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.
| 101. |
`int_(2)^(5)(1)/(sqrt(5+4x-x^(2)))dx=`A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. `(pi)/(2)` |
| Answer» Correct Answer - D | |
| 102. |
`int_(0)^(pi//4)(tan^(4)x + tan^(2)x)dx=`A. 1B. `(1)/(2)`C. `(1)/(3)`D. `(1)/(4)` |
| Answer» Correct Answer - C | |
| 103. |
If `int_(n)^(n+1)f(x)dx = n^(2)`, where n is an integer, then `int_(-2)^(4)f(x)dx=` |
| Answer» Correct Answer - C | |
| 104. |
`int_(-a)^(a){f(x)-f(-x)}dx=`A. `2int_(0)^(a)f(x)dx`B. 0C. `int_(0)^(a)f(2a-x)dx`D. f (a) |
| Answer» Correct Answer - B | |
| 105. |
`int_(-pi//4)^(pi//4) dx/(1+sin x)=`A. 1B. 2C. 3D. 4 |
| Answer» Correct Answer - B | |
| 106. |
`int_(-1//2)^(1) (1)/(sqrt(8+2x-x^(2)))dx=`A. `(pi)/(6)`B. `(pi)/(4)`C. `(pi)/(3)`D. `(pi)/(2)` |
| Answer» Correct Answer - A | |
| 107. |
`int_(2)^(3)(1)/(x^(2)-x)dx=`A. `log((2)/(3))`B. `log((4)/(3))`C. `log((8)/(3))`D. `-log 4` |
| Answer» Correct Answer - B | |
| 108. |
`int_(0)^(2pi)e^(sin^(2)nx)`. tan nx dx = |
| Answer» Correct Answer - A | |
| 109. |
If `{:(f(x)=x^(2)", if "0 le x le 1),(" "= sqrt(x)", if " 1 le x le 2","):}` then `int_(0)^(2)f(x)dx=`A. `(1)/(3)+(4sqrt(2))/(3)`B. `(4-sqrt(2))/(3)`C. `(4sqrt(2)-1)/(3)`D. `(1+4sqrt(2))/(sqrt(3))` |
| Answer» Correct Answer - C | |
| 110. |
`int_(1)^(2)sqrt((x-1)(2-x))dx=`A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(8)`D. `(pi)/(12)` |
| Answer» Correct Answer - C | |
| 111. |
`int_(0)^(3)(x+1)/(x^(2)+9)dx=`A. `(pi)/(12)log(2sqrt(2))`B. `(pi)/(12)+log (sqrt(2))`C. `(pi)/(6)log (2sqrt(2))`D. `(pi)/(3)log(2sqrt(2))` |
| Answer» Correct Answer - B | |
| 112. |
If `2int_0^1 tan^(-1)x dx= int_0^1 cot^(-1)(1-x+x^2) dx` then `int_0^1 tan^(-1)(1-x+x^2) dx=`A. 2B. log 2C. `-log 2`D. 0 |
| Answer» Correct Answer - B | |
| 113. |
If `0 le alpha le 2pi` and `int_(0)^(alpha)cos x dx = cos 2alpha`, the : `alpha =`A. `(pi)/(6)`B. `(pi)/(3)`C. `(pi)/(2)`D. `(pi)/(4)` |
| Answer» Correct Answer - A | |
| 114. |
Evaluate : `int_(0)^((pi)/(2)) sin^(2) x dx `.A. `(pi)/(2)`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(8)` |
| Answer» Correct Answer - B | |
| 115. |
If `int_(0)^(pi)x f(sin x) dx = a int_(0)^(pi)f (sin x) dx`, then a =A. `pi`B. `(pi)/(3)`C. `2pi`D. `(pi)/(2)` |
| Answer» Correct Answer - D | |
| 116. |
Evaluate `int_0^1 tan^(-1) (1/(1-x+x^2)) dx`A. `int_(0)^(1)tan^(-1)x dx`B. `(pi)/(4)`C. `2 int_(0)^(1)tan^(-1)x dx`D. 0 |
