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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. |
`int2^(3x).3^(x)dx=`A. `2^(3x).3^(2x).(log2)(log3)+c`B. `2^(3x-1).3^(2x-1).(log2)(log3)+c`C. `2^(3x).3^(2x).log5+c`D. `2^(3x).3^(2x).log_(72)e+c` |
| Answer» Correct Answer - D | |
| 2. |
`int(1-cosx)."cosec"^(2)xdx=`A. `tan((x)/(2))+c`B. `cot((x)/(2))+c`C. `(1)/(2)tan((x)/(2))+c`D. `2tan((x)/(2))+c` |
| Answer» Correct Answer - A | |
| 3. |
`int sec^(8//9)x cosec^(10//9)x ` dx is equal toA. `-(cot^(1//9)x)+c`B. `9.(tan^(1//9)x)+c`C. `-9(cot^(1//9)x)+c`D. `-(1)/(9)(cot^(9)x)+c` |
| Answer» Correct Answer - C | |
| 4. |
Evaluate: `int1/(sin^2x+sin2x) dx`A. `(1)/(2)log[(tanx)/(2+tanx)]+c`B. `log[sqrt((2+tanx)/(tanx))]+c`C. `(1)/(2)tan^(-1)[(tanx)/(2+tnax)]+c`D. `(sin2x)/(2)-(cos4x)/(4)+c` |
| Answer» Correct Answer - A | |
| 5. |
If the integral `int(5tanx)/(tanx-2)dx = x+a"ln"|sinx-2cosx|+k`, then a is equal to:A. `-1`B. `-2`C. 1D. 2 |
| Answer» Correct Answer - D | |
| 6. |
`int(1)/(3+2cosx)dx=`A. `(2)/(5)tan^(-1)[(tan(x//2))/(5)]+c`B. `(5)/(sqrt2)tan^(-1)[(tan(x//2))/(sqrt2)]+c`C. `(sqrt2)/(5)tan^(-1)[(tan(x//2))/(5)]+c`D. `(2)/(sqrt5)tan^(-1)[(tan(x//2))/(sqrt5)]+c` |
| Answer» Correct Answer - D | |
| 7. |
`int1/(5+3cosx)dx`A. `4log(tanx+5)+c`B. `4tan^(-1)(2tanx)+c`C. `(1)/(4)log((1)/(2)tanx)+c`D. `(1)/(4)tan^(-1)((1)/(2)tanx)+c` |
| Answer» Correct Answer - D | |
| 8. |
`int(3)/(4-5sinx)dx=`A. `log[(tan(x//2)-2)/(tan(x//2)-1)]+c`B. `log[(2tanx-4)/(2tanx-1)]+c`C. `log[(2tan(x//2)-4)/(2tan(x//2)-1)]+c`D. `tan^(-1)(2tan.(x)/(2)-5)+c` |
| Answer» Correct Answer - C | |
| 9. |
If `int(x+1)sqrt(2x-1)dx=a(2x-1)^(5//2)+b(2x-1)^(3//2)+c`, then `(b)/(a)=`A. 6B. 5C. 4D. 3 |
| Answer» Correct Answer - B | |
| 10. |
If `int(1)/(sqrt(1-2x))dx=a(1-2x)^(3//2)+bsqrt(1-2x)+c`, then `(b)/(a)=`A. `-3`B. `-2`C. 3D. 2 |
| Answer» Correct Answer - A | |
| 11. |
`int(1)/((x+1)sqrt(x-1))dx=`A. `(1)/(2sqrt2)tan^(-1)((x-1)/(2))+c`B. `sqrt2 tan^(-1)sqrt((x-1)/(2))+c`C. `(1)/(2sqrt2)log(x+sqrt(x-1))+c`D. `-sqrt2log(x+1+sqrt(x-1))+c` |
| Answer» Correct Answer - B | |
| 12. |
`int(1)/(x^(2)-2x-3)dx=`A. `4log[(x-3)(x+1)]+c`B. `(1)/(4)log[(x+1)/(x-3)]+c`C. `(1)/(4)log[(x-3)/(x+1)]+c`D. `(1)/(sqrt2)tan^(-1)[(x-1)/(sqrt2)]+c` |
