Question 11 Mark
If $3 \sin ^{-1} x+4 \cos ^{-1} x=2 \pi$, then find the value of $x$.
View full question & answer→Question 21 Mark
Find the probability of getting an even prime number when a die is rolled.
Question 31 Mark
If $\vec{a}=3 \hat{i}-\hat{j}+4 \hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$ then find $|\vec{a}-\vec{b}|$.
View full question & answer→Question 41 Mark
If $\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}$, then find unit vector in direction of vector $\vec{a}$.
View full question & answer→Question 51 Mark
Show that the function $f(x)=\cos x$ is decreasing in the interval $\left(0, \frac{\pi}{2}\right)$.
View full question & answer→Question 61 Mark
If matrix $A=\left[\begin{array}{lll}2 & 4 & 6 \\ 1 & 2 & 1\end{array}\right]$, and $2 A+B=\left[\begin{array}{lll}3 & 4 & 2 \\ 4 & 1 & 2\end{array}\right]$ then find matrix $B$.
View full question & answer→Question 71 Mark
Find the direction cosines of normals of the plane $\vec{r} \cdot(3 \hat{i}+\hat{j}+4 \hat{k})=5$.
View full question & answer→Question 81 Mark
Find the area of ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$.
View full question & answer→Question 91 Mark
If the function $f(x)=\left\{\begin{array}{cc}2 x+1 & , x \neq 2 \\ 3 \lambda & , x=2\end{array}\right.$, is continuous at $x=2$, then find the value of $\lambda$.
View full question & answer→Question 101 Mark
Find the equation of normal at point $(1,2)$ on the curve $y=x^2+1$.
View full question & answer→Question 111 Mark
If the line $\frac{2 x-1}{4}=\frac{y-2}{3}=\frac{z-1}{\lambda}$ and plane $x+2 y+z=5$ are parallel, then find the value of $\lambda$.
View full question & answer→Question 121 Mark
Find the coordinates of mid point of line joining the points $(2,-2,0)$ and $(3,1,2)$.
View full question & answer→Question 131 Mark
If the lines $\frac{2 x-1}{4 a}=\frac{y-1}{3}=\frac{2-z}{-1}$ and $\frac{x}{1}=\frac{y}{2 a}=\frac{z}{3}$ are perpendicular to each other, then find the value of a.
View full question & answer→Question 141 Mark
In a box there are 4 white, 3 red and 5 black balls. Two balls are drawn, find the probability of getting two red balls.
Question 151 Mark
Convert the line $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ in vector form.
View full question & answer→Question 161 Mark
Find the length of perpendicular drawn from origin to plane $2 x+3 y+5 z-8=0$
View full question & answer→Question 171 Mark
Find the direction cosines of line $\frac{2 x-1}{4}=\frac{3 y}{-2}=\frac{z+1}{6}$.
View full question & answer→Question 181 Mark
If the vectors $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=2 \hat{i}-\hat{j}+3 \hat{k}, \vec{c}=2 \hat{i}+\hat{j}$ then find a unit vector along the direction $\vec{a}+\vec{b}+\vec{c}$.
View full question & answer→Question 191 Mark
Find the angle between the vectors $2 i-j$ and $\hat{i}+2 \hat{j}$.
View full question & answer→Question 201 Mark
Find the area bounded by parabola $y^2=4 x$ and $x=2$
View full question & answer→Question 211 Mark
Find that interval in which the function $f(x)=x^2-1$ is increasing.
View full question & answer→Question 221 Mark
If the function $f(x)=\left\{\begin{array}{cl}k x+1 & , x \neq 1 \\ 5 & , x=1\end{array}, x=1\right.$ is continuous at $x =1$, then find the value of $k$.
View full question & answer→Question 231 Mark
If the points $(1,2,3 \lambda),(1,0,1)$ and $(2,1,2)$ are collinear then find the value of $\lambda$.
View full question & answer→Question 241 Mark
Find the principle value of $\tan ^{-1}(-1)$.
View full question & answer→Question 251 Mark
Find the sum of vectors AB, BC, CD and DA, where ABCD is a quadrilateral.
