InterviewSolution
Saved Bookmarks
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.
| 51. |
It is given that `int (dx)/(1+x^(2))=tan^(-1) x+c` . Using methods of dimensions find `int (dx)/(a^(2)+x^(2))`. |
|
Answer» Correct Answer - `a tan^(-1) ((x)/(a))+c` |
|
| 52. |
Scattering of light is a process of absorption and prompt re-emission of light by atoms and molecules. Scattering involving particles smaller than wavelength `(lamda)` of light is known as Rayleigh scattering. Let `a_(i)` be amplitude of incident light on a scatterer of volume V. The scattered amplitude at a distance r from the scatterer is `a_(s)`. Assume and `a_(s) alpha a_(i) , a_(s) alpha (1)/(r) and a_(s) alpha V`. (i) Find the dimensions of the proportionality constant occurring in the expression of `a_(s)` (ii) Assuming that this constant depends on `lamda`, find the dependence of ratio `(a_(s))/(a_(i))` on `lamda` (iii) Knowing that intensity of light `I alpha a^(2)` find the dependence of `(I_(s))/(I_(i))` on `lamda`. |
|
Answer» Correct Answer - (i) `[k]=[L^(-2)]` (ii) `(a_(s))/(a_(i))prop lamda^(-2)` (iii) `(I_(s))/(I_(i))prop (a_(s)^(2))/(a_(i)^(2))prop lamda^(-4)` |
|
| 53. |
The Casimir effect describes the attraction between two unchanged conducting plates placed parallel to each other in vacuum. The astonishing force ( predicted in 1948 by Hendrik Casimir) per unit area of each plate depends on the planck’s constant (h), speed of light (c) and separation between the plates (r). (a) Using dimensional analysis prove that the formula for the Casimir force per unit area on the plates is given by `F= k (hc)/(r^(4))` where k is a dimensionless constant (b) If the force acting on `1xx1` cm plates separated by `1 mu m` is 0.013 dyne, calculate the value of constant k. |
|
Answer» Correct Answer - (b) `k=6.5 xx 10^(-3)` |
|
| 54. |
A massive object in space causes gravitational lensing. Light from a distant source gets deflected by a massive lensing object. This was first observed in 1919 and supported Einstein’s general theory of relativity. The angle `theta` by which light gets deflected due to a massive body depends on the mass (M) of the body, universal gravitational constant (G), speed of light (c) and the least distance (r) between the lensing object and the apparent path of light. Derive a formula for `theta` using method of dimensions. Make suitable assumptions. |
|
Answer» Correct Answer - `theta = k (GM)/(cr^(2))` |
|
| 55. |
If `x=1/(2+sqrt3)`,find the value of `x^(3)-x^(2)-11x+4` |
|
Answer» as `x=1/(2+sqrt3xx(2-sqrt3)/(2-sqrt3)=(2-sqrt3)/((2)^(2)-(sqrt3)^(2))` `x=(2-sqrt3)/(4-3)=2-sqrt3` `x-2=-sqrt3` squaring both sides , we get `(x-2)^(2)=(-sqrt3)^(2)rArrx^(2)+4-4x=3` `rArr x^(2)-4x+1=0` Now `x^(3)-x^(2)-11x+41` `=x^(3)=4x^(2)+x+3x^(2)-12x+4` `=x(x^(2)-4x+1)+3(x^(2)-4x+1)+1=xxx0+3(0)+1=0+0=0=1` |
|
| 56. |
The unit vector along `hati+hatj` is :A. `hatk`B. `hati+hatj`C. `(jati+hatj)/sqrt(2)`D. `(hati+hatj)/(2)` |
| Answer» Correct Answer - C | |
| 57. |
Which of the following vector identies is false ?A. `vecP+vecQ=vecQ+vecP`B. `vecP+vecQ+vecQ=vecQxxvecP`C. `vecP.vecQ=vecQ.vecP`D. `vecPxxvecQ=-vecQxxvecP` |
| Answer» Correct Answer - B | |
| 58. |
Which one of the following statement is false:A. Mass, speed and energy are scalarsB. Momentum, force and torque are vectorsC. Distance is a scalar while displacement is a vectorD. A vector has only magnitude where as a scalr has both magnitude and direction |
| Answer» Correct Answer - D | |
| 59. |
If `hatn` is a unit vector in the direction of the vector `vecA`, then:-A. `hatn=(vecA)/(|vecA|)`B. `hatn=vecA|vecA|`C. `hatn=(|vecA|)/(vecA)`D. `hatn=hatnxxvecA` |
