MCQ 11 Mark
If $A$ is square matrix such that $A^2=A$, then $(I+A)^3-7 A$ $=$ _________ .
View full question & answer→MCQ 21 Mark
If $A , B$ are symmetric matrices of same order, then $AB - BA$ is _________ .
View full question & answer→MCQ 31 Mark
Total number of possible matrices of order $3 \times 3$ with each entry 2 or 9 is _________ .
View full question & answer→MCQ 41 Mark
$\sin ^{-1}(1-x)-2 \sin ^{-1} x=\frac{\pi}{2}$, then $x=$ _________.
- A
$0, \frac{1}{2}$
- B
$0$
- C
$1, \frac{1}{2}$
- D
$\frac{1}{2}$
View full question & answer→MCQ 51 Mark
$\sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}$, then $x=$ _________.
- A
- B
$\frac{25}{4}$
- C
- D
$\frac{25}{3}$
View full question & answer→MCQ 61 Mark
$\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})=$ _________.
- A
$\pi$
- B
$0$
- C
$-\frac{\pi}{2}$
- D
$2 \sqrt{3}$
View full question & answer→MCQ 71 Mark
$\cot ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right)=$ _________ where $x >1.$
View full question & answer→MCQ 81 Mark
Number of binary operations on the set $\{3,5\}$ are _________.
View full question & answer→MCQ 91 Mark
If $f: R \rightarrow R$ be given by $f(x)=\left(3-x^5\right)^{\frac{1}{5}}$, then $(f \circ f)(x)$ $=$ _________.
- A
$x^{\frac{1}{5}}$
- B
- C
$x^5$
- D
$3-x^5$
View full question & answer→MCQ 101 Mark
Let R be the relation in the set N given by $R =\{(a, b): a=b-2, b>6\}$. Then choose the correct option from the following.
- A
$(2,4) \in R$
- B
$(8,7) \in R$
- C
$(3,8) \in R$
- D
$(6,8) \in R$
View full question & answer→MCQ 111 Mark
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is _________.
MCQ 121 Mark
If $A$ and $B$ are two events such that $P(A) \neq 0$ and $P(B / A)=1$, then _________ .
- A
$A \subset B$
- B
$B=\varnothing$
- C
$B \subset A$
- D
$A=\varnothing$
View full question & answer→MCQ 131 Mark
Two events $A$ and $B$ will be independent, if _________.
View full question & answer→MCQ 141 Mark
For linear programming problem the objective function $Z=8000 x+12000 y$, if the corner points of the feasible region are $(0,0),(20,0),(12,6)$ and $(0,10)$, then maximum value of $Z$ occur at _________ corner point.
View full question & answer→MCQ 151 Mark
For linear programming problem the objective function $Z =10500 x+9000 y$, if the corner points of the bounded feasible region are $(0,0),(40,0),(30,20)$ and $(0,50)$, then the maximum value of $Z$ is _________ .
View full question & answer→MCQ 161 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 _________.
- A
$p=q$
- B
$p=3 q$
- C
$p=2 q$
- D
$q=3 p$
View full question & answer→MCQ 171 Mark
The direction cosines of the normal to the plane $5 y+8=0$ are _________ .
- A
$5, 8, 0$
- B
$0, 1, 0$
- C
$25, 64, 0$
- D
$0, 5, 0$
View full question & answer→MCQ 181 Mark
The angle between the line $\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}$ and the plane $10 x+2 y-11 z=3$ is _________.
- A
$\cos ^{-1}\left(\frac{8}{21}\right)$
- B
$\sin ^{-1}\left(\frac{8}{21}\right)$
- C
$\cos ^{-1}\left(\frac{8}{\sqrt{21}}\right)$
- D
$\sin ^{-1}\left(\frac{8}{\sqrt{21}}\right)$
View full question & answer→MCQ 191 Mark
Distance between the two planes $2 x+3 y+4 z=4$ and $4 x+6 y+8 z=12$ is_________ units.
