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. |
The general value of ` sin ^(-1) ""((sqrt(3))/(2))`is -A. `n pi -(-1) ""^(n)(pi)/(3)`B. `n pi +(-1)""^(n)(pi)/(3)`C. `n pi +(-1)""^(n)(pi)/(6)`D. `n pi ` |
| Answer» Correct Answer - B | |
| 2. |
The general value of ` cos ^(-1)(-1) ` isA. `2 n pi +- (pi)/(2)`B. `2 n pi +- (pi)/(3)`C. `2 n pi +-pi`D. `2 n pi +- (pi )/(6)` |
| Answer» Correct Answer - C | |
| 3. |
The general value of ` cot ^(-1) (-sqrt(3))` is -A. `n pi +(5pi)/(6)`B. `n pi -(5pi)/(6)`C. `n pi +(pi)/(6)`D. `n pi -(pi)/(6)` |
| Answer» Correct Answer - A | |
| 4. |
The prinicipa value of ` cot ^(-1) (-(1)/(sqrt(3)))` is -A. `(2pi)/(3)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(2)` |
| Answer» Correct Answer - A | |
| 5. |
The principal value of `cot ^(-1) ((1)/(sqrt(3)))` is -A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. `(pi)/(2)` |
| Answer» Correct Answer - C | |
| 6. |
The principal value of ` cos ^(-1) ""(-(1)/(2) ) ` isA. `(pi)/(3) `B. `(2pi)/(3)`C. `(pi)/(4) `D. `(pi)/(2)` |
| Answer» Correct Answer - B | |
| 7. |
state which of the following is the value of ` ( cos ^(-1) ""(1)/(2) + 2 sin ^(-1)""(1)/(2) )?`A. `(5pi ) /(6) `B. `(pi)/(3)`C. `(2pi)/(3)`D. `(pi)/(2)` |
| Answer» Correct Answer - C | |
| 8. |
State which of the statement is false ?A. the formula ` sec ^(-1) x + "cosec" ^(-1) x=(pi)/(2)` holds when `|x|ge 1.`B. `sin ^(-1) cos tan ^(-1) sqrt(3)`represents an angle .C. If ` cos ^(-1) (1)/(sqrt(5))= theta ` , then the value of `"cosec"^(-1) sqrt(5)` will be ` ((pi)/(2) - theta )`D. If `sin ^(-1) x= theta ` , then the value of ` " cosec"^(-1) ((1)/(sqrt(1-x^(2))))` is also ` theta` |
| Answer» Correct Answer - D | |
| 9. |
which of the following is the value of ` cot ( "cosec" ^(-1) 2+cos^(-1)""(1)/(2))`?A. 1B. 0C. `-1`D. `sqrt(3)` |
| Answer» Correct Answer - B | |
| 10. |
If ` sec ^(-1) x ="cosec" ^(-1) y ` . State which of the following is the value of ` ( cos ^(-1) ""(1)/(x)+cos ^(-1) ""(1)/(y ))`?A. `pi`B. `(2pi)/(3)`C. `(5pi)/(6)`D. `(pi)/(2)` |
| Answer» Correct Answer - D | |
| 11. |
The prinicipal value of ` "cosec"^(-1)(-sqrt(2))` is -A. `-(pi)/(4) `B. `(3pi)/(4)`C. `-(pi)/(3)`D. `(2pi)/(3)` |
| Answer» Correct Answer - A | |
| 12. |
The values of x satisfying ` sin ^(-1) x+ sin ^(-1) (1-x) = cos^(-1) x` are - |
| Answer» Correct Answer - A::B | |
| 13. |
If `"cosec" ^(-1) x = sin ^(-1) ((1)/(x))` then x may be -A. 1B. `-(1)/(2)`C. `(3)/(2)`D. `-(3)/(2)` |
| Answer» Correct Answer - A::C::D | |
| 14. |
`Cos^(-1) ( 4x ^(3) - 3x ) =a + b cos ^(-1)x ` is a equation of trigonomatric inverse circular function . If ` x in [-(1)/(2),-1]` then the value of ` a +bpi ` is -A. `2pi `B. `3pi`C. `pi`D. `-2pi` |
| Answer» Correct Answer - C | |
| 15. |
`Cos^(-1) ( 4x ^(3) - 3x ) =a + b cos ^(-1)x ` is a equation of trigonomatric inverse circular function . IF `x in [-(1)/(2) ,(1)/(2)],` then the prinicipal value of `sin ^(-1) ""(sin ""(a)/(b))` isA. `-(pi)/(3)`B. `(pi)/(3)`C. `-(pi)/(6)`D. `(pi)/(6)` |
