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 number of real roots of ` sin (2^x) cos (2^x) =1/4 (2^x+2^-x) ` isA. 1B. 2C. 3D. 0 |
| Answer» Correct Answer - D | |
| 2. |
`log_(16)x^(3)+(log_(2)sqrt(x))^(2) lt 1` iff x lies inA. (2,16)B. `(0,1//16)`C. `(1//16,2)`D. (0,2) |
| Answer» Correct Answer - C | |
| 3. |
The number of solutions of the equation `log_(x-3) (x^3-3x^2-4x+8)=3` isA. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - A | |
| 4. |
If `log_(3)x-log_(x)27 lt 2`, then x belongs to the intervalA. `(1//3,27)`B. `(1//27,3)`C. `(1//9,9)`D. None of these |
| Answer» Correct Answer - D | |
| 5. |
The solution set of the inequation `log_(1//3)(x^(2)+x+1)+1 gt 0`, isA. `(-oo,-2) cup (1,oo)`B. [-1,2]C. (-2,1)D. R |
| Answer» Correct Answer - C | |
| 6. |
The solution set of inequation `log_(1//3)(2^(x+2)-4^(x)) ge-2`, isA. `(-oo,2-sqrt(13))`B. `(-oo,2+sqrt(13))`C. `(-oo,2)`D. None of these |
| Answer» Correct Answer - C | |
| 7. |
If `0 lt a lt 1`, then the solution set of the inequation `(1+(log_(a)x)^(2))/(1+(log_(a)x)) gt1`, isA. `(1,1//a)`B. (0,a)C. `(1,1//a) cup (0,a)`D. None of these |
| Answer» Correct Answer - C | |
| 8. |
The solution set of the inequation `5^((1//4)(log5 x)^(2)) ge 5x^((1//5)(log5 x))` isA. `(0,5^(-2sqrt(5))]`B. `[5^(2sqrt(5)),oo)`C. `(0,5^(-2sqrt(5))] cup[5^(2sqrt(5)),oo)`D. `(0,oo)` |
| Answer» Correct Answer - C | |
| 9. |
The set of all real numbers satisfying the inequation `x^((log_(10) x)^(2)-3(log10 x)+1) gt 1000`, isA. (0,1000)B. `(1000,oo)`C. (0,100)D. None of these |
| Answer» Correct Answer - D | |
| 10. |
The equation `sqrt(x+1)-sqrt(x-1)=sqrt(4x-1)` hasA. no solutionB. one solutionC. two solutionsD. more than two solutions |
| Answer» Correct Answer - A | |
| 11. |
Find the number of positive real roots of `x^4-4x-1=0`A. 3B. 2C. 1D. 0 |
| Answer» Correct Answer - C | |
| 12. |
If `[x]^(2)=[x+6]`, where [x]= the greatest integer less than or equal to x, then x must be such thatA. x=3,-2B. `x in [-2,-1)`C. `x in [3,4)`D. `x in [-2,-1) cup [3,4)` |
| Answer» Correct Answer - D | |
| 13. |
Let a,b be integers and f(x) be a polynomial with integer coefficients such that f(b)-f(a)=1. Then, the value of b-a, isA. 1B. -1C. 1,-1D. 0,1 |
| Answer» Correct Answer - C | |
| 14. |
The number of negative integral solution of the equation `x^2 2^(x+1)+2^(|x-3|+2)=x^2. 2^(|x-3|+4)+ 2^(x-1)` isA. noneB. only oneC. twoD. four |
| Answer» Correct Answer - A | |
| 15. |
Let f(x) be defined by `f(x) = x- [x], 0!=x in R`, where [x] is the greatest integer less than or equal to x then the number of solutions of `f(x) +f(1/x) =1` |
| Answer» Correct Answer - B | |
| 16. |
The number of irrational solutions of the equation `sqrt(x^(2)+sqrt(x^(2)+11))+sqrt(x^(2)-sqrt(x^(2)+11))=4`, is |
| Answer» Correct Answer - B | |
| 17. |
If `3^(x)+2^(2x) ge 5^(x)`, then the solution set for x, isA. `(-oo,2]`B. `[2,oo)`C. `[0,2]`D. {2} |
| Answer» Correct Answer - A | |
| 18. |
Q. if `(log_5 x)^2+log_5 x |
| Answer» Correct Answer - A | |
| 19. |
The number of real solutions of the equation `1-x = [cosx]` isA. 1B. 2C. 3D. 0 |
| Answer» Correct Answer - B | |
| 20. |
The number of real solutions of the equation `27^(1//x)+12^(1//x)=2.8^(1//x)`, isA. 1B. 2C. 0D. infinite |
| Answer» Correct Answer - C | |
| 21. |
The number of values of a for which the system of equations `2^(|x|)+|x|=y+x^(2)+a` and `x^(2)+y^(2)=1` has only one solution where a,x,y are real, isA. 1B. 2C. finitely many but more than 2D. infinitely many |
| Answer» Correct Answer - A | |