MCQ 11 Mark
The area of the region bounded by ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is __________ .
- A
$24 \pi$
- B
$36 \pi$
- C
$13 \pi$
- ✓
$6 \pi$
AnswerCorrect option: D. $6 \pi$
View full question & answer→MCQ 21 Mark
The area of the region bounded by the curve $y=\cos x, x=0$ and $x=\frac{3 \pi}{2}$ is __________ .
View full question & answer→MCQ 31 Mark
$\int \tan ^8 x \cdot \sec ^4 x d x=$ __________ + C .
- A
$\frac{\tan ^9 x}{9}-\frac{\tan ^7 x}{7}$
- B
$\frac{\tan ^{11} x}{11}-\frac{\tan ^9 x}{9}$
- C
$\frac{\tan ^9 x}{9}+\frac{\tan ^7 x}{7}$
- ✓
$\frac{\tan ^{11} x}{11}+\frac{\tan ^9 x}{9}$
AnswerCorrect option: D. $\frac{\tan ^{11} x}{11}+\frac{\tan ^9 x}{9}$
View full question & answer→MCQ 41 Mark
$\int \frac{1-\cos x}{1+\cos x} d x=$ __________ + C .
- ✓
$2 \tan \frac{x}{2}-x$
- B
$2 \tan \frac{x}{2}+x$
- C
$-2 \tan \frac{x}{2}-x$
- D
$-\tan \frac{x}{2}-x$
AnswerCorrect option: A. $2 \tan \frac{x}{2}-x$
View full question & answer→MCQ 51 Mark
$\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{d x}{1+\sqrt{\tan x}}=$ __________ + C.
- A
$0$
- B
$\frac{\pi}{3}$
- ✓
$\frac{\pi}{12}$
- D
$\frac{\pi}{6}$
AnswerCorrect option: C. $\frac{\pi}{12}$
View full question & answer→MCQ 61 Mark
$\int e^x \cdot \sec x(1+\tan x) d x=$ __________ , $+C$.
- A
$e^x \cdot \tan x$
- ✓
$e^x \cdot \sec x$
- C
$e^x \cdot \sin x$
- D
$e^x \cdot \cos x$
AnswerCorrect option: B. $e^x \cdot \sec x$
View full question & answer→MCQ 71 Mark
$\int \frac{e^x(1+x)}{\sin ^2\left(x-e^x\right)} d x=$ __________ +c.
- ✓
$-\cot \left(x \cdot e^x\right)$
- B
$\tan \left(x \cdot e^x\right)$
- C
$-\tan \left(x \cdot e^x\right)$
- D
$\cot \left(x \cdot e^x\right)$
AnswerCorrect option: A. $-\cot \left(x \cdot e^x\right)$
View full question & answer→MCQ 81 Mark
$\int \frac{x}{\sqrt{x+4}} d x=$ __________ , $+ C , x >-4$.
- A
$-\frac{1}{3} \sqrt{x+4}(x-8)$
- ✓
$\frac{2}{3} \sqrt{x+4}(x-8)$
- C
$\frac{1}{3} \sqrt{x+4}(x-8)$
- D
$-\frac{2}{3} \sqrt{x+4}(x-8)$
AnswerCorrect option: B. $\frac{2}{3} \sqrt{x+4}(x-8)$
View full question & answer→MCQ 91 Mark
$\int \frac{\sin \left(\tan ^{-1} x\right)}{1+x^2} d x=$ __________ , + C .
- A
$\cos \left(\tan ^{-1} x\right)$
- B
$-\sin \left(\tan ^{-1} x\right)$
- ✓
$-\cos \left(\tan ^{-1} x\right)$
- D
$\sin \left(\tan ^{-1} x\right)$
AnswerCorrect option: C. $-\cos \left(\tan ^{-1} x\right)$
View full question & answer→MCQ 101 Mark
If $\frac{d}{d x}(f(x))=4 x^3-\frac{3}{x^4}$ and $f(2)=0$, then $f(x)=$ __________ .
