Explore topic-wise InterviewSolutions in Current Affairs.

Two cubes have their faces painted either red or blue. The first cube has five red faces and one blue face. When the two cubes are rolled simultaneously, the probability that the two top faces show the same colour is $\frac{1}{2}.$ The number of red faces on the second cube, is

If $f\left(x\right)=\frac{x-1}{x+1},x\ne -1$ then show that $f\left(f\right(x\left)\right)=\frac{-1}{x}$, where $x\ne 0)$.

If $z=r{e}^{i\theta }$, then $|e^{iz}|$ is equal to

If $(z^3$ + $\frac{1}{z^3})$ - $(z^2$ + $\frac{1}{z^2})$ + $(z+\frac{1}{z})$ - 1 = $(z+\frac{1}{z}-2\alpha$) $(z+\frac{1}{z}-2\beta$) $(z+\frac{1}{z}-2\gamma$) Find the value of $\alpha$.$\beta$.$\gamma$.

If $y\cos \theta -1=\sin \theta$, then $\sin \theta$ is

Two angles whose measures are a & b are such that 2a - 3b = 60${}^{\circ }$ and they form a linear pair. Then, the degree measure of 5b =

Column – 1 represents equation of straight lines
Column – 2 represents position of points A $\equiv$ (1, 4) and B(4, 3) w.r.t. equation of line in Column - 1
Column – 3 represents the sum of length of perpendiculars from points A and B to the lines in Column-1
$\begin{array}{ccc}Column1& Column2& Column3\\ \left(I\right)L_1:y-x+1=0& \left(i\right)Bothpointslieonthesamesideoftheline& \left(p\right)\frac{7\sqrt{5}}{5}units\\ \left(II\right)L_2:6y+x-11=0& \left(ii\right)Bothpointslieontheoppositesideoftheline& \left(Q\right)2\sqrt{2}units\\ \left(III\right)L_3:y-2x+2=0& \left(iii\right)Bothpointslieontheline& \left(R\right)\frac{25\sqrt{37}}{37}units\\ \left(IV\right)L_4:3y+x-13=0& \left(iv\right)Onepoint(outofA,B)lieontheline& \left(S\right)0units\end{array}$
Which of the following options is the only CORRECT combination?

The sum of integeral roots of the equation $(x^2+3x{)}^2-(x^2+3x)-6=0$ is

1. 2

Consider f : R$\to$ given by f(x) = 4x + 3, Show that f is invertible and find the inverse of f.

Find out the appropriate word which fits the 9th blank.

Find the equation of a line parallel to X-axis and passing through the origin.

$p\to \sim q$ can also be written as

The expression $(\sqrt{2x^2+1}+\sqrt{2x^2-1}{)}^6+{\left(\frac{2}{\sqrt{2x^2+1}+\sqrt{2x^2-1}}\right)}^6$ is a polynomial of degree

Show that :
(i) $sinAsin(B—C)+sinBsin(C—A)+sinCsin(A—B)=0$
(ii) $sin(B—C)cos(A—D)+sin(C—A)cos(B—D)+sin(A—B)cos(C—D)=0$

In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics ?

Prove that: 1 + 2 + 3 + ......... + n = $\frac{n(n+1)}{2}$ i.e., the sum of the first n natural numbers is $\frac{n(n+1)}{2}$.

For positive numbers x, y and z the numerical value of the following determinant

$\left|\begin{array}{ccc}1& {log}_{x}y& {log}_{x}z\\ {log}_{y}x& 1& {log}_{y}z\\ {log}_{z}x& {log}_{z}y& 1\end{array}\right|$ is

Let $f\left(n\right)$ denotes the number of different ways in which the positive integer $n$ can be expressed as the sum of $1^{\prime }s$ and $2^{\prime }s$. For example $f\left(4\right)=5$, since
$4=2+2=2+1+1=1+2+1=1+1+2=1+1+1+1$.

Then which of the following(s) is (are) CORRECT ?

Given an example of a statement P(n) such that it is true for all n $ϵ$ N.

