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. |
`int_(0)^(4)(3sqrt(x+5))/(3sqrt(x+5)+3sqrt(9-x))dx=`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 2. |
`int_(4)^(7)((11-x)^(2))/(x^(2)+(11-x)^(2))dx=`A. `(1)/(2)`B. 1C. `(3)/(2)`D. 2 |
| Answer» Correct Answer - C | |
| 3. |
`int_(-pi//2)^(pi//2)(sin^(4)x)/(sin^(4)x + cos^(4)x)dx=`A. 2B. `(pi)/(4)`C. `-2`D. `(pi)/(2)` |
| Answer» Correct Answer - D | |
| 4. |
`int_(-2)^(2)(x^(3))/(4-x^(2))dx=`A. `(pi)/(2)-1`B. 0C. `1-(pi)/(2)`D. `log((2+e)/(2-e))` |
| Answer» Correct Answer - B | |
| 5. |
Evaluate: `int_(1//4)^(1//2)1/(sqrt(x-x^2))dx`A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. `(pi)/(2)` |
| Answer» Correct Answer - A | |
| 6. |
`int_(0)^(pi//2)sin^(3)x dx=`A. `(2)/(3)`B. `(3)/(2)`C. `-(2)/(3)`D. `-(3)/(2)` |
| Answer» Correct Answer - A | |
| 7. |
`int_(a)^(b)(f(x))/(f(x)+f(a+b-x))dx=`A. `(a+b)/(2)`B. `(b-a)/(2)`C. `a+b`D. `b-a` |
| Answer» Correct Answer - B | |
| 8. |
`int_(0)^(pi//2)(1)/(1+sqrt(tan x))dx=`A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. `(pi)/(6)` |
| Answer» Correct Answer - C | |
| 9. |
`int_(-1)^(1)(x^(2))/(1+x^(2))dx=`A. 1B. `pi`C. `2-pi`D. `tan^(-1)e` |
| Answer» Correct Answer - C | |
| 10. |
If `int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a` and `int_(0)^(1)x^(2)f(x)dx=a^(2)`, then : `int_(0)^(1)(a-x)^(2)f(x)dx=`A. `4a^(2)`B. 0C. `2a^(2)`D. `3a^(2)` |
| Answer» Correct Answer - B | |
| 11. |
If `(d)/(dx)[g(x)]=f(x)`, then : `int_(a)^(b)f(x)g(x)dx=`A. `(1)/(2){[f(b)]^(2)-[f(a)]^(2)}`B. `f(b)-f(a)`C. `g(b)-g(a)`D. `(1)/(2){[g(b)]^(2)-[g(a)]^(2)}` |
| Answer» Correct Answer - D | |
| 12. |
`int_(-5)^(5)sqrt(25-x^(2))dx=`A. `(25pi)/(2)`B. `25pi`C. `50pi`D. `75pi` |
| Answer» Correct Answer - A | |
| 13. |
`int_(0)^(4)sqrt(16-x^(2))dx=`A. `-4pi`B. `2pi`C. `4pi`D. `-2pi` |
| Answer» Correct Answer - C | |
| 14. |
If `int_(-3)^(2)f(x)dx=2` and `int_(2)^(5)[5+f(x)]dx=9`, then : `int_(5)^(-3)f(x)dx=`A. 2B. 3C. 4D. 5 |
| Answer» Correct Answer - C | |
| 15. |
If `f(x)+f(pi-x)=1` and `g(x)+g(pi-x)=1`, then : `int_(0)^(pi)[f(x)+g(x)]dx=`A. `(3pi)/(2)`B. `(pi)/(2)`C. `2pi`D. `pi` |
| Answer» Correct Answer - D | |
| 16. |
`int_0^2sqrt((2+x)/(2-x))dx` is equal toA. `1+(pi)/(2)`B. `(3)/(2)+pi`C. `(1)/(2)+pi`D. `2+pi` |
| Answer» Correct Answer - D | |
| 17. |
`int_(0)^(1)(1)/(e^(x)+e^(-x))dx=`A. `tan^(-1)e-(pi)/(4)`B. `tan^(-1)e+(pi)/(4)`C. `tan^(-1)e`D. `(pi)/(4)-tan^(-1)e` |
| Answer» Correct Answer - A | |
| 18. |