- A
$x^3+\frac{1}{x^4}-\frac{129}{8}$
- B
$x^3+\frac{1}{x^4}+\frac{129}{8}$
- C
$x^4+\frac{1}{x^3}+\frac{129}{8}$
- ✓
$x^4+\frac{1}{x^3}-\frac{129}{8}$
AnswerCorrect option: D. $x^4+\frac{1}{x^3}-\frac{129}{8}$
View full question & answer→MCQ 111 Mark
Nearest point on the curve $x^2=2 y$ from point $(0,5)$ is __________ .
- A
$(2,2)$
- B
$(2 \sqrt{2}, 0)$
- C
$(0,0)$
- ✓
$(2 \sqrt{2}, 4)$
AnswerCorrect option: D. $(2 \sqrt{2}, 4)$
View full question & answer→MCQ 121 Mark
What is the maximum value of function $f(x)=\sin x+\cos x$ ?
AnswerCorrect option: B. $\sqrt{2}$
View full question & answer→MCQ 131 Mark
Function $y=6-9 x-x^2$ is strictly increasing function on interval __________ .
- ✓
$\left(-\infty,-\frac{9}{2}\right)$
- B
$\left(-\infty, \frac{9}{2}\right)$
- C
$(-\infty, 0)$
- D
$\left(0,-\frac{9}{2}\right)$
AnswerCorrect option: A. $\left(-\infty,-\frac{9}{2}\right)$
View full question & answer→MCQ 141 Mark
The radius of circle is increasing at rate of 0.7 $cm / s$, then circumference of circle is increasing at rate of __________ .
- A
$-1.4 \pi cm / s$
- B
$14 \pi cm / s$
- C
$0.14 \pi cm / s$
- ✓
$1.4 \pi cm / s$
AnswerCorrect option: D. $1.4 \pi cm / s$
View full question & answer→MCQ 151 Mark
If $x=a t^2, y=2 a t$, then $\frac{d y}{d x}=$ __________ .
- A
$\frac{y}{x}$
- B
$\frac{x}{2 y}$
- ✓
$\frac{y}{2 x}$
- D
$\frac{x}{y}$
AnswerCorrect option: C. $\frac{y}{2 x}$
View full question & answer→MCQ 161 Mark
For $x y=e^{x-y}, \frac{d y}{d x}=$ __________ .
- A
$\frac{y(x+1)}{x(y-1)}$
- ✓
$\frac{y(x-1)}{x(y+1)}$
- C
$\frac{y(y+1)}{x(x-1)}$
- D
$\frac{x(y+1)}{y(x-1)}$
AnswerCorrect option: B. $\frac{y(x-1)}{x(y+1)}$
View full question & answer→MCQ 171 Mark
If $x=\sin y$, then $\frac{d^2 y}{d x^2}=$ __________ . , $(0< x <1)$.
- A
$\frac{-1}{\left(1-x^2\right)^{\frac{3}{2}}}$
- B
$\frac{-x}{\left(1-x^2\right)^{\frac{3}{2}}}$
- ✓
$\frac{x}{\left(1-x^2\right)^{\frac{3}{2}}}$
- D
$\frac{1}{\left(1-x^2\right)^{\frac{3}{2}}}$
AnswerCorrect option: C. $\frac{x}{\left(1-x^2\right)^{\frac{3}{2}}}$
View full question & answer→MCQ 181 Mark
If A and B are $3 \times 3$ order matrices and $| A |=5$, $|B|=3$, then $|3 A B|=$ __________ .
View full question & answer→MCQ 191 Mark
For matrix $A =\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 3 & 0 \\ 0 & 0 & 4\end{array}\right],\left( A ^{-1}\right)^2=$ __________ .
