MCQ 11 Mark
If the matrix A is both symmetric and skew symmetric, then
MCQ 21 Mark
$\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)=$ _________.
- A
$\frac{\pi}{3}$
- B
$\frac{\pi}{2}$
- C
$\frac{3 \pi}{4}$
- D
$\frac{\pi}{4}$
View full question & answer→MCQ 31 Mark
If $\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{2}$ then $\cos ^{-1} x+\cos ^{-1} y=$ _________.
- A
$\frac{\pi}{2}$
- B
$0$
- C
$\pi$
- D
$\frac{2 \pi}{3}$
View full question & answer→MCQ 41 Mark
$\cos \left(\frac{\pi}{3}-\sin ^{-1}\left(-\frac{1}{2}\right)\right)=$ _________.
- A
$\frac{1}{2}$
- B
$0$
- C
- D
$\frac{\sqrt{3}}{2}$
View full question & answer→MCQ 51 Mark
$\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)-\operatorname{cosec}^{-1}(-\sqrt{2})=$ _________.
- A
$\frac{\pi}{6}$
- B
$\frac{3 \pi}{4}$
- C
$\frac{\pi}{2}$
- D
$\frac{\pi}{3}$
View full question & answer→MCQ 61 Mark
If $f: R \rightarrow R$ be given by $f(x)=\left(3-x^3\right)^{\frac{1}{3}}$ then $(f \circ f)(x)$ is _________ .
- A
- B
$x^3$
- C
$x^{\frac{1}{3}}$
- D
$(3-x)^3$
View full question & answer→MCQ 71 Mark
Let $A=\{1,2,3\}$. Then number of equivalence relations containing $(1,2)$ is __________ .
View full question & answer→MCQ 81 Mark
$f: A \rightarrow B$ and $g: B \rightarrow C$ be two invertible functions then $(g \circ f)^{-1}=$ _________.
- A
$g^{-1} \circ f^{-1}$
- B
- C
$f^{-1} \circ g^{-1}$
- D
$g \circ f$
View full question & answer→MCQ 91 Mark
A and B are two events. $P ( A )=\frac{1}{2}, P ( B )=\frac{1}{3}$ and $P ( A \cap B )=\frac{1}{4}$ then $P \left( A ^{\prime} / B \right)=$ _________.
- A
$\frac{1}{6}$
- B
$\frac{1}{5}$
- C
$\frac{1}{4}$
- D
$\frac{1}{7}$
View full question & answer→MCQ 101 Mark
The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students, four are swimmers is __________ .
- A
${ }^5 C _1 \frac{1}{5}\left(\frac{4}{5}\right)^4$
- B
${ }^5 C _4\left(\frac{4}{5}\right)\left(\frac{1}{5}\right)^4$
- C
$\left(\frac{4}{5}\right)\left(\frac{1}{5}\right)^4$
- D
$\left(\frac{5}{4}\right)^3 \frac{1}{5}$
View full question & answer→MCQ 111 Mark
If $A$ and $B$ are any two events such that $P ( A )+ P ( B )- P ( A$ and B $)= P ( A )$ then __________ .
View full question & answer→MCQ 121 Mark
The feasible region is bounded. The coordinates of the comer points of the feasible region are $(0,4),(0,5),(3,5),(5,3)$, $(5.0)$ and $(4,0) . Z=10 x-70 y+1900$, then minimum of $Z$ value is _________.
View full question & answer→MCQ 131 Mark
Points within and on the boundary of the feasible region represents feasible solutions of the constraints. Any point outside the feasible region is an
MCQ 141 Mark
The corner points of the feasible region determined by the following system of linear inequalities : $2 x+y \leq 10, x+3 y \leq 15$, $x, y \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$. Let $Z =p x+q y$ where $p, q>0$, condition on $p$ and $q$ so that the maximum of Z occurs at both $(3,4)$ and $(0,5)$ is
View full question & answer→MCQ 151 Mark
Distance between the two planes : $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is
- A
$\frac{3}{\sqrt{29}}$
- B
$\frac{2}{\sqrt{29}}$
- C
$\frac{8}{\sqrt{29}}$
- D
View full question & answer→MCQ 161 Mark
The angle between line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ and plane $2 x-2 y+z=5$ is _________.
- A
$\sin ^{-1}\left(\frac{\sqrt{2}}{10}\right)$
- B
$\sin ^{-1}\left(\frac{1}{5 \sqrt{2}}\right)$
- C
$\sin ^{-1}\left(\frac{10}{6 \sqrt{5}}\right)$
- D
$\cos ^{-1}\left(\frac{\sqrt{2}}{10}\right)$
View full question & answer→MCQ 171 Mark
The lines $\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles then $p=$ _________.
- A
$\frac{71}{11}$
- B
$\frac{72}{11}$
- C
$\frac{73}{11}$
- D
$\frac{70}{11}$
View full question & answer→MCQ 181 Mark
For vector $\vec{a}$$
(\vec{a} \times \hat{i})^2+(\vec{a} \times \hat{j})^2+(\vec{a} \times \hat{k})^2=
$ _________.