| Answer» Correct Answer - C | |
| 13. |
If `int(5x+2)/(x^(2)-3x+2)dx=log[(x-2)^(m).(x-1)^(n)]+c` then `(m,n)-=`A. `(12, -7)`B. `(-12, 7)`C. `(12, 7)`D. `(-7, 12)` |
| Answer» Correct Answer - A | |
| 14. |
If `int(x+1)/(x(x^(2)-4))dx=log[(x-2)^(m//8).x^(n//4).(x+2)^(p//8)]+c,` then `(m, n,p)-=`A. `(3, -1,1)`B. `(3, -1, -1)`C. `(1, -3, -1)`D. `(-3, 1, -1)` |
| Answer» Correct Answer - B | |
| 15. |
`inte^(x)(x+100)dx=`A. `100e^(x)+c`B. `xe^(x)+100+c`C. `(x+99)e^(x)+c`D. `101xe^(x)+c` |
| Answer» Correct Answer - C | |
| 16. |
If `int(x^(2)+37)/(x^(4)-3x^(2)-28)dx=a log((x-sqrt7)/(x+sqrt7))+b tan^(-1)((x)/(2))+c,` then `(a, b)-=`A. `((2)/(sqrt7),(2)/(3))`B. `((sqrt7)/(2),(3)/(2))`C. `((sqrt7)/(2),(-3)/(2))`D. `((2)/(sqrt7),(-3)/(2))` |
| Answer» Correct Answer - D | |
| 17. |
If `int(tan^(2)x+tan^(4)x)dx=((1)/(n))tan^(n)x+c,` then `n=`A. 2B. 3C. 4D. 6 |
| Answer» Correct Answer - B | |
| 18. |
`int(sec sqrtx)/(sqrtx)dx=`A. `2log(secx+tanx)+c`B. `2log(sect+tant)+c`C. `2log(sec sqrtx+tansqrtx)+c`D. `2sec sqrtx.tanx+c` |
| Answer» Correct Answer - C | |
| 19. |
If `inttan^(3)xdx=a log(secx)+b tan^(2)x+c,` then `(a, b)-=`A. `((1)/(2),1)`B. `(1, (-1)/(2))`C. `(-1, (1)/(2))`D. `(1, (1)/(2))` |
| Answer» Correct Answer - C | |
| 20. |
`intsin sqrtxdx=`A. `2[cossqrtx-sqrtx sin sqrtx]+c`B. `2[sin sqrtx+cos sqrtx]+c`C. `2[sin sqrtx+sqrtx cos x]+c`D. `2[sin sqrtx - sqrtx cos sqrtx]+c` |
| Answer» Correct Answer - D | |
| 21. |
`int(1)/(x^(2)(4x+5))dx=`A. `(1)/(5x)+(4)/(25)log((4x+5)/(x))+c`B. `(-1)/(5x)+(4)/(25)log((4x+5)/(x))+c`C. `(1)/(5x)-(4)/(25)log((4x+5)/(x))+c`D. `-(1)/(x)+(1)/(4)log(4x+5)+c` |
| Answer» Correct Answer - B | |
| 22. |
`int(1)/(x(5-2x^(2)))dx=`A. `(1)/(10)log((2x^(2))/(2x^(2)+5))+c`B. `(1)/(2)log((2x^(2))/(5-2x^(2)))+c`C. `(1)/(2)log((2x^(2))/(2x^(2)-5))+c`D. `(1)/(10)log((2x^(2))/(2x^(2)-5))+c` |
| Answer» Correct Answer - D | |
| 23. |
`int(1)/(x(3x^(2)+2))dx=`A. `(1)/(4)log((3x^(2))/(3x^(2)+2))+c`B. `(1)/(4)log((3x^(2)+2)/(3x^(2)))+c`C. `(1)/(4)log((x^(2))/(3x^(2)+2))+c`D. `(1)/(4)log((3x^(2)+2)/(x^(2)))+c` |
| Answer» Correct Answer - A | |
| 24. |
`int(1)/(sinx-cosx)dx=`A. `(1)/(sqrt2)log[tan((pi)/(4)-(x)/(8))]+c`B. `(1)/(sqrt2)log[cot((pi)/(4)-(x)/(8))]+c`C. `(1)/(sqrt2)tan((x)/(2)-(pi)/(8))+c`D. `(1)/(sqrt2)log[tan((x)/(2)-(pi)/(8))]+c` |