| Answer» Correct Answer - A | |
| 60. |
`x(x+1)(x+2)(x+3)-8` |
|
Answer» `x(x+1)(x+2)(x+3)-8=x(x+1)(x+2)(x+3)-8` `x(x+3)(x+1)(x+2)-8` `(x^(2)+3x)(x^(2)+3x+2)-8` `=(x^(2)+3x)^(2)+2(x^(2)+3x)-8` `(x^(2)+3x)^(2)+4(x^(2)+3x)-2(x^(2)+3x)-8` `=(x^(2)+3x)(x^(2)+3x+4)-2(x^(2)+3x+4)` `=(x^(2)+3x-2)(x^(2)+3x+4)` |
|
| 61. |
Find a fourth proportional to the numbers 2,5,4. |
|
Answer» Let x be the fourth propoetional, then 2: 5 :: 4 : xor `2/5=4/x` `x=(5xx4)/2=10.` If b : : b : x,x is called the third proportional of a, b. We have `a/b=b/x " or " x=b^(2)/a`. Thus, third proportional of a, b is `b/a` |
|
| 62. |
The maximum height of a mountain on earth is limited by the rock flowing under the enormous weight above it. Studies show that maximum height depends on young’s modulus (Y) of the rod, acceleration due to gravity (g) and the density of the rock (d). (a) Write an equation showing the dependence of maximum height (h) of mountain on Y, g and d. It is given that unit of Y is `Nm^(-2)`. (b) Take `d = 3 xx 10^(3) kg m^(-3), Y = 1 xx 10^(10) Nm^(-2) and g = 10 ms^(-2)` and assume that maximum height of a mountain on the surface of earth is limited to 10 km [height of mount Everest is nearly 8 km]. Write the formula for h. |
|
Answer» Correct Answer - (a) `h=k((Y)/(gd)); k=a` const (b) `h=0.03 ((Y)/(gd))` |
|
| 63. |
A man is standing at a distance of 500 m from a building. He notes that angle of elevation of the top of the building is `3.6^(@)`. Find the height of the building. Neglect the height of the man and take `pi = 3.14` |
|
Answer» Correct Answer - 31.40 m |
|
| 64. |
Spirit in a bowl evaporates at a rate that is proportional to the surface area of the liquid. Initially, the height of liquid in the bowl is `H_(0)`. It becomes `(H_(0))/(2)` in time `t_(0)`. How much more time will be needed for the height of liquid tobecome `(H_(0))/(4)` |
|
Answer» Correct Answer - `(t_(0))/(2)` |
|
| 65. |
If `4/(2+sqrt3+sqrt7)=sqrta+sqrtb-sqrtc`,then which of the following can be ture -A. a=1, b=4/3, c=7/3B. `a=1, b=2/3, c=7/9C. a=2/3, b=1, c=7/3D. a= 7/9, b=4/3, c=1 |
| Answer» Correct Answer - A | |
| 66. |
A vector `vecF_(1)` is along the positive `X`-axis. If its vectors product with another vector `vecF_(2)` is zero then `vecF_(2)` could beA. `4 hatj`B. `-(hati+hatj)`C. `(hati+hatk)`D. `(-4hati)` |
| Answer» Correct Answer - D | |
| 67. |
Two force each numerically equal to `10` dynes are acting as shown in the figure, then find resultant of these two vectors.A. 10 dyneB. 20 dyneC. `10 sqrt(3)` dyneD. 5 dyne |
| Answer» Correct Answer - A | |
| 68. |
Force `3N, 4N` and `12 N` act at a point in mutually perpendicular directions. The magnetitude of the resultant resultant force us :-A. 19NB. 13NC. 11ND. 5N |
| Answer» Correct Answer - B | |
| 69. |
Two vectors, both equal in magnitude, have their resultant equal in magnitude of the either. Find the angle between the two vectors.A. `60^(@)`B. `90^(@)`C. `105^(@)`D. `120^(@)` |
| Answer» Correct Answer - D | |
| 70. |
if|`vecAxxvecB|=|vecA.vecB|`, then angle between `vecA` and `vecB` will beA. `30^(@)`B. `45^(@)`C. `60^(@)`D. `75^(@)` |
| Answer» Correct Answer - B | |
| 71. |
A vector `vecA` points vertically upward and `vecB` points towards north. The vector produce `vecAxxvecB` isA. zeroB. along westC. along eastD. vertically downward |
| Answer» Correct Answer - B | |
| 72. |
Electro motive force (EMF) is :A. scalarB. vectorC. neither scalar not vectorD. none of these |
| Answer» Correct Answer - A | |