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. |
Two functions f and g are defined on the set of real numbers `RR` by , `f(x)= cos x and g(x) =x^(2)` , then, `(f o g)(x)=`A. `cos ^(2)x`B. `cos x^(2)`C. ` sin^(2) x`D. `sin x^(2)` |
| Answer» Correct Answer - b | |
| 2. |
Let the mapping `f:[0. infty) rarr [0,2]` be defined by, `f(x)=(2x)/(x+1)` then mapping f will be ____A. injective but not surjectiveB. neither injective nor surjectiveC. onto but not one-oneD. one-one and into |
| Answer» Correct Answer - A | |
| 3. |
The domain for which the functions `f(x)=3x^(2)-2x` and `g(x)=3(3x-2)` are equal will be ___A. `{1,(2)/(3)}`B. `{1,3}`C. `{(2)/(3),(3)}`D. `{(2)/(3),3}` |
| Answer» Correct Answer - C | |
| 4. |
State which of the following statement is false ?A. If `A ={0,1,2,3},B={-3,-2,-1,0,1} and f:A rarr B ` is the mapping defined by `f(x)=x-3` for all `x in A`, then f is a one-one mappingB. A constant mapping will be 0ne-one when its domain constans only one element.C. Functions f and g are defined as follows:`f:RR-{2} rarrRR,` where `f(x)=(x^(2)-4)/(x-2) and g:RR rarrRR,` where `g(x)=x+2,` then `f=g`D. `f(x)=sqrt(x^(2)+4x-1)` then `f(-2)` is not exist. |
| Answer» Correct Answer - C | |
| 5. |
Let the function `f:RR rarr RR` be defined by `f(x)=x^(2) (RR` being the set of real numbers), then f is __A. many - one and onto mappingB. one-one and onto mappingC. one-one and into mappingD. many-one and into mapping |
| Answer» Correct Answer - D | |
| 6. |
Let the function `f:RR rarr RR` be defined by , `f(x)=3x-2 and g(x)=3x-2 (RR` being the set of real numbers), then `(f o g)(x)=`A. `7x-8`B. `9x-7`C. `9x-8`D. `8x-9` |
| Answer» Correct Answer - c | |
| 7. |
The mapping `f:ZZ rarr ZZ` defined by , `f(x)=3x-2`, for all `x in ZZ`, then f will be ___A. onto but not one-oneB. one-one but not ontoC. many-one and intoD. many-one and onto |
| Answer» Correct Answer - B | |
| 8. |
Let RR be the set of real numbers and the mapping `f: RR rarr RR` be defined by `f(x)=2x^(2)`, then `f^(-1) (32)=`A. `{4,-4}`B. `{1,-1}`C. `{2,-2}`D. `{3,-3}` |
| Answer» Correct Answer - a | |
| 9. |
If the function `f:RR rarr RR and g: RR rarr RR` are given by `f(x)=3x+2` and `g(x)=2x-3 (RR` being the set of real numbers), state which of the following is the value of `(g o f) (x)`?A. `6x-7`B. `6x+1`C. 3x+5D. `6x+4` |
| Answer» Correct Answer - b | |
| 10. |
Let the function `f:A rarr B` have an inverse function `f^(-1): B rarr A`, then the nature of the function f is __A. one-one and ontoB. one-one and intoC. many-one and ontoD. many-one and into |
| Answer» Correct Answer - a | |
| 11. |
If `e^(x)+e^(f(x))=e`,then for `f(x)`___A. domain =`( -infty, 1)`B. range `(- infty, 1)`C. domain=`(- infty, 0]`D. range =`(- infty, 1]` |
| Answer» Correct Answer - a,b,c,d | |
| 12. |
Value of `F(3)=`A. 1B. -3C. 5D. 13 |
| Answer» Correct Answer - c | |
| 13. |
Let `A={a,b,c,d} and f: A rarr A` be defined by, `f(a)=d, f(b)=a, f(c)=b and f(d)=c`. State which of the following is equal to `f^(-1)(b)`?A. `{a}`B. `{b}`C. `{c}`D. `{d}` |
| Answer» Correct Answer - c | |
| 14. |
Let `f(x)=2x-sin x and g(x)=3sqrtx` then __A. range of g o f is RB. g o f is one- oneC. both f and g are one-oneD. both f and g are onto |
| Answer» Correct Answer - a,b,c,d | |
| 15. |
D`(f+g)=`A. `RR -[-2,0)`B. `RR-[-1,0)`C. `[-2,(1)/(2)]`D. none of these |
| Answer» Correct Answer - b | |
| 16. |
If `f: RR^(+) rarr RR ^(+)` is a polynomial function satisfying the functional equation `f{f(x)}=6x-f(x)`, then `f(17)` is equal to ___A. 17B. -15C. 34D. -34 |
| Answer» Correct Answer - b,c | |
| 17. |
Value of `f(5)=`A. 1B. -3C. 5D. 13 |
| Answer» Correct Answer - d | |
| 18. |
If the function f satisfies the reation `f(x+y)+f(x-y)=2f(x) f(y) Aax,yin RR and f(0) ne 0` then ____A. `f(x)` is an functionB. `f(x)` is an odd functionC. If `f(2)=a` then `f(-2)=a`D. If `f(4) =b` then `f(-4) =-b` |
| Answer» Correct Answer - a,c | |
| 19. |
Let` f(x)= sin+ cos x, g(x)=(sin x)/(1- cos x)` Statement-I: Let `A=(2,3,7,9} and B={4,9,49,81}`, `f:A rarr B` is a function defined as `f(x)=x^(2)`. Then f is bijection from A to B. Statement -II: A function f from a set A to a set B is a bijection if `f(A)=B, and f(x_(1)) ne f(x_(2))` if `x_(1) ne x_(2)` for all `x_(1),x_(2) in A` and `n(A)=n(B)`.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 True, Statement-II is not a correct explanation for Statement-IC. Statement -I is True , Statement -II is FalseD. Statement-I is False , Statement-II is True |
| Answer» Correct Answer - a | |
| 20. |
If `g(x)=x^(2)+x-2 and (g o f)(x)=2(2x^(2)-5x+2)` , then `f(x)=`A. `2x-3`B. `2x+3`C. `2x^(2)-3x+1`D. `2x^(2)-3x-1` |
| Answer» Correct Answer - a | |
| 21. |
For any one-empaty set A, the identity mapping on A will be____A. bijectiveB. surjective but not injectiveC. injective but not surjectiveD. neither injective nor surjective |
| Answer» Correct Answer - A | |