`int_(1)^(e )(1)/(6x(log x)^(2)+7x log x + 2x)dx=`A. `log((15)/(2))`B. `log((6)/(5))`C. `log((3)/(10))`D. `(1)/(5)log((8)/(3))` |
| Answer» Correct Answer - B | |
| 19. |
`int_(0)^(pi)(e^(cos x))/(e^(cos x)+e^(-cos x))dx=`A. `pi`B. `(pi)/(3)`C. `(pi)/(2)`D. `(pi)/(4)` |
| Answer» Correct Answer - C | |
| 20. |
`int_(0)^(pi)(cos^(4)x-sin^(4)x)dx=`A. 2B. `-2`C. 0D. 4 |
| Answer» Correct Answer - C | |
| 21. |
If `int_(0)^(1)(dx)/((1+x)sqrt(1-x^(2)))=(a)/(b)`, thenA. `a=pi, b = sqrt(2)`B. `a=pi, b = 2sqrt(2)`C. `a=(pi)/(2), b = 2sqrt(2)`D. `a=b` |
| Answer» Correct Answer - D | |
| 22. |
`int_(2)^(3)f(5-x)dx-int_(2)^(3)f(x)dx=`A. 1B. 0C. `-1`D. `(1)/(2)` |
| Answer» Correct Answer - B | |
| 23. |
`int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=`A. `int_(0)^(a)f(x)dx`B. `int_(0)^(a)f(2a-x)dx`C. `int_(0)^(a)f(a-2x)dx`D. `int_(0)^(a)f(a+2x)dx` |
| Answer» Correct Answer - B | |
| 24. |
`int_(0)^(pi//2)(sin^(2)x)/((1+cos x)^(2))dx =`A. `2-(pi)/(2)`B. `2+(pi)/(2)`C. `(pi)/(2)-2`D. `4-pi` |
| Answer» Correct Answer - A | |
| 25. |
`int_(0)^(1)[(d)/(dx)(sqrt(1+x^(3)))]dx=`A. `(2)/(3)2^(3//2)`B. `sqrt(2)-1`C. `sqrt(2)`D. 2 |
| Answer» Correct Answer - B | |
| 26. |
`int_(0)^(1)(3x^(3)-4x^(2)+1)/(sqrt(x))dx=`A. `(44)/(35)`B. `-(44)/(35)`C. `(35)/(44)`D. `(45)/(34)` |
| Answer» Correct Answer - A | |
| 27. |
`int_(0)^(a//2)(a)/((x-a)(x-2a))dx=`A. `log((3a)/(2))`B. `log((2a)/(3))`C. `log((3)/(2))`D. `log((3)/(2a))` |
| Answer» Correct Answer - C | |
| 28. |
`int_(1)^(3)(1)/(sqrt(4x-x^(2)-3))dx=`A. `(pi)/(2)`B. `-(pi)/(2)`C. `pi`D. `2pi` |
| Answer» Correct Answer - C | |
| 29. |
`int_(-1)^(1)sqrt(1-x^(2))dx=`A. `(pi)/(4)`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(5)` |
| Answer» Correct Answer - B | |
| 30. |
`int_(0)^(7)(1)/(sqrt(4+3x))dx=`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 31. |
`int_(-2)^(2)(1)/(1+e^(x^(3)))dx=`A. 2B. 4C. `(e^(2))/(1+e^(8))`D. 1 |
| Answer» Correct Answer - A | |
| 32. |
`int_(0)^(a)[f(x)+f(a-x)]dx=`A. `int_(0)^(a)f(a)dx`B. `int_(0)^(2a)f(a-2x)dx`C. `int_(0)^(2a)f(2a-x)dx`D. `2int_(0)^(a)f(x)dx` |
| Answer» Correct Answer - D | |
| 33. |
If `int_(0)^(1)(1)/(sqrt(x+1)-sqrt(x))dx=(a(sqrt(2)))/(3)`, then a =A. `sqrt(2)(2sqrt(2)-2)`B. `sqrt(2)(2-2sqrt(2))`C. `(2)/(3)(2sqrt(2)-2)`D. 4 |
| Answer» Correct Answer - D | |
| 34. |
`int_(0)^(pi//2)(1)/(5+13 sin x) dx=`A. `-(1)/(12)log 5`B. `(1)/(12)log 5`C. `(1)/(12)`D. `(1)/(5)log 12` |
| Answer» Correct Answer - B | |
| 35. |