| Answer» Correct Answer - D | |
| 25. |
`int(a+bcosx)/(sin^(2)x)dx=`A. `-cotx+bcosx+c`B. `acotx+b cos x+c`C. `-a cotx-b cos x+c`D. `log(a+bcosx)+c` |
| Answer» Correct Answer - C | |
| 26. |
If `intx^(3).e^(-x)dx=-e^(-x).f(x)+c,` then `f(x)=`A. `x^(3)-3x^(2)+6x-6`B. `-x^(3)+3x^(2)-6x+6`C. `x^(3)-3x^(2)+6x+6`D. `x^(3)+3x^(2)+6x+6` |
| Answer» Correct Answer - D | |
| 27. |
`inte^(x+e^(x))dx=`A. `e^(xe^(x))+c`B. `e^(x^(2))+c`C. `e^(e^(x))+c`D. `e^(e^(e ))+c` |
| Answer» Correct Answer - C | |
| 28. |
`int(2x-1)/(x+1)^(3)dx=`A. `(3)/(2(x+1)^(2))+c`B. `(3)/(2(x+1)^(2))+(2)/(x+1)+c`C. `(3)/(2(x+1)^(2))-(2)/(x+1)+c`D. `x^(2)-x-(3)/(2(x+1)^(2))+c` |
| Answer» Correct Answer - C | |
| 29. |
`int(sin4x)/(1+sin^(4)2x)dx=`A. `-(1)/(2)tan^(-1)(sin^(2)2x)+c`B. `(1)/(2)tan^(-1)(sin^(2)2x)+c`C. `tan^(-1)(sin^(2)2x)+c`D. `cot^(-1)(sin^(2)2x)+c` |
| Answer» Correct Answer - B | |
| 30. |
`int(1)/(x)log((1)/(x))dx=`A. `log(logx)+c`B. `-(1)/(2)(logx)^(2)+c`C. `2logx+c`D. `-logx+c` |
| Answer» Correct Answer - B | |
| 31. |
If `intx^(2).e^(x^(3))dx=u.e^(x^(3))+c,` then `u=`A. `(x^(3))/(3)`B. `(x^(3)-1)/(2)`C. `(x^(2)-1)/(2)`D. `(1)/(3)` |
| Answer» Correct Answer - D | |
| 32. |
`int(1)/((x-2)(1+x^(2)))dx=`A. `(1)/(5)[log(x+2)-(1)/(2)log(1+x^(2))+2tan^(-1)x]+c`B. `(1)/(5)[log(x-2)+(1)/(2)log(1+x^(2))+2tan^(-1)x]+c`C. `(1)/(5)[log(x-2)-(1)/(2)log(1+x^(2))-2tan^(-1)x]+c`D. `log(x-2)+tan^(-1)x+c` |
| Answer» Correct Answer - C | |
| 33. |
`inte^(-logx)dx` is equal toA. `(e^(logx))/(x)+c`B. `(x^(2))/(2)+c`C. `logx+c`D. `-logx+c` |
| Answer» Correct Answer - B | |
| 34. |
`inte^(-logx)dx` is equal toA. `-(x^(2))/(2)+c`B. `logx+c`C. `e^(-x)+c`D. `-logx+c` |
| Answer» Correct Answer - B | |
| 35. |
`int(logx)/(x^(2))dx=?`A. `logx.log(logx)+c`B. `(x)/(1+logx)+c`C. `-(1+logx)/(x)+c`D. `e^(-x)(x-logx)+c` |
| Answer» Correct Answer - C | |
| 36. |
If : `int(f(x))/(log(cosx))dx=-log[log(cosx)]+c,` then : `f(x)=`A. `tanx`B. `-sinx`C. `-cosx`D. `-tanx` |
| Answer» Correct Answer - A | |
| 37. |
`int(1)/(sqrt(1+sinx))dx=`A. `(2)/(3)(1-sinx)^(3//2)+c`B. `2[cos((x)/(2))-sin((x)/(2))]+c`C. `-sqrt2log[tan((3pi)/(8)-(x)/(4))]+c`D. `sqrt(x-cosx)+c` |
| Answer» Correct Answer - C | |
| 38. |