Question 261 Mark
Find the principle value of $\cos ^{-1}\left(-\frac{1}{2}\right)$.
View full question & answer→Question 271 Mark
If matrix $A+B=\left[\begin{array}{ll}2 & 4 \\ 1 & 2\end{array}\right], A-B=\left[\begin{array}{ll}0 & 1 \\ 2 & 2\end{array}\right]$, then find matrix $A$.
View full question & answer→Question 281 Mark
A pair of dice is rolled. Find the probability of getting a doublet.
Question 291 Mark
Find the equation of line $\vec{r}=(2 \hat{i}+\hat{j}+\hat{k})+\lambda(2 \hat{j}+3 \hat{k})$ in cartesian form.
View full question & answer→Question 301 Mark
Find the equation of line passing through origin and parallel to $\mathrm{x}$-axis.
View full question & answer→Question 311 Mark
Find the length of foot of perpendicular from the point $(1,2,3)$ on plane $\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=5$.
View full question & answer→Question 321 Mark
Find the projection of vector $\hat{i}+\hat{j}$ on vector $3 \hat{i}+\hat{j}-\hat{k}$.
View full question & answer→Question 331 Mark
Find a vector of magnitude 5 in the direction of vector $2 \hat{i}-\hat{j}+5 \hat{k}$.
View full question & answer→Question 341 Mark
Find the area enclosed by curve $|x|+|y|=1$.
View full question & answer→Question 351 Mark
If the function $f(x)=\frac{\tan x}{x}, x \neq 0$, is continuous at $\mathrm{x}=0$, find the value of $\mathrm{f}(0)$.
View full question & answer→Question 361 Mark
Find the value of $\cot ^{-1}(\sqrt{3})-\tan ^{-1}(-\sqrt{3})$.
View full question & answer→Question 371 Mark
If two events $A$ and $B$ are such that $P(A)=\frac{1}{4}, P(B)=\frac{1}{2}$ and $P(A \cap B)=\frac{1}{8}$, then find the value of $P\left(A^{\prime} \cap B^{\prime}\right)$
View full question & answer→Question 381 Mark
If $P(A)=0.2, P(B)=0.5$ then find $P(A \cup B)$ when $A$ and $B$ are independent events.
View full question & answer→Question 391 Mark
Find the direction cosines of line $\frac{x-2}{3}=\frac{2 y-4}{6}=\frac{z-1}{-3}$
View full question & answer→Question 401 Mark
Find the distance between the parallel planes $x+2 y+3 z-5=0$ and $x+2 y+3 z+7=0$
View full question & answer→Question 411 Mark
Find the equation of line $\vec{r}=(\hat{i}+\hat{j}-3 \hat{k})+\lambda(2 \hat{i}+\hat{j}-\hat{k})$ is cartesian form.
View full question & answer→Question 421 Mark
Find a unit vector in the direction of sum of vectors $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}$
View full question & answer→Question 431 Mark
If the adjacent sides of a parallelogram are denoted by vectors $\hat{i}+\hat{j}+2 \hat{k}$ and $2 \hat{i}+\hat{j}+3 \hat{k}$, then find its area.
View full question & answer→Question 441 Mark
Find the area bounded by lines $y=x, x=4$ and $x$-axis.
View full question & answer→Question 451 Mark
An edge of a variable cube is increasing at the rate of $5 cm$ per second. How fast is the volume increasing when the side is $15 cm$.
View full question & answer→Question 461 Mark
If the function $f(x)=x e^x$ then find the value of $f^{\prime \prime}(x)$.
View full question & answer→Question 471 Mark
If $\left[\begin{array}{cc}\lambda-4 & -3 \\ 1 & 6-\lambda\end{array}\right]=\left[\begin{array}{ll}a & -3 \\ 1 & -4\end{array}\right]$, then find the value of $a$.
View full question & answer→Question 481 Mark
Solve the equation $x-2 y=5$ and $x+2 y=1$ using matrix method.
View full question & answer→Question 491 Mark
Find the area of one quadrant of the circle x² + y² = 1.
Question 501 Mark
Find the direction cosines of x, y and z-axes.