Explore topic-wise InterviewSolutions in Current Affairs.

Show that the function $f:R_{\ast }\to R_{\ast }$ defined by $f\left(x\right)=\frac{1}{x}$ is one-one, where $R_{\ast }$ is the set of all non-zero real numbers. Is the result true, if the domain $R_{\ast }$ is replaced by N with co-domain being same as $R_{\ast }$?

Differentiate the following functions with respect to x :

$\frac{x}{1+tanx}$

The number of solutions of $\sin 3x=\cos 2x,$ in the interval $(\frac{\pi }{2},\pi )$ is :

If $aϵR^{+}$ and the roots of equation $a{x}^2–3x+c=0$ are two consecutive odd positive integers, then

The value of the integral $\underset{0}{\overset{1}{\int }}x{\cot }^{-1}(1-x^2+x^4)dx$ is :

If $\cos (4y-3x-2)-\cos (4y+3x+2)=2+2\ln (k^4-255)$ and $\cos (4y-3x-2)+\cos (4y+3x+2)=2k+8$ have real solutions $(x,y)$, then the range of $k$ is

If the lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to a circle, then the radius of the circle is

In a football tournament, a team $T$ has to play with each of the $6$ other teams once. Each match can result in a win, draw or loss. Then the number of ways in which the team $T$ finishes with more wins than losses, is

Match $\text{List I}$ with the $\text{List II}$ and select the correct answer using the code given below the lists :

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{Area of a triangle with adjacent sides determined by vectors}\overrightarrow{a}\text{and}\overrightarrow{b}\text{is}1\text{. Then the area of}& \text{(P)}& 6\\ & \text{the triangle with adjacent sides determined by}(3\overrightarrow{a}+4\overrightarrow{b})\text{and}(\overrightarrow{a}-3\overrightarrow{b})\text{is}& & \\ \text{(B)}& \text{Volume of parallelopiped determined by vectors}\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}\text{is}\frac{1}{4}\text{. Then the volume of the}& \text{(Q)}& 9\\ & \text{parallelopiped determined by vectors}3(\overrightarrow{a}+\overrightarrow{b}),(\overrightarrow{b}+\overrightarrow{c}),4(\overrightarrow{c}+\overrightarrow{a})\text{is}& & \\ \text{(C)}& \text{Area of a parallelogram with adjacent sides determined by vectors}\overrightarrow{a}\text{and}\overrightarrow{b}\text{is}8\text{. Then the}& \text{(R)}& 13\\ & \text{area of the parallelogram with adjacent sides determined by vectors}(2\overrightarrow{a}-\overrightarrow{b})\text{and}\overrightarrow{b}\text{is}& & \\ \text{(D)}& \text{Volume of tetrahedron determined by vectors}\overrightarrow{a},\overrightarrow{b}\text{and}\overrightarrow{c}\text{is}\frac{1}{2}\text{. Then the volume of the}& \text{(S)}& 16\\ & \text{tetrahedron determined by vectors}2(\overrightarrow{a}\times \overrightarrow{b})\text{,}3(\overrightarrow{b}\times \overrightarrow{c})\text{and}(\overrightarrow{c}\times \overrightarrow{a})\text{is}& & \end{array}$

Which of the following is the only CORRECT combination?

Let A = {1, 2, 3,.....,14}. Define a relation on a set A by

R = {(x, y) : 3x - y = 0, where $x,yϵA$}.

Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.

If $x_1+x_2+x_3=0,y_1+y_2+y_3=0$ and $x_1{y}_1+x_2{y}_2+x_3{y}_3=0,$ then the value of $\frac{x_1^2}{x_1^2+x_2^2+x_3^2}+\frac{y_1^2}{y_1^2+y_2^2+y_3^2}$ is
(correct answer + 2, wrong answer - 0.50)

Let $x,y$ be real variables satisfying the $x^2+y^2+8x-10y-40=0$. Let $a=max\left\{\sqrt{(x+2{)}^2+(y-3{)}^2}\right\}$ and $b=min\left\{\sqrt{(x+2{)}^2+(y-3{)}^2}\right\}$, then

Integrate the following functions.
$\int \frac{x-1}{\sqrt{x^2-1}}dx.$

tan A / 1- cot A + cot A / 1- tan A = 1+ sec A cosec A.

