MCQ 11 Mark
If $P(A / B)=\frac{2}{5}, P(B)=\frac{1}{5}$, then the value of $P(A \cap B)$ is
- A
$\frac{1}{5}$
- B
$\frac{2}{5}$
- ✓
$\frac{2}{25}$
- D
$\frac{1}{2}$
AnswerCorrect option: C. $\frac{2}{25}$
$\frac{2}{25}$
View full question & answer→MCQ 21 Mark
If $P(\operatorname{Not} A)=3 / 5$, then the value of $P(A)$ will be
- ✓
$\frac{2}{5}$
- B
$\frac{1}{5}$
- C
$\frac{4}{5}$
- D
$0$
AnswerCorrect option: A. $\frac{2}{5}$
$\frac{2}{5}$
View full question & answer→MCQ 31 Mark
If $P(A)=0.6, P(B)=0.3$ and $A$ and $B$ are two independent events, the value of $P(A \cap B)$ will be $-$
AnswerCorrect option: C. $0.18$
$0.18$
View full question & answer→MCQ 41 Mark
The distance of $(2,3,5)$ from $z-$ axis is
- A
$\sqrt{2}$
- B
$\sqrt{3}$
- C
$\sqrt{7}$
- ✓
View full question & answer→MCQ 51 Mark
If $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}$, then the value of $\vec{a} \cdot \vec{a}$ will be
View full question & answer→MCQ 61 Mark
If $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ then the value of $|\vec{a}|^2$ will be $-$
View full question & answer→MCQ 71 Mark
The area bounded by lines $y=x$ and $x = 2$ in first quadrant is
- A
$1$ sq unit
- ✓
$2$ sq unit
- C
$3$ sq unit
- D
$4$ sq unit
AnswerCorrect option: B. $2$ sq unit
$2$ sq unit
View full question & answer→MCQ 81 Mark
The value of $\int \cot 2 x\ d x$ will be
AnswerCorrect option: C. $\frac{1}{2} \log |\sin 2 x|+c$
$\frac{1}{2} \log |\sin 2 x|+c$
View full question & answer→MCQ 91 Mark
The value of $\int \cos ^2 x\ d x$ will be
View full question & answer→MCQ 101 Mark
If $y=\cos ^2 x$, then the value of $\frac{d y}{d x}$ is
- A
$\sin^2 x$
- B
$2 \cos x$
- C
$2 \sin x$
- ✓
View full question & answer→MCQ 111 Mark
If matrix $A=\left[\begin{array}{cc}x+y & 3 \\ 4 & y\end{array}\right]=\left[\begin{array}{ll}4 & 3 \\ 4 & 1\end{array}\right]$ then the value of $x$ will be :
- A
$x=2$
- B
$x=1$
- C
$x=-3$
- ✓
$x=3$
View full question & answer→MCQ 121 Mark
If $x R y \Leftrightarrow y=2 x, \forall x \in N, y \in N$, then $R$ will be
View full question & answer→MCQ 131 Mark
A die is thrown once, the probability of getting a number less than $4$ is
- A
$\frac{1}{3}$
- ✓
$\frac{1}{2}$
- C
$\frac{1}{6}$
- D
AnswerCorrect option: B. $\frac{1}{2}$
$\frac{1}{2}$
View full question & answer→MCQ 141 Mark
If $P\left(A^{\prime}\right)=\frac{3}{5}$ and $P(A \cap B)=\frac{1}{5}$ then the value of $P(B / A)$ will be
- A
$\frac{1}{10}$
- B
$\frac{3}{25}$
- ✓
$\frac{1}{2}$
- D
AnswerCorrect option: C. $\frac{1}{2}$
$\frac{1}{2}$
View full question & answer→MCQ 151 Mark
If the events $A$ and $B$ are mutually disjoint then the value of $P(A \cap B)$ is
- A
$P(A)-P(B)$
- B
$1$
- C
$P(A)+P(B)$
- ✓
$0$
View full question & answer→MCQ 161 Mark
The direction cosines of $z$ axis are
- A
$1,0,0$
- B
$0,1,0$
- C
$1,1,0$
- ✓
$0,0,1$
AnswerCorrect option: D. $0,0,1$
$0,0,1$
View full question & answer→MCQ 171 Mark
If $|\vec{a}-\vec{b}|=|\vec{a}+\vec{b}|$ then the angle between $\vec{a}$ and $\vec{b}$ will be $-$