| Answer» Correct Answer - A | |
| 16. |
`2 cot ^(-1) 7+ cos ^(-1) ((3)/(5))` is equal to -A. `cot^(-1)""((44)/(117))`B. `"cosec"^(-1)""((125)/(117 ))`C. `tan ^(-1)""((4)/(117))`D. `cos^(-1)""((44)/(125))` |
| Answer» Correct Answer - A::B::D | |
| 17. |
`theta = tan ^(-1)(2 tan ^(2) theta )- tan ^(-1) ((1)/(3) tan theta )` if -A. `tan theta =-2`B. ` tan theta =0`C. ` tan theta=1`D. `tan theta = 2` |
| Answer» Correct Answer - A::B::C | |
| 18. |
If ` sin ^(-1) x- cos ^(-1) x=(pi)/(6)` state which of the following is the value of x?A. `1`B. `(1)/(2)`C. `(1)/(sqrt(2))`D. `(sqrt(3))/(2)` |
| Answer» Correct Answer - D | |
| 19. |
`Cos^(-1) ( 4x ^(3) - 3x ) =a + b cos ^(-1)x ` is a equation of trigonomatric inverse circular function . If `x in ((1)/(2),1)` , then the value of `lim_(y to a) b cos (y) ` is -A. `-(1)/(3)`B. `-3`C. `(1)/(3)`D. `3` |
| Answer» Correct Answer - D | |
| 20. |
State which of the statement is true ?A. `sin cos^(-1) tan 30^(@)` represents an angle .B. `sin ^(-1) (-(1.5)/(1.4))` is undefined but ` "cosec"^(-1) (-(1.5)/(1.4))` is defined .C. `cos ^(-1) (sqrt(2)) ` is undefinedD. `sin ( cos^(-1) x) = cos (sin ^(-1)(sqrt(2))` is true for all values of x/ |
| Answer» Correct Answer - B | |
| 21. |
If ` 2 tan ^(-1) x = sin ^(-1) k` then the value of k is -A. ` (1-x^(2))/(1+x^(2))`B. `(2x)/(1-x^(2))`C. `(2x)/(1+x^(2))`D. `(2x^(2))/(1+x^(2))` |
| Answer» Correct Answer - C | |
| 22. |
State which of the statement is true ?A. `sin cos^(-1) tan 30^(@)` represents an angle .B. `sin ^(-1) (-(1.5)/(1.4))` is undefined but ` "cosec"^(-1) (-(1.5)/(1.4))` is defined .C. `cos ^(-1) (sqrt(2)) ` is undefinedD. `sin ( cos^(-1) x) = cos (sin ^(-1)(sqrt(2))` is true for all values of x/ |
| Answer» Correct Answer - B | |
| 23. |
The prinicipal value of ` tan ^(-1) (-sqrt(3))` is -A. `(pi)/(6)`B. `(pi)/(4)`C. `-(pi)/(4)`D. `-(pi)/(3)` |
| Answer» Correct Answer - D | |
| 24. |
`tan ^(-1) ""(1)/(2) + tan ^(-1) ""(1)/(3)=`A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(6)`D. `(pi)/(4)` |
| Answer» Correct Answer - D | |
| 25. |
Statement -I : `tan ^(-1)""((3)/(4))+tan ^(-1) ""((1)/(7))= (pi)/(4)` statement -II: `"for" x gt 0 , y gt 0` `tan^(-1 ) ((x)/(y))+tan^(-1)""((y-x)/(y+x))=(pi)/(4)`A. Statement - I is true statement -II is true , statement -II is a correct explanation for statement -IB. Statement -I is true statement -II is ture : statement -II statement -II is not a correct explantion for statement -IC. Statement -I is ture statement -II is FalseD. Statement -I is False , statement -II is true . |
| Answer» Correct Answer - d | |
| 26. |
State which of the following is the value of ` tan""(1)/(3)( tan ^(-1) x + tan ^(-1)""(1)/(x))(x gt 0) ` ?A. `(1)/(sqrt(3))`B. `sqrt(3)`C. `1`D. `0` |
| Answer» Correct Answer - A | |
| 27. |
`sin^(-1)x gt cos^(-1)x ` golds for -A. all values of xB. `x in (0,(1)/(sqrt(2)))`C. `x in ((1)/(sqrt(2)),1)`D. `x = 0.75` |
| Answer» Correct Answer - C::D | |