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)^((pi)/(4))(dx)/(acos^(2)x+bsin^(2)x)=`A. `(1)/(ab)tan^(-1)((b)/(a))" if "agt0,bgt0`B. `(1)/(ab)tan^(-1)((b)/(a))" if "alt0,blt0`C. `(pi)/(4)" if "a=1, b=1`D. none of these |
| Answer» Correct Answer - A::B::C | |
| 2. |
The value of `int_(0)^((pi)/(4))tan^(2)thetad theta` is-A. `(pi)/(4)-1`B. `1-(pi)/(4)`C. `(pi)/(2)-1`D. `pi-2` |
| Answer» Correct Answer - B | |
| 3. |
`int_0^(pi/4) (sinx+cosx)/(9+16sin2x)dx`A. `1/10 log 3`B. `1/20log3`C. `1/10log5`D. `1/20log5` |
| Answer» Correct Answer - B | |
| 4. |
integrate `int_0^(2pi) e^x . sin (pi/4 + x/2) dx`A. `(-3sqrt(2))/ 5 (e^(2pi)-1)`B. `(3sqrt(2))/ 5 (e^(2pi)-1)`C. `(-3sqrt(2))/ 5 (e^(2pi)+1)`D. `(3sqrt(2))/ 5 (e^(2pi)+1)` |
| Answer» Correct Answer - C | |
| 5. |
`int_0^1(cos^(- 1)x)^2dx`A. `pi/2 +1`B. `pi/2-1`C. `pi+2`D. `pi-2` |
| Answer» Correct Answer - D | |
| 6. |
`int_0^pisin^3x(1+2cosx)(1+cosx)^2dx`A. `8/3`B. `(-8)/3`C. `4/3`D. `(-4)/3` |
| Answer» Correct Answer - A | |
| 7. |
If `int_0^a3x^2dx=8,`find the value of `adot` |
| Answer» Correct Answer - C | |
| 8. |
The integral `int_0^pisqrt(1+4sin^2x/2-4sinx/2dx)`equal(1) `pi-4`(2) `(2pi)/3-4-4sqrt(3)`(3) `4""sqrt(3)-4`(4) `4""sqrt(3)-4-pi/3`A. `pi-4`B. `4sqrt(3)-4`C. `(2pi)/3 -4-4sqrt(3)`D. `4sqrt(3) - 4 - pi/3` |
| Answer» Correct Answer - D | |
| 9. |
Evaluate :`int_0^(pi/2)(dx)/(1+sqrt(tanx))`A. `(3pi)/2`B. `(3pi)/4`C. `pi/2`D. `pi/4` |
| Answer» Correct Answer - D | |
| 10. |
`int_0^(pi//2)(theta/sintheta)^2d theta=`A. `pi/(log2)`B. `log 2`C. `pi log 2`D. `pi` |
| Answer» Correct Answer - C | |
| 11. |
Evaluate:`int_0^(pi//4)sqrt(1+sin2x)dx`(ii)`int_0^(pi//4)sqrt(1-sin2x)dx`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - A | |
| 12. |
Evaluate `int_0^(pi/4) log(1+tanx)dx`A. `(-pi)/8 log 2`B. `(-pi)/4 log 2`C. `pi/8 log2`D. `pi/log2` |
| Answer» Correct Answer - C | |
| 13. |
`int_0^(pi/2)sqrt(sinphi)cos^5phidphi`A. `32/321`B. `64/321`C. `8/321`D. `16/321` |
| Answer» Correct Answer - B | |
| 14. |
If `int_(0)^(pi//2) log cos x dx =(pi)/(2)log ((1)/(2)),` then `int_(0)^(pi//2) log sec x dx =`A. `pi/2 log 2`B. `(-pi)/2log2`C. `pi/4 log 2`D. `(-pi)/4 log 2` |
| Answer» Correct Answer - A | |
| 15. |
`int_(1) ^(pi//2) (sin(log x ) + cos (log x )) dx = `A. `-picos (log (pi/2))`B. `picos (log (pi/2))`C. `-pi/2sin (log (pi/2))`D. `pi/2sin (log (pi/2))` |
| Answer» Correct Answer - D | |
| 16. |