- ✓
$90^{\circ}$
- B
$45^{\circ}$
- C
$30^{\circ}$
- D
$0$
AnswerCorrect option: A. $90^{\circ}$
$90^{\circ}$
View full question & answer→MCQ 181 Mark
The value of $(2 \hat{i}+3 \hat{j}-5 \hat{k}) \cdot(\hat{i}+\hat{j}+\hat{k})$ is
- ✓
$0$
- B
$-10$
- C
$\sqrt{38}$
- D
$15$
View full question & answer→MCQ 191 Mark
The area of circle $x^2+y^2=4$ is
- ✓
$4 \pi$ sq. unit
- B
$\pi$ sq. unit
- C
$16 \pi$ sq. unit
- D
$8 \pi$ sq. unit
AnswerCorrect option: A. $4 \pi$ sq. unit
$4 \pi$ sq. unit
View full question & answer→MCQ 201 Mark
The value of $\int \frac{1}{\sin ^2 x \cdot \cos ^2 x} d x$ is
- A
$\sec x+\tan x+c$
- B
$\sin x+\cos x+c$
- C
$0$
- ✓
$\tan x-\cot x+c$
AnswerCorrect option: D. $\tan x-\cot x+c$
$\tan x-\cot x+c$
View full question & answer→MCQ 211 Mark
The value of $\int \sec ^2(2 x+1) d x$ is
AnswerCorrect option: C. $\frac{1}{2} \tan (2 x+1)+c$
$\frac{1}{2} \tan (2 x+1)+c$
View full question & answer→MCQ 221 Mark
If $y=\sin x^{\circ}$ then the value of $\frac{d y}{d x}$ is
AnswerCorrect option: C. $\frac{\pi}{180} \cos x^{\circ}$
$\frac{\pi}{180} \cos x^{\circ}$
View full question & answer→MCQ 231 Mark
If matrix $A=\left[a_{i j}\right]_{m \times n}$ is a square matrix, then
- A
$m > n$
- B
$n > m$
- ✓
$m = n$
- D
AnswerCorrect option: C. $m = n$
$m = n$
View full question & answer→MCQ 241 Mark
If $f: R \rightarrow R, f(x)=2 x+1$, then the value of $f^{-1}(5)$ is
View full question & answer→MCQ 251 Mark
The value of $P(X=2)$ for bernoulli's function $B\left(5, \frac{1}{2}\right)$ is
- A
$\frac{5}{13}$
- B
$\frac{7}{32}$
- ✓
$\frac{5}{16}$
- D
$\frac{5}{32}$
AnswerCorrect option: C. $\frac{5}{16}$
$\frac{5}{16}$
View full question & answer→MCQ 261 Mark
If $P(A / B)=\frac{3}{5}$ and $P(B)=\frac{2}{5}$ , then the value of $P(A \cap B)$ is
- ✓
$\frac{6}{25}$
- B
$\frac{1}{5}$
- C
$\frac{1}{25}$
- D
$\frac{3}{25}$
AnswerCorrect option: A. $\frac{6}{25}$
$\frac{6}{25}$
View full question & answer→MCQ 271 Mark
If $A$ and $B $ are independent events and $P(A) = 0.2, P(B)=0.3$ then the value of $P ($neither $A$ nor $B)$ will be
- A
$0.6$
- ✓
$0.5$
- C
$0.94$
- D
$0.7$
View full question & answer→MCQ 281 Mark
The distance of point $(1, 2, 3)$ from origin is
AnswerCorrect option: D. $\sqrt{14}$
$\sqrt{14}$
View full question & answer→MCQ 291 Mark
If the vectors $a \hat{i}+\hat{j}-2 \hat{k}$ and $2 \hat{i}+3 \hat{j}-\hat{k}$ are perpendicular to each other, then the value of a will be $-$
- A
$2$
- B
$0$
- C
$\frac{5}{2}$
- ✓
$\frac{-5}{2}$
AnswerCorrect option: D. $\frac{-5}{2}$
$\frac{-5}{2}$
View full question & answer→MCQ 301 Mark
If $|(2 \hat{i}+\hat{j}-\hat{k}) \times(5 \lambda-6 i+j)|=17$ then the value of $\lambda$ is
View full question & answer→MCQ 311 Mark
The area bounded by curve $x + y = 2, x-$ axis, and $y$ axis is
- ✓
$2$ sq units
- B
$4$ sq units
- C
$8$ sq units
- D
$12$ sq units
AnswerCorrect option: A. $2$ sq units
$2$ sq units
View full question & answer→MCQ 321 Mark
