Explore topic-wise InterviewSolutions in Current Affairs.

If $\underset{0}{\overset{x}{\int }}f\left(t\right)dt=x^2+\underset{x}{\overset{1}{\int }}{t}^{2}f\left(t\right)dt$, then $f^{\prime }\left(\frac{1}{2}\right)$ is:

If $m$ is a non-zero number and $\int \frac{x^{5m-1}+2.x^{4m-1}}{(x^{2m}+x^m+1{)}^3}dx=f\left(x\right)+c,$ then $f\left(x\right)$ is

Let A and B be two events such that $P\left(A\right)=\frac{1}{3},P\left(\frac{A}{B}\right)=\frac{1}{2}$ and $P\left(\frac{B}{A}\right)=\frac{2}{5}$

$P(A\cup B)=$

Let $f\left(x\right)=e^{x+sinx}$ and $g\left(x\right)=f^{-1}\left(x\right),h\left(x\right)=g\left(x\right)+g^{\prime }\left(x\right)$ then $4h\left(1\right)$ is : ___

Considering the performance of P and Q together, who in which paper has put the best performance?

If $a_n=\sqrt{7+\sqrt{7+\sqrt{7}+....}}$ has n radical signs, then by the method of mathematical induction, which is true?

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

What is $\frac{dy}{dx}ify=(x-1{)}^2(x+2{)}^3$

Let $f\left(x\right)=\{\begin{array}{cc}\frac{kcosx}{\pi -2x},& \text{where x}\ne \frac{\pi }{2}\\ 3,& \text{where x}=\frac{\pi }{2}\text{and if}\end{array}$ ${lim}_{x\to \frac{\pi }{2}}f\left(x\right)=f\left(\frac{\pi }{2}\right)$, find the value of k.

Find the equation of a circle.
(i) which touches both the axes at a distance of 6 units from the origin.
(ii) which touches x-axis at a distance 5 from the origin and radius 6 units.
(iii) which touches both the axes and passes through the point (2, 1).

(iv) passing through the origin, radius 17 and ordinate of the centre is -15.

Let $S=\left\{xϵ\right(-\pi ,\pi ):x\ne 0,\pm \frac{\pi }{2}\}$. The sum of all distinct solutions of the equation $\sqrt{3}secx+cosecx+2(tanx-cotx)=0$ in the set S is equal to

If $A,B,C$ are mutually exclusive and exhaustive events such that $P\left(A\right)=2P\left(B\right)=3P\left(C\right)$, then $P(B\cup C)=$

There is a solution to $x^5-2x^3-2=0$ between x=0 and x=2

1. T

Equation $\begin{array}{c}a{x}^2+b{y}^2+c{z}^2+2fyz+2gxz+2hxy\\ +2ux+2vy+2wz+d=0\end{array}$ represents a sphere, if
[MP PET 1990]

The value of the integral $\int (x^2+x)(x^{-8}+2x^{-9}{)}^{1/10}dx$ is

If $u=\sqrt{a^{2}co{s}^2\theta +b^{2}si{n}^2\theta }+\sqrt{a^{2}si{n}^2\theta +b^{2}co{s}^2\theta }$, then the difference between the maximum and minimum values of $u^2$ is given by

Find the image of the point $(3,8)$ with respect to the line $x+3y=7$ assuming the line to be a plane mirror.

For the straight lines 4x+3y-5 = 0 and 12x-5y+6 = 0, find the equation of the bisector which contains (1,3)

Find the number of solutions for the equation $co{s}^{-1}\left(cosx\right)=-\frac{1}{2}$.

Given angle $A={60}^{\circ },c=\sqrt{3}-1,b=\sqrt{3}+1$. Solve the triangle

The length of the chord of the parabola $x^2=4y$ passing through the vertex and having slope $cot\alpha$ is

Ashu studies at Byju's classes and her probability of selection in $IIT-JEE$ is $\frac{4}{5}$. Ridhima took coaching at $FIIT-JEE$ and the probability of her selection is $\frac{2}{3}$. What is the probability that only 1 of them cracks the Exam?

If $\tan A$ and $\tan B$ are the roots of $x^2-3x-7=0$, then the value of $\sin 2(A+B)$ is

The solution of the differential equation is

[IIT 1986; AIEEE 2005]

Divya is older than Rohan and they are siblings. Then Divya is his elder _______.

Let $\left[x\right]$ denote the greatest integer less than or equal to $x$. Then the value of $\alpha$ for which the function $f\left(x\right)=\{\begin{array}{cc}\frac{\sin [-x^2]}{[-x^2]},& x\ne 0\\ \alpha ,& x=0\end{array}$

is continuous at $x=0$ is

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides are

Find the principal values of the following questions:

$co{t}^{-1}\left(\sqrt{3}\right)$

f(x)=$\{\begin{array}{c}\frac{|x|}{x},ifx\ne 0\\ 0,ifx=0\end{array}$

A coin is tossed. IF it shows tail, we draw a ball from a box which contains 2 red 3 black balls; if it shows head, we throw a die. Find the sample space of this experiment.

$\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=5,thenthevalueof\left|\begin{array}{ccc}{b}_2{c}_3-b_3{c}_2& a_3{c}_2-a_2{c}_3& a_2{b}_3-a_3{b}_2\\ b_3{c}_1-b_1{c}_3& a_1{c}_3-a_3{c}_1& a_3{b}_1-a_1{b}_3\\ b_1{c}_2-b_2{c}_1& a_2{c}_1-a_1{c}_2& a_1{b}_2-a_2{b}_1\end{array}\right|is$

All the numbers that can be formed using 1, 2 ,3, 4, 5 are arranged in the decreasing order then the rank of 35 241 is

If $|2\sin \theta -\text{cosec}\theta |\ge 1$, then complete set of values of $\theta$ is
(where $n\in Z$)

show that ${lim}_{x\to 0}sin\frac{1}{x}$does not exist.

Find the area of the region in the first quadrant enclosed by X-axis and $x=\sqrt{3}$ y and the circle $x^2+y^2=4$

If $A=\left[\begin{array}{ccc}1& 02& 3\\ 4& 26& 4\end{array}\right]$ then fourth element of second column of $A^T$ = ________

The feasible region for an LPP is shown in the following figure. Let F=3x-4y be the objective function. Maximum value of F is

(a)0
(b)8
(c)12
(d)-18

The determinant $\left|\begin{array}{ccc}xp+y& x& y\\ yp+z& y& z\\ 0& xp+y& yp+z\end{array}\right|=0,$ if