- A
$\left[\begin{array}{ccc}-\frac{1}{4} & 0 & 0 \\ 0 & -\frac{1}{9} & 0 \\ 0 & 0 & -\frac{1}{16}\end{array}\right]$
- B
$\left[\begin{array}{ccc}-4 & 0 & 0 \\ 0 & -9 & 0 \\ 0 & 0 & -16\end{array}\right]$
- ✓
$\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{9} & 0 \\ 0 & 0 & \frac{1}{16}\end{array}\right]$
- D
$\left[\begin{array}{ccc}4 & 0 & 0 \\ 0 & 9 & 0 \\ 0 & 0 & 16\end{array}\right]$
AnswerCorrect option: C. $\left[\begin{array}{ccc}\frac{1}{4} & 0 & 0 \\ 0 & \frac{1}{9} & 0 \\ 0 & 0 & \frac{1}{16}\end{array}\right]$
View full question & answer→MCQ 201 Mark
The area of triangle whose vertices are $(2,-6),(5,4)$ and $(k, 4)$ is 35 sq. unit then, value of $k$ is __________ .
AnswerCorrect option: A. $12,-2$
View full question & answer→MCQ 211 Mark
If A is $2 \times 2$ order non-singular matrix then, determinant of $A ^{-1}$ is __________ .
AnswerCorrect option: B. $\frac{1}{\operatorname{det}(A)}$
View full question & answer→MCQ 221 Mark
If $A$ and $B$ are same order skew symmetric matrices then, $( AB )^{\prime}=$ ___________ .
View full question & answer→MCQ 231 Mark
If for $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right], A^2=I$, then __________ .
- A
$1+\alpha^2-\beta \gamma=0$
- B
$1-\alpha^2+\beta \gamma=0$
- ✓
$1-\alpha^2-\beta \gamma=0$
- D
$1+\alpha^2+\beta \gamma=0$
AnswerCorrect option: C. $1-\alpha^2-\beta \gamma=0$
View full question & answer→MCQ 241 Mark
For $3 \times 3$ order matrix $A$ and $B$, which of the following is correct ?
- A
$AB =1$
- ✓
$AB \neq BA$
- C
$AB = O$
- D
$AB = BA$
AnswerCorrect option: B. $AB \neq BA$
View full question & answer→MCQ 251 Mark
The order of matrix A is $m \times n$ and for matrix B , if $AB ^{\prime}$ and $B ^{\prime} A$ are defined then, order of matrix B is __________ .
- ✓
$m \times n$
- B
$n \times n$
- C
$n \times m$
- D
$m \times m$
AnswerCorrect option: A. $m \times n$
View full question & answer→MCQ 261 Mark
$\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)+\tan ^{-1}\left(\tan \frac{7 \pi}{6}\right)=$ __________ .
- A
$0$
- ✓
$\frac{\pi}{3}$
- C
$\frac{\pi}{6}$
- D
$\pi$
AnswerCorrect option: B. $\frac{\pi}{3}$
View full question & answer→MCQ 271 Mark
The simplest form of $\cot ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right), x>1$ is __________ .
AnswerCorrect option: D. $\sec ^{-1} x$
View full question & answer→MCQ 281 Mark
$\sin \left(\tan ^{-1} x\right),|x|<1=$ __________ .
- ✓
$\frac{x}{\sqrt{1+x^2}}$
- B
$\frac{1}{\sqrt{1-x^2}}$
- C
$\frac{1}{\sqrt{1+x^2}}$
- D
$\frac{x}{\sqrt{1-x^2}}$
AnswerCorrect option: A. $\frac{x}{\sqrt{1+x^2}}$
View full question & answer→MCQ 291 Mark
$\tan ^{-1}(-\sqrt{3})-\sec ^{-1}(-2)=$ __________ .
- A
$\frac{2 \pi}{3}$
- B
$\pi$
- ✓
$-\pi$
- D
$-\frac{2 \pi}{3}$
AnswerCorrect option: C. $-\pi$
View full question & answer→MCQ 301 Mark
$f: R \rightarrow R , f(x)=4 x+3$ is defined then, $f^{-1}(x)=$ __________ .
- ✓
$\frac{x-3}{4}$
- B
$\frac{x-4}{3}$
- C
$\frac{x+3}{4}$
- D
$\frac{x+4}{3}$
AnswerCorrect option: A. $\frac{x-3}{4}$
View full question & answer→MCQ 311 Mark
Function $f: N \rightarrow N , f(x)=\left\{\begin{array}{l}x+1, x \text { is odd } \\ x-1, x \text { is even }\end{array}\right.$ is defined then, $f$ is __________ .