The value of $\int_0^{\pi / 2} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x$ will be
- A
$\frac{\pi}{2}$
- B
$0$
- C
$\pi$
- ✓
$\frac{\pi}{4}$
AnswerCorrect option: D. $\frac{\pi}{4}$
$\frac{\pi}{4}$
View full question & answer→MCQ 331 Mark
The value of $\int e^{5 x-3} d x$ is
AnswerCorrect option: B. $\frac{1}{5}\left(e^{5 x-3}\right)+c$
$\frac{1}{5}\left(e^{5 x-3}\right)+c$
View full question & answer→MCQ 341 Mark
If $y= \text{log} , x$ then the value of $\frac{d y}{d x}$ is
- ✓
$\frac{1}{x}$
- B
$\frac{5}{x}$
- C
$x \text{ log _e} _5$
- D
AnswerCorrect option: A. $\frac{1}{x}$
$\frac{1}{x}$
View full question & answer→MCQ 351 Mark
If $A$ is a matrix of order $2 \times 3$ and $B$ is of $2 \times 2,$ then the order of matrix $BA$ will be $-$
- A
$2\times 2$
- B
$3\times 3$
- ✓
$2 \times 3$
- D
$3 \times 2$
AnswerCorrect option: C. $2 \times 3$
$2 \times 3$
View full question & answer→MCQ 361 Mark
If $f:R\rightarrow R, f(x)=2x+1 $, then the value of $ f^{-1} (2)$ is
View full question & answer→MCQ 371 Mark
If $A$ and $B$ are two independent events and $P ( A )=\frac{2}{5}, P ( A \cap B )=\frac{1}{5}$, then the value of $P ( B )$ will be
- A
$\frac{1}{5}$
- ✓
$\frac{1}{2}$
- C
$0$
- D
$\frac{2}{25}$
AnswerCorrect option: B. $\frac{1}{2}$
$\frac{1}{2}$
View full question & answer→MCQ 381 Mark
If $A \subset B$, then the value of $P(A \cap B)$ will be $-$
- ✓
$P(A)$
- B
$P(B)$
- C
$P(A \cup B)$
- D
$0$
AnswerCorrect option: A. $P(A)$
$P(A)$
View full question & answer→MCQ 391 Mark
If $P(A)=\left(\frac{1}{2}\right), P(B)=0$, then the value of $P(A / B)$ will be
View full question & answer→MCQ 401 Mark
The distance of point $(3, 5, 7)$ from $x$ axis is
View full question & answer→MCQ 411 Mark
If $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$ then the value of $\vec{b} \times \vec{a}$
- A
$0$
- B
$\hat{i}+\hat{j}$
- ✓
$-\hat{i}+\hat{j}$
- D
$-\hat{i}-\hat{j}$
AnswerCorrect option: C. $-\hat{i}+\hat{j}$
$-\hat{i}+\hat{j}$
View full question & answer→MCQ 421 Mark
The value of $\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k}(\hat{i} \times \hat{j})$ is
View full question & answer→MCQ 431 Mark
The area of region bounded by $y= \sin x $ and $x-$ axis is, when $0 \leq x \leq 2n \ ($in sq units$)$
View full question & answer→MCQ 441 Mark
The value of $\int_{-\pi / 2}^{\pi / 2}\left(x^3+x \cos x+\tan 5 x+1\right) d x$ is
- A
$0$
- B
$1$
- ✓
$\pi$
- D
$\frac{\pi}{2}$
View full question & answer→MCQ 451 Mark
The value of $\int \frac{1}{e^x+e^{-x}} d x$ is
- A
$\tan ^{-1}\left(e^x\right)+c$
- B
$\tan ^{-1}\left(e^{-x}\right)+c$
- C
$\log \left(e^x+e^{-x}\right)+c$
- ✓
View full question & answer→MCQ 461 Mark
If $y=x^x$, then the value of $\frac{d y}{d x}$ will be
- A
$x \cdot x^{x-1}$
- B
$x \log x$
- C
$x^x \cdot \log x$
- ✓
$x^x(1+\log x)$
AnswerCorrect option: D. $x^x(1+\log x)$
$x^x(1+\log x)$
View full question & answer→MCQ 471 Mark
If $*$ is a binary operation in $R$ defined as $a ^* b = a + b - ab$, then identity element for $"*"$ will be
