| 40. |
Given that A=B. What is the angle between `(vecA+vecB)` and `(vecA-vecB)` ?A. `30^(@)`B. `60^(@)`C. `90^(@)`D. `180^(@)` |
| Answer» Correct Answer - C | |
| 41. |
The forces, which meet at one point but their line of action do not lie in one plane,are calledA. non-coplanar and non-concurrent forcesB. coplanar and non-concurrent forcesC. non-coplanar and concurrent forcesD. coplanar and concurrent forces |
| Answer» Correct Answer - C | |
| 42. |
The square root `5+2sqrt6` is :A. `sqrt3+2`B. `sqrt3-sqrt2`C. `sqrt2-sqrt3`D. `sqrt3+sqrt2` |
| Answer» Correct Answer - D | |
| 43. |
The sqyuare root of `11+sqrt112` is-A. `sqrt7+2`B. `sqrt7+sqrt2`C. `2-sqrt7`D. None |
| Answer» Correct Answer - A | |
| 44. |
If `(4+3sqrt5)/(4-3sqrt5)=a+bsqrt5`,a, b are rational numbers, them (a, b)=A. `(61/29,(-24)/29)`B. `((-61)/29,24/29)`C. `(61/29,24/29)`D. `((-61)/29,(-24)/29)` |
| Answer» Correct Answer - D | |
| 45. |
If `x=8-sqrt60, "then "1/2[sqrtx+2/sqrtx]=`A. `sqrt5`B. `sqrt3`C. `2sqrt5`D. `2sqrt3` |
| Answer» Correct Answer - A | |
| 46. |
You inhale about 0.5 liter of air in each breath and breath once in every five seconds. Air has about 1% argon. Mass of each air particle can be assumed to be nearly `5 xx 10^(-26) kg`. Atmosphere can be assumed to be around 20 km thick having a uniform density of `1.2 kg m^(-3)`. Radius of the earth is `R = 6.4 xx 10^(6) m`. Assume that when a person breathes, half of the argon atoms in each breath have never been in that person’s lungs before. Argon atoms remain in atmosphere for long-long time without reacting with any other substance. Given : one year `= 3.2 xx 10^(7)s` (a) Estimate the number of argon atoms that passed through Newton’s lungs in his 84 years of life. (b) Estimate the total number of argon atoms in the Earth’s atmosphere. (c) Assume that the argon atoms breathed by Newton is now mixed uniformly through the atmosphere, estimate the number of argon atoms in each of your breath that were once in Newton’s lungs. |
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Answer» Correct Answer - (a) `3.2 xx 10^(28)` (b) `2.5 xx 10^(42)` (c) `1.5 xx 10^(6)` |
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| 47. |
`sqrt(6+sqrt(6+sqrt(6+sqrt(6+....................infty" times"))))=`A. 3B. 2C. 1D. `pm3` |
| Answer» Correct Answer - A | |
| 48. |
The line of sight of the brightest star in the sky, Sirius has a maximum parallax angle of `delta = 0.74 pm 0.02` arc second when observed at six month interval. The distance between two positions of earth (at six - month interval) is `r = 3.000 xx 10^(11) m` Calculate the distance of Sirius form the Sun with uncertainty, in unit of light year. Given 1 `1y = 9.460 xx 10^(15) m , pi = 3.14` |
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Answer» Correct Answer - `8.84 pm 0.24 ly` |
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| 49. |
The speed (V) of wave on surface of water is given by `V=sqrt((a lamda)/(2pi)+(2pib)/(rho lamda))` where `lamda` is the wavelength of the wave and `rho` is density of water. a is a constant and b is a quantity that changes with liquid temperature. (a) Find the dimensional formulae for a and b. (b) Surface wave of wavelength 30 mm have a speed of `0.240 ms^(-1)`. If the temperature of water changes by `50^(@)C`, the speed of waves for same wavelength changes to `0.230 ms^(-1)`. Assuming that the density of water remains constant at `1 xx 10^(3) kg m^(-3)`, estimate the change in value of ‘b’ for temperature change of `50^(@)C`. |
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Answer» Correct Answer - (a) `[a]=[M^(@)L^(1)T^(-2)];[b]=[M^(1)L^(@)T^(-2)]` (b) `Delta b = -0.022 kg s^(-2)` |
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| 50. |
Two point sources of light are fixed at the centre (A) and circumference (point B) of a rotating turn table. A photograph of the rotating table is taken. On the photograph a point A and an arc BC appear. The angle `theta` was measured to be `theta = 10.8^(@) pm 0.1^(@)` and the angular speed of the turntable was measured to be `omega = (33.3 pm 0.1)` revolution per minute. Calculate the exposure time of the camera. |
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Answer» Correct Answer - `(0.054 pm 0.003)s` |
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