View full question & answer→MCQ 321 Mark
Relation $R =\{(a, b): a < b\}$ is defined on set of real number then R is __________ .
- A
reflexive and transitive but not symmetric.
- ✓
transitive but not reflexive and symmetric.
- C
reflexive and symmetric but not transitive.
- D
Symmetric but not reflexive and transitive.
AnswerCorrect option: B. transitive but not reflexive and symmetric.
View full question & answer→MCQ 331 Mark
For two events $A$ and $B$,
$P(A)+P(B)-P(A$ and $B)=P(A)$, then __________ .
- A
$P(A \mid B)=0$
- ✓
$P ( A \mid B )=1$
- C
$P ( B \mid A )=0$
- D
$P(B \mid A)=1$
AnswerCorrect option: B. $P ( A \mid B )=1$
View full question & answer→MCQ 341 Mark
If $2 P(A)=P(B)=\frac{5}{13}$ and $P(A \mid B)=\frac{2}{5}$, then $P ( A \cup B )=$ __________ .
- A
$\frac{10}{26}$
- B
$\frac{10}{13}$
- ✓
$\frac{11}{26}$
- D
$\frac{11}{13}$
AnswerCorrect option: C. $\frac{11}{26}$
View full question & answer→MCQ 351 Mark
The minimum value of $Z=3 x+4 y$ subject to the constraints $x+y \leq 4, x \geq 0, y \geq 0$ is __________ .
View full question & answer→MCQ 361 Mark
The corner points of the feasible region are $(0,10),(5,5),(15,15),(0,20)$. The maximum value of $Z=3 x+9 y$ is __________ .
View full question & answer→MCQ 371 Mark
Angle between lines $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{x-5}{4}=\frac{y-2}{1}=\frac{z-3}{8}$ is __________ .
- A
$\sin ^{-1}\left(\frac{2}{3}\right)$
- B
$\pi-\cos ^{-1}\left(\frac{2}{3}\right)$
- C
$-\cos ^{-1}\left(\frac{2}{3}\right)$
- ✓
$\cos ^{-1}\left(\frac{2}{3}\right)$
AnswerCorrect option: D. $\cos ^{-1}\left(\frac{2}{3}\right)$
View full question & answer→MCQ 381 Mark
The cartesian equation of line which is parallel to $3 \hat{i}+2 \hat{j}-8 \hat{k}$ and passes through the point $(5,2,-4)$ is __________ .
- A
$\frac{x-5}{-3}=\frac{y-2}{-2}=\frac{z+4}{-8}$
- B
$\frac{x+5}{3}=\frac{y+2}{2}=\frac{z-4}{-8}$
- C
$\frac{x-5}{3}=\frac{y-2}{2}=\frac{z-4}{-8}$
- ✓
$\frac{x-5}{3}=\frac{y-2}{2}=\frac{z+4}{-8}$
AnswerCorrect option: D. $\frac{x-5}{3}=\frac{y-2}{2}=\frac{z+4}{-8}$
View full question & answer→MCQ 391 Mark
If 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 mutually perpendicular to each other then, $p=$ __________ .
- A
$-70$
- ✓
$\frac{70}{11}$
- C
$-\frac{70}{11}$
- D
$70$
AnswerCorrect option: B. $\frac{70}{11}$
View full question & answer→MCQ 401 Mark
$(\vec{a}+\vec{b}) \cdot(\vec{a}+\vec{b})=|\vec{a}|^2+|\vec{b}|^2$ if and only if __________ . $(\vec{a} \neq \overrightarrow{0}, \vec{b} \neq \overrightarrow{0})$.
- A
$\vec{a}$ and $\vec{b}$ are not parallel and perpendicular to each other.
- ✓
$\vec{a}$ and $\vec{b}$ are perpendicular to each other.
- C
$\vec{a}$ and $\vec{b}$ are in opposite direction.
- D
$\vec{a}$ and $\vec{b}$ are in same direction.
AnswerCorrect option: B. $\vec{a}$ and $\vec{b}$ are perpendicular to each other.