- A
- B
- C
- D
$\frac{2}{\sqrt{29}}$
View full question & answer→MCQ 201 Mark
For any vectors $\vec{a}$ and $\vec{b}$, we always have $|\vec{a}||\vec{b}|$_________ $|\vec{a} \cdot \vec{b}|$.
View full question & answer→MCQ 211 Mark
If the vectors $\vec{a}=\hat{i}+3 \hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}-\hat{k} $ and $\vec{c}=\lambda \hat{i}+7 \hat{j}+3 \hat{k}$ are coplanar then $\lambda=$ _________.
View full question & answer→MCQ 221 Mark
For vectors $\vec{a}, \vec{b}, \vec{c}$, if $\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$ and $|\vec{a}|=2,|\vec{b}|=3,|\vec{c}|=5$ then $\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}=$ _________ .
View full question & answer→MCQ 231 Mark
The value of $\hat{k} \cdot(\hat{i} \times \hat{j})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{i} \cdot(\hat{j} \times \hat{k})$ is _________.
View full question & answer→MCQ 241 Mark
For the vectors $\vec{a}$ and $\vec{b}$, if $|\vec{a}|=3$ and $|\vec{b}|=\frac{\sqrt{2}}{3}$ and $\vec{a} \times \vec{b}$ is unit vector, then the angle between $\vec{a}$ and $\vec{b}$ is _________ .
- A
$\frac{\pi}{6}$
- B
$\frac{\pi}{3}$
- C
$\frac{\pi}{4}$
- D
$\frac{\pi}{2}$
View full question & answer→MCQ 251 Mark
The area of a triangle having the points A(1, 1, 1), B(1, 2, 3) and C (2, 3, 1) as its vertices is _________.
- A
$\frac{\sqrt{21}}{2}$
- B
$2 \sqrt{21}$
- C
$\sqrt{21}$
- D
$\frac{21}{2}$
View full question & answer→MCQ 261 Mark
The general solution of the differential equation $\frac{y d x-x d y}{y}=0$ is _________.
- A
$x y=c$
- B
$y=c x$
- C
$x=c y^2$
- D
$y=c x^2$
View full question & answer→MCQ 271 Mark
The number of arbitrary constants in the particular solution of a differential equation of third order are _________.
MCQ 281 Mark
The order and degree of the differential equation
$\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$
are _________ and _________ respectively.
View full question & answer→MCQ 291 Mark
The area bounded by the curve $y=\cos x$ between $x=0$ and $x=\frac{3 \pi}{2}$ is _________ sq. unit.
View full question & answer→MCQ 301 Mark
The area of the region bounded by the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ is _________ sq. unit.
- A
$144 \pi$
- B
- C
$12 \pi$
- D
$\frac{16 \pi}{9}$
View full question & answer→MCQ 311 Mark
Area lying between the curves $y^2=4 x$ and $y=2 x$ is _________.
- A
$\frac{2}{3}$
- B
$\frac{1}{4}$
- C
$\frac{1}{3}$
- D
$\frac{3}{4}$
View full question & answer→MCQ 321 Mark
$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x=$ _________.
View full question & answer→MCQ 331 Mark
$\int_0^1 x(1-x)^n d x=$ _________.
- A
$\frac{1}{n^2-3 n+2}$
- B
$\frac{1}{n^2-3 n-2}$
- C
$\frac{1}{n^2+3 n+2}$
- D
$\frac{1}{n^2+3 n-2}$
View full question & answer→MCQ 341 Mark
If $f(a+b-x)=f(x)$, then $\int_a^b x f(x) d x=$ _________.
- A
$\frac{a+b}{2} \int_a^b f(x) d x$
- B
$\frac{b-a}{2} \int_a^b f(x) d x$
- C
$\frac{a+b}{2} \int_a^b f(b+x) d x$
- D
$\frac{a+b}{2} \int_a^b f(b-x) d x$
View full question & answer→MCQ 351 Mark
$\int \frac{d x}{e^x+e^{-x}}=$ _________ + C.