If $A>0,c,d,u,v$ are non-zero constants, and the graphs of $f\left(x\right)=|Ax+c|+d$ and $g\left(x\right)=-|Ax+u|+v$ intersect exactly at 2 points (1, 4) and (3, 1) then the value of $\frac{u+c}{A}$ equals to

In $\Delta ABC,$ prove that

$\frac{(b-c)}{b+c}=\frac{tan\frac{1}{2}(B-C)}{tan\frac{1}{2}(B+C)}$

Find the sum of the following series upto n terms :

$\frac{1^3}{1}+\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}+\dots \dots$

The sum of roots of the equation $x^8=1$ whose real part is positive is

Two straight lines are perpendicular to each other one of them touches the parabola $y^2=4a(x+a)$ and the other touches $y^2=4b(x+b).$ The locus of the point of intersection of these two lines is

Equation of the tangent to $y^2=6x$ at the positive end of the latusrectum is

Let $a,b$ be the roots of the equation $x^2-x+\sin 2\theta \cos \theta =x\sin \theta (2-\sin \theta )$ where $\frac{\pi }{4}<\theta <\frac{\pi }{2}$ and a>b. Find the value of $a+\frac{b}{a+\frac{b}{a+\frac{b}{a+...}}}$

What is the sentence type?

The wounded soldier was immediately taken to the military hospital.

In the figure given below, If
A
B
∥
C
D
and
C
D
∥
E
F
and y : z = 3 : 7, find x. [4 MARKS]

The $3^{rd}$ term in the expansion of ${(3x-\frac{y^3}{6})}^4$is

If $\sin 6\theta +\sin 4\theta +\sin 2\theta =0,$ then general value of $\theta$ is

Find the degree measure of -4

The equation of the normal to the curve $\frac{x^2}{16}-\frac{y^2}{9}=1$ at $(8,3\sqrt{3})$ is

Evaluate the definite integrals.
${\int }_4^5{e}^{x}dx.$

Determine order and degree (when defined) of differential equations.
$y^{\prime \prime }+(y^{\prime }{)}^2+2y=0.$

Each entry of $\text{List I}$ is to be matched with one entry of $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& 100(\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{99\cdot 100})\text{equals}& \text{(P)}& 7\\ \text{(B)}& \text{If}x\text{is the arithmetic mean between two real numbers}a\text{and}b\text{,}& \text{(Q)}& 9\\ & y=a^{2/3}\cdot b^{1/3}\text{and}z=a^{1/3}\cdot b^{2/3},\text{then}\frac{y^3+z^3}{xyz}\text{equals}& & \\ \text{(C)}& \text{If}198\text{arithmetic means are inserted between}\frac{1}{4}\text{and}\frac{3}{4}\text{, then}& \text{(R)}& 99\\ & \text{the sum of these arithmetic means is}& & \\ \text{(D)}& \text{If}n\text{is a positive integer such that}n\text{,}\frac{n(n-1)}{2}\text{and}& \text{(S)}& 100\\ & \frac{n(n-1)(n-2)}{6}\text{are in A.P., then the value of}n\text{is}& & \\ & & \text{(T)}& 2\end{array}$

Which of the following is the only CORRECT combination?

Find the equation of the locus of a point which moves such that the ratio of its distances from (2,0) and (1,3) is 5 : 4.

Solve the equation

6÷x+y=7÷x-y+3

1÷2(x+y)=1÷3(x-y)

The area of the region bounded by the curves y=f(x), y=0, x=-1 and x=1 is

If m,n are roots of equation x^{​​​​​​2} +px +q and g,h are roots of equation x^{​​​​​​2} + px - r . Find (m-g)(m-g).

The value of ${\sin }^2\frac{\pi }{6}+{\cos }^2\frac{\pi }{3}-{\tan }^2\frac{\pi }{4}+{\cot }^2\frac{\pi }{2}$ is equal to

The circles $x^2+y^2+kx+4y=20$ and $x^2+y^2+6x-8y+10=0$ intersect orthogonally. Also circles $x^2+y^2-p(x-y)+1=0$ and $p(x^2+y^2)+x-y=1$ intersect orthogonally. Then $\frac{k}{p}$ equals