- A
$4|a|^2$
- B
$3|\vec{a}|^2$
- C
$|\vec{a}|^2$
- D
$2|\vec{a}|^2$
View full question & answer→MCQ 191 Mark
If two vectors $\vec{a}$ and $\vec{b}$ are such that $|\vec{a}|=2,|\vec{b}|=3$ and $\vec{a} \cdot \vec{b}=4$ then $|\vec{a}-\bar{b}|=$_________ .
- A
$\sqrt{5}$
- B
$\sqrt{3}$
- C
$\sqrt{2}$
- D
$\sqrt{6}$
View full question & answer→MCQ 201 Mark
The projection of vectors $\vec{a}=2 \dot{i}-\hat{j}+\vec{k}$ on the vector $\vec{b}=\dot{i}+2 \dot{j}+2 \dot{k}$ is _________ .
- A
- B
$\frac{1}{3}$
- C
$\frac{2}{3}$
- D
$\sqrt{6}$
View full question & answer→MCQ 211 Mark
Let the vectors $\vec{a}$ and $\vec{b}$ be such that $|\vec{a}|=3$ and $|\vec{b}|=\frac{\sqrt{2}}{3}$ then $\vec{a} \times \vec{b}$ is a unit vector. If the angle between $\vec{a}$ and $\vec{b}$ is
- A
$\frac{\pi}{4}$
- B
$\frac{\pi}{2}$
- C
$\frac{\pi}{3}$
- D
$\frac{\pi}{6}$
View full question & answer→MCQ 221 Mark
If $|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144$ and $|\vec{a}|=4$ then $|\vec{b}|=$ _________.
View full question & answer→MCQ 231 Mark
The area of a parallelogram where adjacent sides are given by the vectors $\vec{a}=3 \hat{i}+\hat{j}+4 \hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ is
- A
$\sqrt{42}$
- B
$\sqrt{52}$
- C
$\sqrt{32}$
- D
$\sqrt{62}$
View full question & answer→MCQ 241 Mark
The general solution of the differential equation $\frac{d y}{d x}+\frac{y}{x}=1$ is
- A
$x y=\frac{x^3}{2}+C$
- B
$x y=\frac{x^2}{2}+C$
- C
$x y=\frac{y^2}{2}+C$
- D
$x y=\frac{y^3}{2}+C$
View full question & answer→MCQ 251 Mark
A homogeneous differential equation of the form $\frac{d x}{d y}=h\left(\frac{x}{y}\right)$ can be solved by making the substitution
- A
$v = yx$
- B
$y = vx$
- C
$x = vy$
- D
$x = v$
View full question & answer→MCQ 261 Mark
The degree of the differential equation $\left(1+\frac{d y}{d x}\right)^3=\left(\frac{d^2 y}{d x^2}\right)^2$
View full question & answer→MCQ 271 Mark
The area bounded by the Y -axis, $y=\cos x$ and $y=\sin x$ when $0 \leq x \leq \frac{\pi}{2}$.
- A
$\sqrt{2}$
- B
$2(\sqrt{2}-1)$
- C
$\sqrt{2}-1$
- D
$\sqrt{2}+1$
View full question & answer→MCQ 281 Mark
The area of the region bounded by the two parabolas $y=x^2$ and $y^2=x$ is _________.
- A
$\frac{1}{2}$
- B
$\frac{1}{4}$
- C
$\frac{1}{6}$
- D
$\frac{1}{3}$
View full question & answer→MCQ 291 Mark
Area of the region bounded by the curve $y^2=4 x, Y$-axis and the line $y=3$ is _________.
- A
$\frac{9}{4}$
- B
$\frac{9}{2}$
- C
$\frac{9}{5}$
- D
View full question & answer→MCQ 301 Mark
$\int_{-1}^1 \sin ^5 x \cos ^4 x d x=$ _________.
- A
$\frac{\pi}{2}$
- B
$0$
- C
- D
$\pi$
View full question & answer→MCQ 311 Mark
If $f(a+b-x)=f(x)$, then $\int_a^b x f(x) d x=$ _________.
- A
$\frac{b-a}{2} \int_a^b f(x) d x$
- B
$\frac{a+b}{2} \int_a^b f(b+x) d x$
- C
$\frac{a+b}{2} \int_a^b f(x) d x$
- D
$\frac{a+b}{2} \int_a^b f(b-x) d x$
View full question & answer→MCQ 321 Mark
$\int \frac{x^3}{x+1} d x=$ _________.
- A
$x-\frac{x^2}{2}-\frac{x^3}{3}-\log |1+x|+C$
- B
$x+\frac{x^2}{2}-\frac{x^3}{3}-\log |1-x|+ C$
- C
$x+\frac{x^2}{2}+\frac{x^3}{3}-\log |1-x|+C$
- D
$x-\frac{x^2}{2}+\frac{x^3}{3}-\log |1+x|+C$
View full question & answer→MCQ 331 Mark
$\int \frac{x+3}{(x+4)^2} e^x d x$
- A
$\frac{e^x}{x+3}+C$
- B
$e^x(x+4)+ C$
- C
$\frac{e^x}{x+4}+C$
- D
$e^x(x+3)+ C$
View full question & answer→MCQ 341 Mark
$\int \sec ^2 x \operatorname{cosec}^2 x d x=$ _________.