View full question & answer→MCQ 411 Mark
The vector which is parallel to the resultant vector of $\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-2 \hat{j}+\hat{k}$ and having magnitude of 5 unit, is __________ .
- ✓
$\frac{3 \sqrt{10}}{2} \hat{i}+\frac{\sqrt{10}}{2} \hat{j}$
- B
$\frac{3 \sqrt{10}}{2} \hat{i}-\frac{10 \sqrt{2}}{2} \hat{j}$
- C
$\frac{3 \sqrt{10}}{2} \hat{i}+\frac{10 \sqrt{2}}{2} \hat{j}+\frac{\sqrt{2}}{2} \hat{k}$
- D
$\frac{5}{\sqrt{51}} \hat{i}-\frac{5}{\sqrt{51}} \hat{j}-\frac{35}{\sqrt{51}} \hat{k}$
AnswerCorrect option: A. $\frac{3 \sqrt{10}}{2} \hat{i}+\frac{\sqrt{10}}{2} \hat{j}$
View full question & answer→MCQ 421 Mark
The direction cosine of vector $\hat{i}-2 \hat{j}+3 \hat{k}$ is __________ .
- A
$\frac{1}{14}, \frac{2}{14}, \frac{3}{14}$
- B
$\frac{-1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}$
- ✓
$\frac{1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$
- D
$1,-2,3$
AnswerCorrect option: C. $\frac{1}{\sqrt{14}}, \frac{-2}{\sqrt{14}}, \frac{3}{\sqrt{14}}$
View full question & answer→MCQ 431 Mark
$\hat{i} \cdot(\hat{j} \times \hat{k})+\hat{j} \cdot(\hat{i} \times \hat{k})+\hat{k} \cdot(\hat{i} \times \hat{j})$ $+\hat{j} \cdot(\hat{j} \times \hat{k})=$ __________ .
View full question & answer→MCQ 441 Mark
The adjacent sides of Parallelogram are $\vec{a}=\hat{i}-\hat{j}+3 \hat{k}$ and $\vec{b}=2 \hat{i}-7 \hat{j}+\hat{k}$, then its area is __________ .
- A
- B
- C
$\frac{15}{\sqrt{2}}$
- ✓
$15 \sqrt{2}$
AnswerCorrect option: D. $15 \sqrt{2}$
View full question & answer→MCQ 451 Mark
The angle between vectors $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ is __________ .
- A
$\cos ^{-1}\left(\frac{2}{3}\right)$
- ✓
$\pi-\cos ^{-1}\left(\frac{1}{3}\right)$
- C
$\pi-\cos ^{-1}\left(\frac{2}{3}\right)$
- D
$\cos ^{-1}\left(\frac{1}{3}\right)$
AnswerCorrect option: B. $\pi-\cos ^{-1}\left(\frac{1}{3}\right)$
View full question & answer→MCQ 461 Mark
Homogeneous differential equation of the form
$\left(1+e^{\frac{x}{y}}\right) d x+e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) d y=0$
can be solved by making the substitution.
- A
$x=y$
- B
$v=y x$
- ✓
$x=v y$
- D
$y=v x$
AnswerCorrect option: C. $x=v y$
View full question & answer→MCQ 471 Mark
The general solution of differential equation $y \log y d x-x d y=0$ is __________ .
- A
$x=e^{c y}$
- ✓
$y=e^{c x}$
- C
$y=e^{-c x}$
- D
$x=e^{-c y}$
AnswerCorrect option: B. $y=e^{c x}$
View full question & answer→MCQ 481 Mark
The number of arbitary constant in general solution of fourth order differential equation is __________ .
MCQ 491 Mark
The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ is __________ .
View full question & answer→MCQ 501 Mark
The area of the region bounded by the curve $y=x|x|$, lines $x=-1$ and $x=1$ is, __________ .
- A
$\frac{4}{3}$
- B
$\frac{1}{3}$
- ✓
$\frac{2}{3}$
- D
$0$
AnswerCorrect option: C. $\frac{2}{3}$
View full question & answer→