Explore topic-wise InterviewSolutions in Current Affairs.

If ${\cos }^{-1}\left(\frac{2}{3x}\right)+{\cos }^{-1}\left(\frac{3}{4x}\right)=\frac{\pi }{2}(x>\frac{3}{4})$, then $x$ is equal to:

Let $\overrightarrow{a}=\hat{i}-\hat{j},\overrightarrow{b}=\hat{i}+\hat{j}+\hat{k}$ and $\overrightarrow{c}$ be a vector such that $\overrightarrow{a}\times \overrightarrow{c}+\overrightarrow{b}=\overrightarrow{0}$ and $\overrightarrow{a}\cdot \overrightarrow{c}=4$, then $|\overrightarrow{c}{|}^2$ is equal to:

In a $\Delta$ ABC, R = circumradius and r = inradius. The value of $\frac{acosA+bcosB+ccosC}{a+b+c}$ is equal to

The solution of the differential equation $\frac{dy}{dx}+\frac{3x^2}{1+x^3}y=\frac{si{n}^{2}x}{1+x^3}$ is

If two spheres of radii $r_1$ and $r_2$ cut orthogonally, then the radius of the common circle is

Write the contrapositive of the following statement.

'If you live in Delhi, then you have winter clothes.'

The fourth power of the common difference of an A.P with integer entries is added to the product of any four consecutive terms of it, resulting sum is

Number of ways to divide $21$ different things into two groups of $10$ and $11$ things are?

Water is dripping out from a conical funnel of semi-vertical angle π/4 at the uniform rate of 2 square cms /sec in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is 4 cm, then the rate of decrease of the slant height of water is

How many sons does Deepak have ?

Statement I. Alisha's father has three children.

Statement II. Basha is Alisha's brother and son of Deepak.

If $AB=\left[\begin{array}{cc}4& 11\\ 4& 5\end{array}\right]\text{and}A=\left[\begin{array}{cc}3& 2\\ 1& 2\end{array}\right]$, then the value of the determinant of the matrix B is

If in a $△ABC,a^{2}co{s}^{2}A=b^2+c^2$ then

If sin^-1x = y then the range of y is:

In the binomial expansion of $(a+b{)}^n$, the sum of $5^{th}and{6}^{th}$ terms is zero, then $\frac{a}{b}$ is equal to

Let P(x) be a polynomial of least degree whose graph has three points of inflection as (–1, – 1), (1, 1) and a point with abscissa 0 at which the curve is inclined to the axis of abscissa at an angle of ${60}^{\circ }$. Then ${\int }_0^{1}P\left(x\right)dx$ equals to

Find the value of $e^{i2\pi }$ .

If n is a rational number, which is not a whole number, then the number of terms in the expansion of $(1+x{)}^n,$ |x|< 1, is:

If $f:R\to R$ is defined by $f\left(x\right)=\frac{sin\left[x\right]\pi +tan\left[x\right]\pi }{1+\left[x^2\right]}$, then the range of f(x) (where [x] denotes integral part of x)

Point R (h, k) divides a line segment between the axes in the ratio 1 : 2. Find the equation of the line.

Complete set of values of ‘a’ for which $asi{n}^{2}x+|cosx|-2a=0$ has alteast one solution belongs to the interval

Line inclination with
$\begin{array}{cc}Positivex-direction& Slopeofline\\ 1.0^o& p.0\\ 2.{90}^o& q.-\sqrt{3}\\ 3.{120}^o& r.-\frac{1}{\sqrt{3}}\\ 4.{150}^o& s.Notdefined\end{array}$

Find the equation of the line passing through $(2,2\sqrt{3})$ and inclined with x-axis at an angle of ${75}^{\circ }.$

Find the value of x, if $5{\tan }^{-1}x+2co{t}^{-1}x=2\pi .$

The equation of the plane passing through the point (-1, 3, 2) and perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + = 0, is

The equation of the circle having centre (1, –2) and passing through the point of intersection of lines 3x + y = 14, 2x + 5y = 18 is

If ${\log }_{2}6+\frac{1}{2x}={\log }_2(2^{\frac{1}{x}}+8),$ then the value of $x$ are

Differentiate the following functions with respect to x :

${(\sqrt{x}+\frac{1}{\sqrt{x}})}^3$

Differentiate the following functions with respect to x :

$\frac{x+cosx}{tanx}$

The value of $x$, for which the $8^{\text{th}}$ term in the expansion of ${[3^{{\log }_{27}({16}^{x-2}+5)}+\frac{1}{3^{\frac{1}{7}{\log }_3(4^{x-2}+1)}}]}^{10}$ is $360$, is equal to

Set $a,bϵ[-\pi ,\pi ]$ be such that cos (a - b) = 1 and cos (a + b) $=\frac{1}{e}$. The number of pairs of a, b satisfying the above system of equation is

In how many ways 4 women draw water from 4 taps, if no tap remains unused ?

$cosec\theta (sec\theta -1)-cot\theta (1-cos\theta )=tan\theta -sin\theta$

Write the solution set of values of x satisfying $|x-1|\le 3and|x-1|\le 1$.

If $f\left(x\right)=\frac{2^x+2^{-x}}{2}$, then $f(x+y)f(x-y)$ is equal to

Sum of series $S=\sum _{r=0}^n\frac{3^{r+4}\cdot {}^n{C}_r}{{}^{r+4}{C}_4}+\sum _{r=0}^3\frac{3^r\cdot {}^{n+4}{C}_r}{{}^{n+4}{C}_4}$

If $(1+x{)}^n=C_0+C_{1}x+\dots ..+C_n{x}^n,$ then the value of $\sum _{r=0}^n\sum _{s=0}^n(C_r+C_s)$ is equal to

The tangent to the circle $C_1:x^2+y^2-2x-1=0$ at the point $(2,1)$ cuts off a chord of length $4$ from a circle $C_2$ whose centre is $(3,-2)$. The radius of $C_2$ is :

If $3^x=4^{x-1}$, then $x=$

Let $\Delta =\left|\begin{array}{ccc}Ax& x^2& 1\\ By& y^2& 1\\ Cz& z^2& 1\end{array}\right|$ and ${\Delta }_1=\left|\begin{array}{ccc}A& B& C\\ x& y& z\\ zy& zx& xy\end{array}\right|$ then

Let $y=f\left(x\right)=2x^2-3x+2$. The differential of $y$ when $x$ changes from $2$ to $1.99$ is

Minimize Z = -3x + 4y, subject to constraints are $x+2y\le 8,3x+2y\le 12,x\ge 0andy\ge 0$.