- A
$\tan x \cot x+C$
- B
$\tan x-\cot x+C$
- C
$\tan x+\cot x+C$
- D
$\tan x-\cot 2 x+C$
View full question & answer→MCQ 351 Mark
$\int_0^{\frac{2}{3}} \frac{d x}{4+9 x^2}=$ _________.
- A
$\frac{\pi}{6}$
- B
$\frac{\pi}{12}$
- C
$\frac{\pi}{24}$
- D
$\frac{\pi}{4}$
View full question & answer→MCQ 361 Mark
$\int_0^{\frac{\pi}{2}} \frac{\sin ^n x}{\sin ^n x+\cos ^n x} d x=$ _________.
- A
$\frac{\pi}{4}$
- B
$\frac{\pi}{3}$
- C
$\frac{\pi}{2}$
- D
$\pi$
View full question & answer→MCQ 371 Mark
$\int \frac{e^x(1+x)}{\sin ^2\left(x e^x\right)} d x=$ _________.
- A
$\cot \left(e^x\right)+C$
- B
$\tan \left(x e^x\right)+C$
- C
$-\cot \left(x e^x\right)+C$
- D
$\tan \left(e^x\right)+C$
View full question & answer→MCQ 381 Mark
If $f(x)=3 x^2+15 x+5$, then the approximate value of $f(3.02)$ is __________ .
View full question & answer→MCQ 391 Mark
The line $y=m x+1$ is a tangent to the curve $y^2=4 x$ then $m=$ _________.
View full question & answer→MCQ 401 Mark
On which of the following intervals is the function $f$ given by $f(x)=x^{100}+\sin x-1$ decreasing?
- A
- B
$\left(\frac{\pi}{2}, \pi\right)$
- C
$\left(0, \frac{\pi}{2}\right)$
- D
View full question & answer→MCQ 411 Mark
The rate of change of the area of a circle with respect to its radius $r$ at $r=4 cm$ is
- A
$8 \pi$
- B
$12 \pi$
- C
$10 \pi$
- D
$11 \pi$
View full question & answer→MCQ 421 Mark
If $y=\log \left(\frac{1-x^2}{1+x^2}\right)$ then $\frac{d y}{d x}=$ _________.
- A
$\frac{-4 x}{1-x^4}$
- B
$\frac{1}{4-x^4}$
- C
$\frac{-4 x^3}{1-x^4}$
- D
$\frac{4 x^3}{1-x^4}$
View full question & answer→MCQ 431 Mark
$\frac{d}{d x}\left(5^{\sin ^{-1} x+\cos ^{-1} x}\right)=$ _________ $(|x| < 1)$
- A
$0$
- B
$\frac{2}{\sqrt{1-x^2}}$
- C
$\frac{1}{\sqrt{1-x^2}}$
- D
$\frac{5}{\sqrt{1-x^2}}$
View full question & answer→MCQ 441 Mark
If $y=\sqrt{\sin x+y}$ then $\frac{d y}{d x}=$ _________.
- A
$\frac{\sin x}{1-2 y}$
- B
$\frac{\cos x}{1-2 y}$
- C
$\frac{\cos x}{2 y-1}$
- D
$\frac{\sin x}{2 y-1}$
View full question & answer→MCQ 451 Mark
Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|\operatorname{adj} A|$ is equal to _________ .
- A
$|A|^3$
- B
$|A|^2$
- C
$|A|$
- D
$3|A|$
View full question & answer→MCQ 461 Mark
If area of triangle is 35 sq. units with vertices $(2,-6),(5,4)$ and $(k, 4)$, then $k=$ _________ .
- A
$-12, -2$
- B
$12, -2$
- C
- D
$-12, 2$
View full question & answer→MCQ 471 Mark
If $\left|\begin{array}{cc}x & 2 \\ 15 & x\end{array}\right|=\left|\begin{array}{ll}6 & 6 \\ 3 & 4\end{array}\right|$ then $x=$ _________.
View full question & answer→MCQ 481 Mark
The number of all possible matrices of order $3 \times 3$ with each entry 0 or 1 is_________ .
View full question & answer→MCQ 491 Mark
If $A =\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ and $A ^2=1$, then _________.
- A
$1-\alpha^2-\beta \gamma=0$
- B
$1-\alpha^2+\beta \gamma=0$
- C
$1+\alpha^2+\beta \gamma=0$
- D
$1+\alpha^2-\beta \gamma=0$
View full question & answer→MCQ 501 Mark
If $A=\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ and $A+A^{\prime}=I$ then $\alpha=$ _________.
- A
$\pi$
- B
$\frac{\pi}{6}$
- C
$\frac{\pi}{3}$
- D
$\frac{3 \pi}{2}$
View full question & answer→