If `int_(0)^(pi//2) log(cosx) dx=pi/2 log (1/2),` then `int_(0) ^(pi//2) log (sec x ) dx = `A. `pi/2 log (1/2)`B. `1-pi/2 log (1/2)`C. `1+pi/2 log (1/2)`D. `pi/2 log 2` |
| Answer» Correct Answer - D | |
| 17. |
`int_(-pi//4) ^(pi//4) tan^(2) x sec (x)dx =`A. `pi/4`B. `(-pi)/4`C. 0D. `pi/2` |
| Answer» Correct Answer - C | |
| 18. |
`int_(-1//2) ^(1//2) (cos x ) log ((1-x)/(1+x)) dx = ` |
| Answer» Correct Answer - A | |
| 19. |
`int_(-pi//2)^(pi//2) sqrt((1-cos2x)/2)dx = ` |
| Answer» Correct Answer - A | |
| 20. |
`int_(0)^(pi//4)(tan^(3)x)/((1+cos2x))dx`A. `1/2`B. `1/4`C. `1/8`D. `1/16` |
| Answer» Correct Answer - C | |
| 21. |
Evaluate:`int_(pi//4)^(pi//4)(x+pi//4)/(2-cos2x)dx`A. `pi^(2)/(3sqrt(3))`B. `pi^(2)/(6sqrt(3))`C. `pi/(3sqrt(3))`D. `pi/(6sqrt(3))` |
| Answer» Correct Answer - B | |
| 22. |
`int_(0)^(pi//2) sin 2 x (tan x) dx=` |
| Answer» Correct Answer - C | |
| 23. |
Evaluate :`int_0^(pi//2)(a^2cos^2x+b^2sin^2x)dx`A. `pi/2 (a-b)`B. `pi/2(a+b)`C. `pi/4 (a-b)`D. `pi/4(a+b)` |
| Answer» Correct Answer - D | |
| 24. |
Evaluate the following : `int_(0)^(pi)(x tanx)/(secx "cosec x")dx`A. `pi^(2) /2`B. `pi^(2)/4`C. `pi/2`D. `pi/4` |
| Answer» Correct Answer - B | |
| 25. |
`int_0^pix/(a^2cos^2x+b^2sin^2x)dx`A. `pi ab`B. `2pi ab`C. `pi/(ab)`D. `π^(2)/(2ab)` |
| Answer» Correct Answer - D | |
| 26. |
`int_(0)^(1) tan ^(-1) ((2x-1)/(1+x-x^(2)))dx = `A. `-1`B. 0C. 1D. `pm1` |
| Answer» Correct Answer - B | |
| 27. |
`int_(-1) ^(1) x^(2) /(1+x^(2)) dx =`A. `2-pi/2`B. `2+pi/2`C. `1-pi/2`D. `1+pi/2` |
| Answer» Correct Answer - A | |
| 28. |
The value of `underset(0)overset(oo)int (logx)/(1+x^(2))dx`, isA. `log 2`B. `-log 2`C. `log 1`D. `log 4` |
| Answer» Correct Answer - C | |
| 29. |
`int_(-a) ^(a) dx/(x+x^(3)) =` |
| Answer» Correct Answer - A | |
| 30. |
The value of the integral `overset(e )underset(1//e)int |logx|dx`, isA. `1+1/e`B. `1-1/e`C. `2+2/e`D. `2-2/e` |
| Answer» Correct Answer - D | |
| 31. |
Theintegral `int_2^4(logx^2)/(logx^2+log(36-12 x+x^2)dx`is equal to:(1) 2 (2) 4 (3) 1 (4) 6A. 1B. 6C. 2D. 4 |
| Answer» Correct Answer - A | |
| 32. |
`int_(0)^(1) log (1/x-1) dx =` |
| Answer» Correct Answer - A | |
| 33. |
`int_(0)^(pi//2)x cosx " " dx = `A. `pi/2-2`B. `pi/2+2`C. `pi/2-1`D. `pi/2+1` |
| Answer» Correct Answer - C | |
| 34. |
`int_(1) ^(2) dx/((x+1)(x+3)) = `A. `1/2 log (6/5)`B. `1/2 log (5/6)`C. `1/2 log (3/5)`D. `1/2 log (5/3)` |
| Answer» Correct Answer - A | |
| 35. |