| Answer» Correct Answer - C | |
| 117. |
`int_(0)^(pi//4)sin^(2)x dx=`A. `(pi)/(4)+(1)/(2)`B. `(pi)/(4)+2`C. `(pi-2)/(8)`D. `(pi-2)/(4)` |
| Answer» Correct Answer - C | |
| 118. |
`int_(-2)^(3)[cot^(-1)((x-1)/(x+1))+cot^(-1)((x+1)/(x-1))]dx=`A. `(5pi)/(2)`B. `(3pi)/(2)`C. `(pi)/(2)`D. `2 cot^(-1)e` |
| Answer» Correct Answer - A | |
| 119. |
`int_(0)^(pi//2)(1)/(1+tan^(3)x)dx=` |
| Answer» Correct Answer - D | |
| 120. |
`int_(pi//4)^(pi//2)(e^(cot x))/(sin^(2)x)dx=`A. `e-1`B. `e+1`C. eD. `e-2` |
| Answer» Correct Answer - A | |
| 121. |
`int_(pi//4)^(pi//2)cot^(2)x dx =`A. `(pi-4)/(4)`B. `1-(pi)/(4)`C. `1-(pi)/(2)`D. `(pi)/(8)` |
| Answer» Correct Answer - B | |
| 122. |
`int_(-pi//2)^(pi//2)(sin^(2)x.cos^(2)x(sin x+cos x))dx=`A. `(15)/(4)`B. `(4)/(15)`C. `(5)/(16)`D. `(16)/(5)` |
| Answer» Correct Answer - B | |
| 123. |
`int_(pi//6)^(pi//3)(1)/(1+tan x) dx=`A. `pi`B. `(pi)/(4)`C. `(pi)/(6)`D. `(pi)/(12)` |
| Answer» Correct Answer - D | |
| 124. |
`int_(0)^(pi//2)(1)/(sqrt(tan x)-sqrt(cot x))dx=`A. `(pi)/(2)`B. `(pi)/(4)`C. 0D. 1 |
| Answer» Correct Answer - C | |
| 125. |
`int_(pi/3)^(pi/2) sqrt(1+cosx)/(1-cosx)^(5/2) dx`A. `(5)/(2)`B. `(3)/(2)`C. `(1)/(2)`D. `(2)/(5)` |
| Answer» Correct Answer - B | |
| 126. |
`int_(-1//2)^(1//2)(1)/(sqrt(1-x^(2))dx=`A. 1B. `pi`C. `(pi)/(2)`D. `(pi)/(3)` |
| Answer» Correct Answer - D | |
| 127. |
The value of `int_0^1(sin^(- 1)x)/(sqrt(1-x^2))dx` isA. `(pi^(2))/(4)`B. `(pi^(2))/(8)`C. `(pi^(2))/(2)`D. `pi^(2)` |
| Answer» Correct Answer - B | |
| 128. |
`int_(0)^(pi//2)sin^(2)x dx =`A. 1B. `(2)/(pi)`C. `(pi)/(2)`D. `(pi)/(4)` |
| Answer» Correct Answer - D | |
| 129. |
`int_(0)^(pi//2)(sin x - cos x)/(1-sin x cos x)dx=`A. 1B. `(pi)/(4)`C. 2D. 0 |
| Answer» Correct Answer - D | |
| 130. |
`int_0^a1/(x+sqrt(a^2-x^2))dx`A. `(pi)/(3)`B. `(pi)/(4)`C. `log(a+sqrt(a^(2)-1))`D. `log(1+sqrt(2))` |
| Answer» Correct Answer - B | |
| 131. |
`int_(0)^(pi//2)(sin x)/((sin x + cos x)^(3))dx=`A. `(1)/(2)`B. `(1)/(3)`C. `(1)/(4)`D. `(1)/(5)` |
| Answer» Correct Answer - A | |
| 132. |
`int_(pi//6)^(pi//3)cos^(2)x dx=`A. `(pi)/(6)`B. `(pi)/(12)`C. `(sqrt(3)-1)/(2)`D. `(sqrt(3)+1)/(2)` |
| Answer» Correct Answer - B | |
| 133. |
`int_(0)^(pi//2)(cos x)/((1+sin x)^(3))dx=`A. `(8)/(3)`B. `(3)/(8)`C. `(33)/(88)`D. `(88)/(33)` |
| Answer» Correct Answer - B | |
| 134. |