$Inany\Delta ABC,if{a}^2,b^2,c^2\text{are in A.P., prove that cot A, cot B and cot C are also in A.P.}$

If $x_1,x_2,x_3,x_4$ are roots of the equation $x^4–x^3$ $sin2\beta +x^{2}cos2\beta –xcos\beta –sin\beta =0then{\sum }_{i=1}^{4}ta{n}^{-1}{x}_i$ is equal to

Let $g\left(x\right)=2f\left(\frac{x}{2}\right)+f(2-x)$ and $f^{\prime \prime }x)<0\forall xϵ(0,2),$ then $g\left(x\right)$ increases in

The condition that the equation $\frac{1}{x}+\frac{1}{x+b}=\frac{1}{m}+\frac{1}{m+b}$ has real roots, that are equal in magnitude but opposite in sign, is

The number of roots of the equation $\frac{(x+2)(x-5)}{(x-3)(x+6)}=\frac{x-2}{x+4}$ is

If $x=3\cos \theta -\cos 3\theta$ and $y=3\sin \theta -\sin 3\theta ,$ then $\frac{dy}{dx}$ is

If $|a|<1and|b|<1$, then the sum fo the series $1+(1+a)b+(1+a+a^2)b^2+(1+a+a^2+a^3)b^3+...is$

In a $\angle ABC,$ if $\angle A={45}^{\circ },\angle B={60}^{\circ },and\angle C={75}^{\circ },$ find the ratio of its sides.

If $\alpha ,\beta \in R$ are such that $1-2i$ (here $i^2=-1$) is a root of $z^2+\alpha z+\beta =0,$ then $(\alpha -\beta )$ is equal to

Solve $-18\le 3(2x-4)<12$

Find the equation to the straight line which bisects the distance between the points (a, b), (a', b') and also bisects the distance between the points (- a, b) and a', - b).

If the $2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ terms in the expansion of $(x+a{)}^n$ are $240,720$ and $1080$ respectively, then the value of $(x-a{)}^n$ is

A polygon has $20$ diagonals then the number of its sides are:

If a, b, c are distinct positive numbers, then the expression (b + c - a) (c + a - b) (a + b - c) - abc

If a, b, c are the sides of a triangle then (a)/(b+c-a) + (b)/(c+a-b) + (c)/(a+b-c)

Let $f:R\to R$ be defined by
$f\left(x\right)=\{\begin{array}{c}2x,x>3\\ x^2,1<x\le 3\\ 3x,x\le 1\end{array}$

Then $f(-1)+f\left(2\right)+f\left(4\right)$ is

Show that $\underset{x\to 0}{lim}\frac{x}{|x|}$ does not exist.

If $1,d_1,d_2,d_3,d_4$ are roots of $x^5=1$ then the value of expression :$E=\frac{\omega -d_1}{{\omega }^2-d_1}\cdot \frac{\omega -d_2}{{\omega }^2-d_2}\cdot \frac{\omega -d_3}{{\omega }^2-d_3}\cdot \frac{\omega -d_4}{{\omega }^2-d_4}$ is
[Here $\omega$ is the cube root of unity]

If $f\left(x\right)=\{\begin{array}{cc}|x+1|& x\le 0;\\ x& x>0;\end{array}$ and
$g\left(x\right)=\{\begin{array}{cc}|x|+2& x<2;\\ -|x-2|& x\ge 2;\end{array}$ then $f\left(x\right)-g\left(x\right)$ is continuous at

Which of the following are differential equations ?

If $y=2\left[x\right]+30,y=3[x-2]+15$, then $[x+y]$ is equal to
(where [.] denotes greatest integer function)

If A(z₁), B(z₂) and C(z₃) are three points on the argand plane where |z₁ + z₂| = ||z₁| - |z₂|| and |(1 - i)z₁ + iz₃| = |z₁| + |z₃ - z₁|,

where i= √(- 1) then

(a) A, B and C lie on the fixed circle with centre (z₁ + z₂)/2

(b) A, B and C are collinear points

(c) ABC form an equilateral triangle

(d) ABC form an obtuse angled triangle

If 1/2 is a root of the equation x²+kx - 5/4 =0, then the other

root of the quadratic equation is

Given that she is successful, the probability she studied for 4 hours is