`int_(0)^(pi//2)(1)/(13+5sin x)dx=`A. `tan^(-1)((2)/(3))`B. `(1)/(6)tan^(-1)((3)/(2))`C. `6 tan^(-1)((2)/(3))`D. `(1)/(6)tan^(-1)((2)/(3))` |
| Answer» Correct Answer - D | |
| 36. |
If `f and g` are continuous functions on `[0, a]` such that `f(x) = f(a - x) and g(x) + g(a - x)=2,` then show that `int_0^a f(x)g(x) dx = int_0^a f(x) dx`.A. `int_(0)^(a)f(x)dx`B. `int_(0)^(a)g(x)dx`C. 0D. `int_(0)^(a//2)f(x)dx` |
| Answer» Correct Answer - A | |
| 37. |
If `int_(0)^(b-c)f(x+c)dx=a int_(b)^(c )f(x)dx`, then a = |
| Answer» Correct Answer - B | |
| 38. |
`int_(1)^(2)(1)/(x+x^(3))dx=`A. `log((8)/(5))`B. `log((5)/(8))`C. `(1)/(2)log((8)/(5))`D. `(1)/(2)log((5)/(8))` |
| Answer» Correct Answer - C | |
| 39. |
`int_(0)^(pi)(x sin x)/(1-sin x)dx=`A. `pi.log4`B. `pi log 2`C. 2 log 2D. `2 log pi` |
| Answer» Correct Answer - A | |
| 40. |
`int_(0)^(4)(1)/((x+4)(x+6))dx=`A. `(1)/(2)log((5)/(6))`B. `(1)/(2)log((6)/(5))`C. `log((6)/(5))`D. `log((5)/(6))` |
| Answer» Correct Answer - B | |
| 41. |
`int_(0)^(2)x^(2)sqrt(4-x^(2))dx=`A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(16)`D. `pi` |
| Answer» Correct Answer - D | |
| 42. |
`int_0^1sqrt((1-x)/(1+x))dx`A. `(pi)/(2)+1`B. `(pi)/(2)`C. `(pi)/(2)-1`D. `1-(pi)/(2)` |
| Answer» Correct Answer - C | |
| 43. |
If `int_(0)^(1)(1)/(e^(x)+e^(-x))dx = tan^(-1)p`, then : p =A. `(e^(2)-1)/(e^(2)+1)`B. `(e-1)/(e+1)`C. `(1-e)/(1+e)`D. `(e-1)/(1+e^(2))` |
| Answer» Correct Answer - B | |
| 44. |
`int_(-a)^(a)(x^(2))/(a^(2)+x^(2))dx=`A. `(a(pi+4))/(2)`B. `(pi a)/(2)`C. `(4-pi)/(2)`D. `(a(4-pi))/(2)` |
| Answer» Correct Answer - D | |
| 45. |
If `a, b, gt 0`, then `int_(1)^(a)(1)/(x)dx + int_(1)^(b)(1)/(x)dx=`A. `int_(1)^(a+1)(1)/(x)dx`B. `int_(a)^(b)(1)/(x)dx`C. `int_(1)^(ab)(1)/(x)dx`D. `int_(1//a)^(1//b)x dx` |
| Answer» Correct Answer - C | |
| 46. |
`int_(-a)^(a)(1)/(a^(2)+x^(2))dx=`A. `(pi a)/(2)`B. `(pi)/(2a)`C. `(pi)/(4a)`D. `(pi)/(8a)` |
| Answer» Correct Answer - B | |
| 47. |
If `a gt 0`, then : `int_(-a)^(a)(1)/(sqrt(a^(2)-x^(2)))dx=`A. `pi`B. `(pi)/(2)`C. `(pi)/(4)`D. `(pi)/(8)` |
| Answer» Correct Answer - A | |
| 48. |
`int_(-pi//4)^(pi//4)sin^(2)x dx=`A. `(pi-4)/(8)`B. `(pi-2)/(4)`C. `(pi-2)/(2)`D. `pi` |
| Answer» Correct Answer - B | |
| 49. |
`int_(-pi//2)^(pi//2)sqrt(1+sin 2x)dx=`A. `sqrt(2)`B. `2`C. 3D. `-2sqrt(2)` |
| Answer» Correct Answer - B | |
| 50. |
`int_(pi//6)^(pi//4)(sec^(2)x+cos^(2)x)dx=`A. `(sqrt(3))/(2)`B. `(2)/(sqrt(3))`C. 2D. `sqrt(3)` |
| Answer» Correct Answer - B | |