Explore topic-wise InterviewSolutions in .

Let $n(A-B)=25+x,n(B-A)=2x$ and $n(A\cap B)=2x.$ If $n\left(A\right)=2\left(n\right(B\left)\right),$ then $x$ = ___.

If ${\tan }^{-1}2,{\tan }^{-1}3$ are two angles of a triangle, then the third angle is

The orthogonal trajectories of the family of curves $x^{2/3}+y^{2/3}=a^{2/3}$, where $a$ is the parameter, is

Prove that square root 31 is irrational.

Distance between the directrices of the ellipse $9x^2+5y^2-30y$ = 0 is

For $x>0$, which of the following is true :

Find the equation of the hyperbola satisfying the give conditions: Foci, the latus rectum is of length 8.

If $\alpha ,\beta$ are the roots of the equation $3x^2+5x-7=0$, then the equation whose roots are $\frac{1}{3\alpha +5},\frac{1}{3\beta +5}$ is

1. 0.693

If $x\in [\frac{3}{2},3],$ then $\frac{d}{dx}\left\{{\cos }^{-1}(\frac{4x^3}{27}-x)\right\}$ is equal to

If $\Delta =\left|\begin{array}{ccc}-x& a& b\\ b& -x& a\\ a& b& -x\end{array}\right|$, then a factor of $\Delta$ is

The distance of the point $(1,-2,3)$ from the plane $x-y+z=5$, measured parallel to the line $\frac{x}{2}=\frac{y}{3}=\frac{z}{-6}$

The area (in sq. units) of the region

$\left\{\right(x,y):x\ge 0,x+y\le 3,x^2\le 4y$ and $y\le 1+\sqrt{x}\}$ is:

Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are collinear and find the ratio in which B divides AC.

If $x,y\in [-1,1],$ $\cos \left({\sin }^{-1}x\right)+\sin \left({\cos }^{-1}y\right)=\frac{\sqrt{11}}{2},$ $(1-x^2)(1-y^2)=\frac{4}{9},$ and $x^2+y^2=\frac{a}{b^2+3}$ for positive integers $a$ and $b,$ then the value of $a+b$ is

Find the equation of the line perpendicular to x-axis and having intercept -2 on x-axis.

The equation of the plane passing through the line of intersection of the planes $\overrightarrow{r}\cdot (\hat{i}+\hat{j}+\hat{k})=1$ and $\overrightarrow{r}\cdot (2\hat{i}+3\hat{j}-\hat{k})+4=0$ and parallel to the $x-$axis is

If $f\left(x\right)=\frac{\sqrt{1+x}-\sqrt[3]{31+x}}{x}$ is continuous at $x=0$, then the value of $f\left(0\right)$ is

AB is a chord of the parabola $y^2=4ax$ with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-

If the circle $C_1:x^2+y^2=16$ intersect another circle $C_2$ of radius $5$ in such a manner that the common chord is of maximum length and has slope equal to $\frac{3}{4}$, then coordinates of the centre of $C_2$ are

$co{s}^{-1}\left(cos\frac{7\pi }{6}\right)=$

For each real number x such that -1 < x <1, let A(x) be the matrix $(1-x{)}^{-1}\left[\begin{array}{cc}1& -x\\ -x& 1\end{array}\right]$ and $z=\frac{x+y}{1+xy}$ Then

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

There are total ${}^{17}{C}_6-k{}^{11}{C}_5$ ways to get a sum of atmost $17$ by throwing six distinct dice ,then $k$ is equal to :

The equation of the line(s) which passes through the point $(3,4)$ and its sum of the intercepts on the axes is 14 is/are

For the vectors $\overrightarrow{a}=3\hat{i}+2\hat{j}+4\hat{k}$ and $\overrightarrow{b}=2\hat{i}+5\hat{j}$. If $\overrightarrow{a}=\overrightarrow{x}+\overrightarrow{y}$ where $\overrightarrow{x}$ is parallel to $\overrightarrow{b}$ and $\overrightarrow{y}$ is perpendicular to$\overrightarrow{b}$,

then $\overrightarrow{y}$ is

Which of the following numbers has the positive value?

The range of $f\left(x\right)=\frac{3}{5+4sin3x}$ is

The line x + y = 1 meets x-axis at A and y axis at B, P is the mid point of AB, $P_1$ is the foot of the perpendicular from P to OA; $M_1$ is that of $P_1$ from OP; $P_2$ is that of $M_1$ from OA; $M_2$ is that of $P_2$ from OP; $P_3$ is that of $M_2$ from OA and so on. If $P_n$ denotes the $n^{th}$ foot of the perpendicular on OA from $M_{n-1},$ then O$P_n$ is equal to

If $\omega (\ne 1)$ is cube root of unity satisfying $\frac{1}{a+\omega }+\frac{1}{b+\omega }+\frac{1}{c+\omega }=2{\omega }^2$ and $\frac{1}{a+{\omega }^2}+\frac{1}{b+{\omega }^2}+\frac{1}{c+{\omega }^2}=2\omega$, then the value of $\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}$ is :

Let $S$ be the set of all real values of $\lambda$ such that plane passing through the points $(-{\lambda }^2,1,1),(1,-{\lambda }^2,1)$ and $(1,1,-{\lambda }^2)$ also passes through the point $(-1,-1,1)$. Then $S$ is equal to :