View full question & answer→MCQ 481 Mark
If $f: R \rightarrow R_{,} f(x)=3 x-5$, then the value of $\text{fof}(3)$ is
View full question & answer→MCQ 491 Mark
If $P(E) = 0.35$ and $P(E \cup F) = 0.6$ and $E$ and $F$ are independent events, then $P(F)$ is equal to $-$
- ✓
$\frac{5}{13}$
- B
$\frac{7}{13}$
- C
$\frac{9}{13}$
- D
$\frac{11}{13}$
AnswerCorrect option: A. $\frac{5}{13}$
$\frac{5}{13}$
View full question & answer→MCQ 501 Mark
$A$ and $B$ are two events such that $P(A / B) =P(B/A). \neq 0$ then which of the following is correct $-$
- A
$A \subset B$
- B
$A = R$
- C
$A \cap B=\phi$
- ✓
$P(A) = P(B)$
AnswerCorrect option: D. $P(A) = P(B)$
$P(A) = P(B)$
View full question & answer→MCQ 511 Mark
If $P(A)=\left(\frac{3}{10}\right), P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{3}{5}$, then $P\left(\frac{B}{A}\right)+P\left(\frac{A}{B}\right)$ is equal to $-$
- A
$\frac{1}{4}$
- B
$\frac{1}{3}$
- C
$\frac{5}{12}$
- ✓
$\frac{7}{12}$
AnswerCorrect option: D. $\frac{7}{12}$
$\frac{7}{12}$
View full question & answer→MCQ 521 Mark
The distance of point $(\alpha, \beta, \gamma)$ from $y$ axis is $-$
AnswerCorrect option: D. $\sqrt{\alpha^2+\gamma^2}$
$\sqrt{\alpha^2+\gamma^2}$
View full question & answer→MCQ 531 Mark
The angle between the vectors $\vec{a} \times \vec{b}$ and $\vec{b} \times \vec{a}$ is
- A
$0$
- B
$90^\circ$
- C
$135^\circ$
- ✓
$180^\circ$
AnswerCorrect option: D. $180^\circ$
$180^\circ$
View full question & answer→MCQ 541 Mark
The value of expression $\hat{i}, \hat{i}-\hat{j} \cdot \hat{j}+\hat{k} \cdot \hat{k}$ is $-$
View full question & answer→MCQ 551 Mark
Area bounded by curve $y^2 = 4x, y-$ axis and line $y = 3$ is $($in sq units$)$
- ✓
$2$
- B
$\frac{9}{4}$
- C
$\frac{9}{3}$
- D
$\frac{9}{2}$
View full question & answer→MCQ 561 Mark
Solution of $\int x \sin x\ d x$ is $-$
- A
$x \sin x+\cos x + c$
- ✓
$-x \cos x+ \sin x + c$
- C
$x \sin x-6 \cos x+c$
- D
$x \cos x+ \sin x + c$
AnswerCorrect option: B. $-x \cos x+ \sin x + c$
$-x \cos x+ \sin x + c$
View full question & answer→MCQ 571 Mark
Solution of $\int \sin 3 x\ d x$ is
AnswerCorrect option: D. $-\cos 3 x+c$
$-\cos 3 x+c$
View full question & answer→MCQ 581 Mark
Which of the following functions is discontinuous function ?
- A
$\sin x$
- B
$X^2$
- ✓
$\frac{1}{1-2 x}$
- D
$\frac{1}{1+x^2}$
AnswerCorrect option: C. $\frac{1}{1-2 x}$
$\frac{1}{1-2 x}$
View full question & answer→MCQ 591 Mark
If matrix $A$ and $B$ are of the order $m \times n$ and $n \times p$ respectively, then order of $AB$ is
- A
$p \times m$
- B
$n \times m$
- ✓
$m \times p$
- D
$m \times n$
AnswerCorrect option: C. $m \times p$
$m \times p$
View full question & answer→MCQ 601 Mark
Relation $R$ is defined in set $N$ as following : $R = \{(a, b) : a = b - 2, b > 6\}$ Then which of the following is correct.
- A
$(2,4) \in R$
- B
$(3,8) \in R$
- ✓
$(6,8) \in R$
- D
$(8,7) \in R$
AnswerCorrect option: C. $(6,8) \in R$
$(6,8) \in R$
View full question & answer→