Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)=x^2-3x+4$, then find the values of x satisfying the equation $f\left(x\right)=f(2x+1)$.

How do we multiply vectors?

In a $△$ABC (c+a+b) (a+b-c)=ab. The measure of C is

The L.C.M. of the numbers $32,80,108$ is

The range of the function $2\sin x+7$ is

If $z=\sin \theta -i\cos \theta$, then for any integer $n$

In a shooting competition the scores of a competitor were as given below:

If $f\left(x\right)=sinx+cosx,g\left(x\right)=x^2-1theng\left(f\right(x\left)\right)$ in invertible in the Domain

$\frac{1}{tan3A-tanA}$ - $\frac{1}{cot3A-cotA}$ =

A circle is given by $x^2+y^2-6x+8y-11=0$ and there are two points (0,0) and (1,8). These points lie

Suppose f and g are functions having second derivatives f'' and g'' every where, if f(x).g(x)=1 for all x and f' and g' are never zero, then $\frac{f^{\prime \prime }\left(x\right)}{f^{\prime }\left(x\right)}-\frac{g^{\prime \prime }\left(x\right)}{g^{\prime }\left(x\right)}$ equals

$\frac{1}{\sqrt[3]{36-3x}}$ =

If ${\cos }^{4}x-(\lambda +2){\cos }^{2}x-(\lambda +3)=0$ has a solution, then

The product of slope of tangents from point $(0,1)$ to circle $x^2+y^2-2x+4y=0$ is:

In how many ways can a pack of 52 cards be equally among 4 players in order?

$\begin{array}{cccccc}& \text{Column I}& & \text{Column 2}& & \text{Column 3}\\ \text{(I)}& \text{If}I={\int }_{-2}^2(\alpha x^3+\beta x+\gamma )dx\text{then I is}& \text{(i)}& \text{Independent of}\alpha & \text{(P)}& \text{dependent on}\alpha \\ \text{(II)}& \text{Let}\alpha ,\beta \text{be distinct roots of}& \text{(ii)}& \text{Independent of}\gamma & \text{(Q)}& \text{dependent on}\beta \\ & \text{the equation tanx = 2x, then}& & & & \\ & \gamma {\int }_0^1(sin\alpha x.sin\beta x)dx\text{is}(\gamma \ne 0)& & & & \\ \text{(III)}& \text{If}f(x+\alpha )+f\left(x\right)=0\text{where}\alpha >0,& \text{(iii)}& \text{Independent of}\beta & \text{(R)}& \text{dependent on}\gamma \\ & \text{then}{\int }_{\beta }^{\beta +2\gamma \alpha }\text{f(x)dx is},\gamma ϵN& & & & \\ \text{(IV)}& \gamma {\int }_0^{\alpha }\left[sinx\right]dx\text{is};& \text{(iv)}& \text{dependent on}\alpha & \text{(S)}& \text{independent of}\beta \\ & \gamma \ne 0,\alpha ϵ\left[\right(2\beta +1)\pi ,(2\beta +2\left)\pi \right],& & & & \\ & \beta ϵN,[.]\text{denotes G.I.F.}& & & & \end{array}$

Which of the following combination is incorrect?

The eccentricity of the hyperbola $x^2-y^2=25$ is

What is the equation of chord of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ whose middle point is $(x_1,y_1)$ ? You are given. $T=\frac{x{x}_1}{a^2}+\frac{y{y}_1}{b^2}-1and{S}_1\frac{x_1^2}{a^2}+\frac{y_1^2}{b^2}-1$

Let z, w be complex numbers such that $\overline{z}+\overline{iw}=0andargzw=\pi$. Then arg z equals

If${\sum }_{i-l}^{20}si{n}^{-1}{x}_i=10\pi$, then ${\sum }_{i-l}^{20}{x}_i$ is equal to

$Equationofcircletouchingtheline|x-2|+|y-3|=4willbe$

If $A$ and $B$ are two events, then which one of the following is not always true

If the radius of the sphere $x^2+y^2+z^2-2x-4y-6z$ = 0 is r, then find the value of $r^2$

If a >b >c >0, then $co{t}^{-1}\frac{1+ab}{a-b}+co{t}^{-1}\frac{1+bc}{b-c}+co{t}^{-1}\frac{1+ca}{c-a}=$

The equation of the curve passing through the point (1, 1) such that the slope of the tangent at any point (x, y) is equal to the product of its co-ordinates is

$Ina\Delta ABC,\text{prove that}a(cosC-cosB)=2(b-c)co{s}^2\frac{A}{2}.$

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that $A\cup B$ can have.

If U= {2,3,5,7,9} is the universal set and A = {3,7} , B = {2,5,7,9}, then prove that :

(i) $A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$

(ii) $A\cap B{)}^{\prime }=A^{\prime }\cup B^{\prime }$

Which of the following functions are derivable and why???

I) tan x

II) cosec

If sin a +sinß =0= cos a+cos ß, where 0<ß<a<2π, then which one of the following is correct?

a) a = π - ß

b) a = π + ß

c) a = 2π - ß

d) 2a = π + 2ß

If $f\left(x\right)={\log }_e\left(\frac{1-x}{1+x}\right),|x|<1$, then $f\left(\frac{2x}{1+x^2}\right)$ is equal to:

If $A=\left[\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right]$
and $|(A^2-pA-qI)|=0$, then $p+q=$

The number of integral solutions of $x+y+z=0$ with $x\ge -5,y\ge -5,z\ge -5$ is

Let A and B be two sets show that the set A×B and B×A an element in common IFF the sets A and B have an element in common.

If $z=(i{)}^i$, where $i=\sqrt{-1}$, then Re(z) is:

If in the triangle ABC, $B={45}^0,then{a}^4+b^4+c^4$ is equal to

If PS is the median of the triangle with vertices P(2, 2), Q(6, -1) and R(7, 3) then equation of the line passing through (1, -1) and parallel to PS is

Let n $ϵ$ N, n > 25. Let A, G, H denote arithmetic mean, geometric mean and harmonic mean of 25 and n. The least value of 'n' for which A, G, H $ϵ$ {25, 26, - - - -, n} is