Explore topic-wise InterviewSolutions in Current Affairs.

$\text{If}f\left(x\right)=\{\begin{array}{cc}\frac{sinx}{x},& x\ne 0\\ 1,& x=0\end{array},\text{then}{lim}_{x\to 0}f\left(x\right)=$is

The medians AD and BE of a triangle with vertices A(0, b), B(0, 0) and C(a, 0) are perpendicular to each
other if

If $\alpha ,\beta ,\gamma$ be the angles which a line makes with the positive direction of co-ordinate axes, then $si{n}^2\alpha +sin$
[RPET 2000; AMU 2002; MP PET 1989, 98, 2000, 03,Pb. CET 2001]

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically :

(i) $A\times B$ (ii) $B\times A$

(iii) $A\times A$ (iv) $B\times B$

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance $d$ apart are $\alpha$ and $\beta .$ The height of the lighthouse is

Write the solution set of the equation |2-x|=x-2.

If $f\left(x\right)=x^2+2bx+2c^{2}andg\left(x\right)=-x^2-2cx+b^2$ are such that min f(x) > max g (x), then relation between b and c, is

Centre of circle $(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$ is

Prove that ${lim}_{x\to a^{+}}\left[x\right]$ =[a] for all $a\in R$. Also, prove that ${lim}_{x\to 1^{-}}\left[x\right]=0$

Two vectors $\overrightarrow{A}=3\hat{i}+8\hat{j}-2\hat{k}$ and $\overrightarrow{B}=6\hat{i}+16\hat{j}+x\hat{k}$ are such that the component of $\overrightarrow{B}$ perpendicular to $\overrightarrow{A}$ is zero. Then the value of x will be:

Let $A=\{a,b,c,d\},$ $B=\{b,c,e,f\},$ then $n\left(\right(A-B)\times (B-A\left)\right)=$

If in the expansion of ${(x^4-\frac{1}{x^3})}^{15},x^{-17}$ occurs in rth term, then

Shamshad Ali buys a scooter for Rs. 22000. He pays Rs. 4000 cash and agrees to pay the balance in annual instalments of Rs. 10000 plus $10\%$ interest on the unpaid amount. How much the scooter will cost him.

If ${}^{100}{C}_{50}$ can be prime factorised as $2^{\alpha }\cdot 3^{\beta }\cdot 5^{\gamma }\cdot 7^{\delta }\dots$ where $\alpha ,\beta ,\gamma ,\delta ,\dots$ are non-negative integers, then the CORRECT relation(s) is (are)

The equation of circle touching the line $2x+3y+1=0$ at $(1,-1)$ and cutting orthogonally the cirlce having line segment joining $(0,3)$ and $(-2,-1)$ as diameter is

The set of real values of `K' for which the lines x+3y+1=0,Kx+2y-2=0 and 2x-y+3=0 form a triangle is

Distance of the point (2,3,4) from the plane $3x-6y+2z+11=0$ is

If the mode of a data is $18$ and the mean is $24$, then median is

The integral $\int \frac{{\sec }^{2}x}{(\sec x+\tan x{)}^{\frac{9}{2}}}dx$ equals (for some arbitrary constant $k$)

Addition of two matrices of order $3\times 3$ results in a matrix of order

The vector equation of the plane passing through the intersection of the planes $\overrightarrow{r}\cdot (\hat{i}+\hat{j}+\hat{k})=1$ and $\overrightarrow{r}\cdot (\hat{i}-2\hat{j})=-2,$ and the point $(1,0,2)$ is

Two charges $q_1$ and $q_2$ are placed at -a and a on x-axis. List-1 represent some quantities and List-2 represent their corresponding graphs. Use sign convention. In list-1 E and V represent electric field and potential and x and y represent x, y coordinates. In list-2 y-axis of graph represent E or V and x-axis of graph represent x or y coordinates.
If $q_1=+Q$ and $q_2=-Q$, match correct option.

Which of the following sets are equal ?

$A=\{x:xϵN,x<3\}=\{1,2\},$

C= {3, 1}

D = {$x:xϵN$, x is odd, x < 5}

E= {1, 2, 1, 1}, F = {1, 1, 3}.

An element of a set can never be a subset of itself. Prove.

If $A$ and $B$ are square matrices of the same order and $A$ is non-singular, then for a positive integer $n,(A^{-1}BA{)}^n$ is equal to

If $\alpha =\cos \left(\frac{8\pi }{11}\right)+i\sin \left(\frac{8\pi }{11}\right),$ then $Re(\alpha +{\alpha }^2+{\alpha }^3+{\alpha }^4+{\alpha }^5)$ is equal to

$a(sinB-sinC)+b(sinC-sinA)+c(sinA-sinB)=0$

Given $2A^{\ast }+B^{\ast }=\left[\begin{array}{cc}-2i& -4i\\ -6i& -8i\end{array}\right]$ and all the elements of B are 2. Then matrix A is given by. ($\ast$ represents transpose conjugate operator)

How many garlands can be formed using 10 different flowers?

$\text{Find what the following equations become when the origin is shifted to the point(1,1)}?\left(i\right)x^2+xy-3y-y+2=0\left(ii\right)x^2-y^2-2x+2y=0\left(iii\right)xy-x-y+1=0\left(iv\right)xy-y^2-x+y=0$

Which of the following cases may lead to non trivial solutions in case of system of linear equations according to Cramer's rule Convention?

Find the intercepts cut-off by the plane 2x+y-z=5.

$\int \frac{dx}{\sqrt{16-9x^2}}=$

A straight line has its extremities on two fixed straight lines and cuts off from them a triangle of constant area of $2c^2$. Then, the locus of the middle point of the line is _____

What is the value of [x] + [-x] , where [x] is the greatest integer function

If $(\frac{1}{1+2i}+\frac{3}{1-i})\left(\frac{3-2i}{1+3i}\right)$ is reducible to $a+ib$, then values of $a$ and $b$ are

Solve the inequality $\frac{2x+1}{x+1}<2$

Find the point where the graph of the function Sgn (x) breaks (or becomes discontinuous)
(Sgn is the signum function)