`int(3x)/((x-2)(x+1))dx`A. `(2)/(5)log((x-1)/(x+1))+(1)/(x-1)+c`B. `(2)/(5)log((x-1)/(x+1))-(1)/(x-1)+c`C. `(5)/(2)log((x+1)/(x-1))+(1)/(x+1)+c`D. `(5)/(2)log((x+1)/(x-1))-(1)/(x-1)+c` |
| Answer» Correct Answer - B | |
| 39. |
`inte^(2x^(2)+logx)dx=`A. `(1)/(4)e^(2x^(2))+c`B. `(1)/(4)e^(4x)+c`C. `e^(4x+(1)/(x))+c`D. `(1)/(4)e^(2logx)+c` |
| Answer» Correct Answer - A | |
| 40. |
`int((logx)^(2))/(x)dx.`A. `(1)/(3)log(x^(3))+c`B. `3logx+c`C. `3e^(-x)logx+c`D. `(1)/(3)(logx)^(3)+c` |
| Answer» Correct Answer - D | |
| 41. |
`intsqrt((1+sinx)/(1-sinx))dx=`A. `tanx-secx+c`B. `cosx+cotx+c`C. `log[sin((pi)/(4)-(x)/(2))]+c`D. `-log(1-sinx)+c` |
| Answer» Correct Answer - D | |
| 42. |
`int(3x+1)/(x^(2)(x+1))dx=`A. `2logx-(1)/(2x)-2log(x+1)+c`B. `2logx-(1)/(2x)-2log(x-1)+c`C. `2logx-(1)/(2x)+2log(x-1)+c`D. `3log((x)/(x+1))+c` |
| Answer» Correct Answer - A | |
| 43. |
`int(2x-3)/(x^(3)(x-1))dx=`A. `logx+(1)/(x)+(3)/(2x^(2))+log(x-1)+c`B. `logx-(1)/(x)+(3)/(2x^(2))+log(x-1)+c`C. `logx+(1)/(x)-(3)/(2x^(2))-log(x-1)+c`D. `2log((x)/(x-1))+c` |
| Answer» Correct Answer - C | |
| 44. |
`int(tan(logx))/(x)dx=?`A. `log(secx)+c`B. `sec(logx)+c`C. `log[sec(logx)]+c`D. `log[log(secx)]+c` |
| Answer» Correct Answer - C | |
| 45. |
`int(logx)/(x)dx=?`A. `log(logx)+c`B. `(1)/(2)(logx)^(2)+x`C. `2logx+c`D. `logx+c` |
| Answer» Correct Answer - B | |
| 46. |
If `int(2^(x))/(sqrt(1-4^(x)))dx=k.sin^(-1)(2^(x))+c`, then : `k=`A. `log2`B. `log(sqrt2)`C. `(1)/(2)`D. `(1)/(log2)` |
| Answer» Correct Answer - D | |
| 47. |
If `int(k)/(cos(x-a)cos(x-b))dx=log[(cos(x-a))/(cos(x-b))]+c`, then `k=`A. `cos(a+b)`B. `sin(a-b)`C. `cos(a+b)`D. `cos(a-b)` |
| Answer» Correct Answer - B | |
| 48. |
The value of the integral `int(log(x+1)-logx)/(x(x+1))dx` isA. `-log((x+1)/(x))+c`B. `log[log(x+1)]-log(logx)+x`C. `-(1)/(2)[log((x+1)/(x))]^(2)+c`D. `e^(x)[(1)/(x)-(1)/(x+1)]+c` |
| Answer» Correct Answer - C | |
| 49. |
`int(d^(2))/(dx^(2))(tan^(-1)x)dx=`A. `(1)/(1+x^(2))+c`B. `tan^(-1)x+c`C. `x tan^(-1)x-(1)/(2)log(1+x^(2))+c`D. `(2tan^(-1)x)/(1+x^(2))+c` |
| Answer» Correct Answer - A | |
| 50. |
Integral of `(1)/(1+(logx)^(2))` w.r.t. `(logx)` isA. `(1)/(x)tan^(-1)(logx)+c`B. `tan^(-1)(logx)+c`C. `(1)/(x)tan^(-1)x+c`D. `sin^(-1)(logx)+c` |
| Answer» Correct Answer - B | |