- A
$\tan ^{-1}\left(e^x\right)$
- B
$\log \left(e^x-e^{-x}\right)$
- C
$\tan ^{-1}\left(e^{-x}\right)$
- D
$\log \left(e^x+e^{-x}\right)$
View full question & answer→MCQ 361 Mark
$\int \sqrt{x^2-8 x+7} d x=$ _________ + C.
- A
$\frac{1}{2}(x-4) \sqrt{x^2-8 x+7}+9 \log \left|x-4+\sqrt{x^2-8 x+7}\right|$
- B
$\frac{1}{2}(x-4) \sqrt{x^2-8 x+7}-3 \sqrt{2} \log \left|x-4+\sqrt{x^2-8 x+7}\right|$
- C
$\frac{1}{2}(x+4) \sqrt{x^2-8 x+7}+9 \log \left|x+4+\sqrt{x^2-8 x+7}\right|$
- D
$\frac{1}{2}(x-4) \sqrt{x^2-8 x+7}-\frac{9}{2} \log \left|x-4+\sqrt{x^2-8 x+7}\right|$
View full question & answer→MCQ 371 Mark
$\int \frac{(x-3) e^x}{(x-1)^3} d x=$ _________ + C.
- A
$\frac{e^x}{(x-1)^3}$
- B
$\frac{e^x}{(x-3)^3}$
- C
$\frac{e^x}{(x-3)^2}$
- D
$\frac{e^x}{(x-1)^2}$
View full question & answer→MCQ 381 Mark
$\int \frac{d x}{\sqrt{2 x-x^2}}=$ _________ + C.
View full question & answer→MCQ 391 Mark
$\int \frac{1}{x+x \log x} d x=$ _________ + C.
View full question & answer→MCQ 401 Mark
The maximum value of $[x(x-1)+1]^{\frac{1}{3}}, 0 \leq x \leq 1$ is _________.
View full question & answer→MCQ 411 Mark
The slope of the normal to the curve $y=2 x^2+3 \sin x$ at $x=0$ is _________.
- A
- B
$-3$
- C
$\frac{1}{3}$
- D
$-\frac{1}{3}$
View full question & answer→MCQ 421 Mark
The interval in which $y=x^2 e^{-x}$ is increasing is _________.
- A
$(-\infty, \infty)$
- B
$(2, \infty)$
- C
$(-2, 0)$
- D
View full question & answer→MCQ 431 Mark
The rate of change of the area of a circle with respect to its radius $r$ at $r=6 cm$ is _________ .
- A
$10 \pi$
- B
$8 \pi$
- C
$12 \pi$
- D
$11 \pi$
View full question & answer→MCQ 441 Mark
If $x=a(\theta+\sin \theta), y=a(1-\cos \theta)$, then $\frac{d y}{d x}=$ _________.
View full question & answer→MCQ 451 Mark
If $y=5 \cos x-3 \sin x$, then $\frac{d^2 y}{d x^2}=$ _________.
- A
$0$
- B
- C
$-y$
- D
$-\frac{d y}{d x}$
View full question & answer→MCQ 461 Mark
$f(x)=\left\{\begin{array}{cc}\frac{k \cos x}{\pi-2 x} & , \text { if } x \neq \frac{\pi}{2} \\ 3 & , \text { if } x=\frac{\pi}{2}\end{array}\right.$ is continuous function at $x=\frac{\pi}{2}$ then $k=$ _________.
View full question & answer→MCQ 471 Mark
If area of triangle is 35 sq. units with vertices (2, -6), (5, 4) and (k, 4), then k = _________.
MCQ 481 Mark
Let $A$ be a nonsingular square matrix of order $3 \times 3$. Then $|\operatorname{adj} A |=$ __________ .
View full question & answer→MCQ 491 Mark
For determinant A, if $A=\left|\begin{array}{ccc}1 & 2 & 13 \\ 3 & 0 & 5 \\ 6 & 7 & 11\end{array}\right|$ and p, q and r are cofactors of 13, 5 and 11 respectively, then p + 3q + 6r = _________.
View full question & answer→MCQ 501 Mark
For square matrix A if $A = B +\frac{ C }{2}$, where B is skew symmetric matrix and C is symmetric matrix, then C = _________.
View full question & answer→