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.
| 51. |
Solve the following equation `(i) 5cos2theta+2cos^(2)"(theta)/(2)+1=0`, `-(pi)/(2) lt theta lt (pi)/(2)` `(ii) sin7theta+sin4theta+sintheta=0`, `0 le theta le pi` `(iii) tantheta+sectheta=sqrt(3)`, `0 le theta le 2pi` |
| Answer» Correct Answer - `(i)(pi)/(3),(-pi)/(3)` `(ii) 0,(pi)/(4),(pi)/(2),(3pi)/(4),pi,(2pi)/(9),(4pi)/(9),(8pi)/(9)` `(iii) (pi)/(6)` | |
| 52. |
Let `S={xepsilon(-pi,pi):x!=0,+pi/2}`The sum of all distinct solutions of the equation `sqrt3secx+cosecx+2(tan x-cot x)=0` in the set S is equal toA. `-(7pi)/(9)`B. `-(2pi)/(9)`C. `0`D. `(5pi)/(9)` |
| Answer» Correct Answer - C | |
| 53. |
If the arithmetic mean of the roots of the equation `4cos^(3)x-4cos^(2)x-cos(pi+x)-1=0` in the interval `[0,315]` is equal to `kpi`, then the value of `k` isA. `10`B. `20`C. `50`D. `80` |
| Answer» Correct Answer - C | |
| 54. |
if the equation `sin (pi x^2) - sin(pi x^2 + 2 pi x) = 0` is solved for positive roots, then in the increasing sequence of positive rootA. first term is `(-1+sqrt(7))/(2)`B. first term is `(-1+sqrt(3))/(2)`C. third term is `1`D. third term is `(-1+sqrt(11))/(2)` |
| Answer» Correct Answer - B::C | |
| 55. |
In `(0,6pi)`, the number of solutions of the equation `tantheta+tan2theta+tan3theta=tantheta*tan2theta*tan3theta` is/areA. `15`B. `17`C. `20`D. `12` |
| Answer» Correct Answer - B | |
| 56. |
Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such thatA. `a=-1`, `b=3`B. `theta=pi//4`C. `a=3`, `b=-1`D. `theta=(pi)/(3)` |
| Answer» Correct Answer - B::C | |
| 57. |
The number of solution of the equation `sgn({x})=|1-x|` is/are (where `{*}` represent fractional part function and sgn represent signum function)A. `4`B. `3`C. `2`D. `1` |
| Answer» Correct Answer - D | |
| 58. |
Number of solution pair of equations `y=||x|-2|-2| and y=(x+2)/2`equals toA. `1`B. `2`C. `3`D. `4` |
| Answer» Correct Answer - C | |
| 59. |
For making graph of equations `|y|=|f(|x|)|` through `y=f(x)` which order of step is right among the following order of Step `I : y=f(|x|)` (replace `x` by `|x|`) Step `II : y=|f(x)|` (take modulus of `R.H.S`) `Step `III : |y|=f(x)` (replace `y` by `|y|`)A. `I`, `II`, `III`B. `II`, `I`, `III`C. `III`, `II`, `I`D. `III`, `I`, `II` |
| Answer» Correct Answer - B | |
| 60. |
The sum of all the integral values of a {where `a in (-10, 10)}` such that the graph of the function `f(x)=||x-2|-a|-3` has exastly three x-intercepts isA. `10`B. `5`C. `3`D. `0` |
| Answer» Correct Answer - C | |
| 61. |
Complete set of solution of inequation `sqrt(3x^2+5x+7)-sqrt(3x^2+5x+2)gt1` is `(-a,-b)uu(-c,-d)` then find the value of a+b+c+dA. `4`B. `3`C. `2`D. `1` |
| Answer» Correct Answer - A | |
| 62. |
Complete set of solution of inequation `(3)/(sqrt(2-x))-sqrt(2-x) lt 2` isA. `(-oo,1)`B. `(-oo,1]`C. `(1,oo)`D. `[1,oo)` |
| Answer» Correct Answer - A | |
| 63. |
Complete set of solution of inequation `sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1))>3/2`A. `(-oo,1)`B. `(-oo,1]`C. `[1,oo)`D. `(1,oo)` |
| Answer» Correct Answer - C | |
| 64. |
The complete set of soluton of equation `|1-(|x|)/(1+|x|)|=(1)/(2)` is `{a,b}` thenA. `a+b=8`B. `a+b=3`C. `a+b=0`D. `a+b=-3` |
| Answer» Correct Answer - C | |
| 65. |
If `a!=0` then complete set of solution of `(x^2-2x+2^(|x|))/(x^2-a^2)>0` isA. `(-oo,-|a|)uu(|a|,oo)`B. `(-oo,-a)uu(a,oo)`C. `(-oo,-a)uu[a,oo)`D. `(-|a|,|a|) |
| Answer» Correct Answer - A | |
| 66. |
Which of the following venn-diagrams best represents the sets of females, mothers and doctors ?A. B. C. D. |
| Answer» Correct Answer - D | |
| 67. |
The number of solution of equation `x^3-21 x-20=e^x` is/areA. `0`B. `1`C. `2`D. `3` |
| Answer» Correct Answer - C | |
| 68. |
`A` and `B` two sets such that `n(A)=3` and `n(B)=6`, thenA. minimum value of `n(AuuB)=6`B. minimum value of `n(AuuB)=9`C. maximum value of `n(AuuB)=6`D. maximum value of `n(AuuB)=9` |
| Answer» Correct Answer - A::D | |
| 69. |
In an examination of a certain class, at least `70%` of the students failed in Physics, at least `72%` failed in Chemistry, at least `80%` failed in Mathematics and at least `85%` failed in English. How many at least must have failed in all the four subjects ?A. `5%`B. `7%`C. `15%`D. Cannot be determined due to insufficient data |
| Answer» Correct Answer - B | |