`int_(0)^(pi//2)(cos x)/(4-sin^(2)x)dx =`A. `(1)/(4)log 3`B. `(1)/(3)log 4`C. `4log((1)/(3))`D. `(1)/(2)log 3` |
| Answer» Correct Answer - A | |
| 135. |
Evaluate the integrals`int0pi/2(sinx)/(1+cos^2x)dx`A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. `(pi)/(6)` |
| Answer» Correct Answer - C | |
| 136. |
`int_(0)^(pi//2)(1)/(5+4cos x)dx=`A. `(2)/(3)tan^(-1)((1)/(3))`B. `(pi)/(3)`C. `(1)/(3)tan^(-1)((2)/(3))`D. `(pi)/(6)` |
| Answer» Correct Answer - A | |
| 137. |
`int_(0)^(1)x e^(x)dx=`A. 1B. `e^(2)`C. `1+e^(2)`D. 2 |
| Answer» Correct Answer - C | |
| 138. |
`int_(e )^(e^(2))log x dx =`A. 1B. `e^(2)`C. `e^(2)-1`D. `1+e^(2)` |
| Answer» Correct Answer - B | |
| 139. |
`int_(-a)^(a)x^(2)(e^(x^(3))-e^(-x^(3)))/(e^(x^(3))+e^(-x^(3)))dx=` |
| Answer» Correct Answer - A | |
| 140. |
`int_(1)^(2)x log x dx =`A. `(3)/(4)-(log 4)`B. `(log 4)-(3)/(4)`C. `e^(2)-e`D. `e+e^(2)` |
| Answer» Correct Answer - B | |
| 141. |
If `int_(a)^(b)(f(a+b-x))/(f(x)+f(a+b-x))dx=4`, then (a, b) can have the valuesA. `(-2, 10)`B. (10, 18)C. (8, 0)D. (10, 14) |
| Answer» Correct Answer - B | |
| 142. |
`int_(0)^(pi//2)x sin x dx=`A. `(pi)/(2)`B. `-pi`C. `-2`D. 1 |
| Answer» Correct Answer - D | |
| 143. |
`int_(0)^(pi/2)(x)/(1+cos x)dx =`A. `pi-(log 2)`B. `(pi)/(4)-(log 2)`C. `(pi)/(3)-(log 2)`D. `(pi)/(2)-(log 2)` |
| Answer» Correct Answer - D | |
| 144. |
If `f(a+b-x)=f(x)`, then `int_(a)^(b)x f(x)dx=`A. `(a-b)/(2)int_(a)^(b)f(x)dx`B. `(a+b)/(2)int_(a)^(b)f(x)dx`C. 0D. `b-a` |
| Answer» Correct Answer - B | |
| 145. |
`int_(0)^(1)x tan^(-1)x dx=`A. `(pi)/(4)-(log 2)`B. `(pi)/(4)-(1)/(2)`C. `(pi)/(4)-1`D. `(pi)/(4)+(log 2)` |
| Answer» Correct Answer - B | |
| 146. |
`(1)/(c )int_(ac)^(bc)f((x)/(c ))dx=`A. `(1)/(c )int_(a)^(b)f(x)dx`B. `int_(ac^(2))^(bc^(2))f(x)dx`C. `c int_(a)^(b)f(x)dx`D. `int_(a)^(b)f(x) dx` |
| Answer» Correct Answer - D | |
| 147. |
`int_(0)^(1//sqrt(2))(x sin^(-1)x)/(sqrt(1-x^(2)))dx=`A. `(pi)/(4)+(2)/(sqrt(2))`B. `(pi+4)/(4sqrt(2))`C. `(pi)/(4)-(2)/(sqrt(2))`D. `(pi)/(4)-(1)/(sqrt(2))` |
| Answer» Correct Answer - B | |
| 148. |
`int_(-pi//4)^(pi//4)(e^(x)x sin x)/(e^(2x)-1)dx=`A. eB. 0C. 2D. 1 |
| Answer» Correct Answer - B | |
| 149. |
`int_(-2)^(2)(1)/(1+e^(x^(3)))dx=`A. `(e^(2))/(1+e^(8))`B. 4C. 2D. 1 |
| Answer» Correct Answer - C | |
| 150. |
`int_(0)^(pi//4)e^(x)(1+tan x + tan^(2)x)dx=`A. tan 1B. e. tan 1C. `e^(pi//4)`D. tan e |
| Answer» Correct Answer - C | |