`int_(0)^(pi//2) (cos x ) / ((sin x + cos x)^(2) )dx =`A. `1/sqrt(2) log ((sqrt(2)+1)/(sqrt(2)-1))`B. `1/sqrt(2) log ((sqrt(2)-1)/(sqrt(2)+1))`C. `1/(2sqrt(2)) log ((sqrt(2)+1)/(sqrt(2)-1))`D. `1/(2sqrt(2)) log ((sqrt(2)-1)/(sqrt(2)+1))` |
| Answer» Correct Answer - C | |
| 36. |
`int_(-3) ^(3) log ((9-x)/(9+x)) dx=`A. 4B. `-4`C. 8D. 0 |
| Answer» Correct Answer - D | |
| 37. |
`int_(0)^(pi//2)x sin x dx=` |
| Answer» Correct Answer - D | |
| 38. |
`int_(2)^(3)(x)/((x+2)(x+3))dx=`A. `log ((1728)/3125)`B. `log (3456/3125)`C. `log (1728/625)`D. `log (3456/625)` |
| Answer» Correct Answer - B | |
| 39. |
`int_(1) ^(3) dx/(x(1+x^(2)))=`A. `1/2 log (5/9)`B. `1/2 log (9/5)`C. `1/2 log (10/9)`D. `1/2 log (9/10)` |
| Answer» Correct Answer - B | |
| 40. |
`int_(1)^(e) log (x) dx=`A. 1B. eC. `e-1`D. `1-e` |
| Answer» Correct Answer - A | |
| 41. |
`int_(1)^(3) x^(3) log x dx=`A. `3 log - 26/3`B. `3log 3 - 26/9`C. `9log 3 - 26/3`D. `9 log 3 - 26/9` |
| Answer» Correct Answer - D | |
| 42. |
`int_(0) ^(pi//2) (sin x) /(sin x + cos x )^(2)dx=`A. `1/(2sqrt(2)) log ((sqrt(2)+1)/(sqrt(2)-1))`B. `1/(2sqrt(2)) log ((sqrt(2)-1)/(sqrt(2)+1))`C. `1/(sqrt(2)) log ((sqrt(2)+1)/(sqrt(2)-1))`D. `1/(sqrt(2)) log ((sqrt(2)-1)/(sqrt(2)+1))` |
| Answer» Correct Answer - A | |
| 43. |
`int_1^3cos(logx)/x dx`A. `cos (log 3)`B. `sin (log 3)`C. 1D. `pi/4` |
| Answer» Correct Answer - B | |
| 44. |
`int_(0)^(2pi)e^(x) (x/2+pi/4) dx = `A. `sqrt(2)`B. `2sqrt(2)`C. `e^(2pi)((5pi)/4-1/2) + 1/2 - pi/4 `D. `e^(2pi)((5pi)/4-1/2) + 1/2 + pi/4 ` |
| Answer» Correct Answer - C | |
| 45. |
Evaluate the following definite integral: `int_1^2logx dx`A. `2 log 2 -1`B. `2 log 2 + 1`C. `2log 2-2`D. `2log 2 + 2` |
| Answer» Correct Answer - A | |
| 46. |
If `I_1=int_e^(e^2)dx/(lnx)` and `I_2=int_1^2e^x/xdx`A. `I_(1)+I_(2)`B. `I_(1)gtI_(2)`C. `I_(1)ltI_(2)`D. `I_(1)=I_(2)` |
| Answer» Correct Answer - D | |
| 47. |
Evaluate :`int_1^2(x+3)/(x(x+2))dx`A. `2log 3`B. `2 log 6`C. `1/2 log 3`D. `1/2 log 6` |
| Answer» Correct Answer - D | |
| 48. |
`int_(0)^(pi//2) (sin x cos x) / ((1 + 2 sin x ) ( 1+ sin x))dx = `A. `1/2 log (3/4)`B. `1/2 log (4/3)`C. `1/2 log (3/2)`D. `1/2 log (2/3)` |
| Answer» Correct Answer - B | |
| 49. |
`int_(0)^(pi//2) (sin x) / ((sinx + cosx)^(3) ) dx =`A. `1/4`B. `(-1)/4`C. `1/2`D. `(-1)/2` |
| Answer» Correct Answer - C | |
| 50. |
`int_(pi/5)^(3pi/ 10)(sinx)/((sinx+cosx)dx`A. `(3pi)/4`B. `pi/10`C. `pi/5`D. `pi/20` |
| Answer» Correct Answer - D | |