Explore topic-wise InterviewSolutions in Current Affairs.

If $R=\left\{\right(x,y):x+2y-8\}$ is a relation on N, write the range of R

Show that $A=\left[\begin{array}{c}53\\ -1-2\end{array}\right]$ satisfies the equation $A^2$ - 3A - 7I = 0 and hence find the value of $A^{-1}$.

Show that the points (a + 5, a - 4), (a - 2, a + 3) and (a, a) do not lie on a straight line for any value of a.

Find the middle terms in the expansion of ${(3x-\frac{x^3}{6})}^7$

If A = $\left[\begin{array}{cc}cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{array}\right]$ and $A^{-1}$ = A', then find the value of $\alpha$.

$\underset{x\to \infty }{lim}\left[\frac{\sum n^2}{n^3}\right]$

the question given below is of matrix :-

If A=[cos2theta sin2theta]

[-sin2theta cos2theta] find A^2

What is the locus of midpoint of chords of $x^2+y^2+2gx+2fy+c=0$ that pass through the point (1, 1)?

Tangents drawn at A$(a{t}_1^2,2a{t}_1)$ and B $(a{t}_2^2,2a{t}_2)$ intersect at (p,q).

Then p and q are ____and ____ of corresponding x and y coordinates of A and B respectively $(given{t}_1\ne t_2)$

The numerical value of $(1-\cos x)(1+\cos x)(1+{\cot }^{2}x)$ is

$\text{If tan A and tan B are the roots of}ab{x}^2-c^{2}x+ab=0\text{where a, b, c are the sides of the triangle ABC, then the value of}si{n}^{2}A+si{n}^{2}B+si{n}^{2}Cis$

Let $A$ is a $3\times 3$ matrix and $B$ is its adjoint matrix. If $|B|=64,$ then $|A|=$

Using elementary transformations, find the inverse of the followng matrix.

$\left[\begin{array}{cc}2& 1\\ 4& 2\end{array}\right]$

Find the equation of the hyperbola whose vertices are $(0,\pm 3)$ and the foci are $(0,\pm 5).$

$sinx=\frac{2t}{1+t^2},tany=\frac{2t}{1-t^2}$

Find $\frac{dy}{dx}$

If $20$ persons are invited for a party then number of different ways the persons and the host can be seated in a circular table, if two particular persons are to be seated on either side of the host is

Determine order and degree (when defined) of differential equations.
$(y^{\prime \prime \prime }{)}^2+(y^{\prime \prime }{)}^3+(y^{\prime }{)}^4+y^5=0.$

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find
$P(A\cup B)$

If $|4x-5|+|6x-12|=|2x-7|$, then $x$ belongs to

if a = cos 2B + cos 2A. , b= cos 2B - cos 2 A

c= sin 2A+ sin 2B, d= sin = sin2A-sin2B

Then which of the first is true.

(A) a/b= cot(A+B) cot(A-B)

(B) c/d= tan(A+B)/ tan(A-B)

(C ) b/ c= tan(A-B)

(D) none of these

If N the set of natural numbers is partitioned into groups S₁ ={1} , S₂ = {2,3}, S₃ = {4,5,6},...., find the sum of the numbers in S₅₀

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 min each for cutting and 10 min each for assembling. Souvenirs of type B require 8 min each for cutting and 8 min each for assembling. There are 3 h 20 min available for cutting and 4 h for assembling. The profit is Rs. 5 each for type A and Rs. 6 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximise the profit?

If 8,2 are the roots of $x^2+ax+\beta =0$ , and 3,3 are the roots of $x^2+\alpha x+b=0$ ,then the roots of $x^2$ + ax + b = 0 are :

Form the differential equation of all circles which pass through origin and whose centres lie on Y-axis.

A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

A$(x_1,y_1)$ and B$(x_2,y_2)$ are the end-points of diameter of a circle. Find the equation of the circle.

The mean age of a group of persons is $72$ years and another group of persons is $63$ years. If the mean age of all the persons of these two groups is $70,$ then the ratio of number of persons in the two groups is

Let f(x) be a real valued function defined on (-1,1) and $e^{-x}f\left(x\right)=2+{\int }_0^x\sqrt{t^4+dt}$. Then the value of $f^{\prime }\left(0\right)$ is

A class consists of 80 students, 25 are girls 55 are boys, 10 are rich remaining poor, 20 of them are fair complexioned. If we consider selecting girls and selecting rich, selecting fair complexioned, are all these events are independent?

Is probability of selecting fair complexioned rich girls is simply multiplying the probabilities

The mid -points of the sides of a triangle are$(1,5-1),(0,4,-2)and(2,3,4).$ Find its vertices.

$\sum _{n=1}^{\infty }\frac{1}{(n+1)(n+2)(n+3)....(n+k)}$ is equal to

log_0.0110 is equal to

Let P(x, y) lies in the region satisfying $si{n}^{-1}(\frac{x^2}{9}+\frac{y^2}{4})\le \frac{\pi }{2}$ and $co{t}^{-1}(x^2-y^2)>\frac{\pi }{2}$ such that area bounded by locus of P is a $si{n}^{-1}\frac{b}{\sqrt{c}}$, where b and c are co-primes, then a + b + c is equal to

$({}^{2n}{C}_1{)}^2+2\times ({}^{2n}{C}_2{)}^2+3.({}^{2n}{C}_3{)}^2.....+2n({}^{2n}{C}_{2n}{)}^2$,When n = 100

If $a{x}^2+bx+c=0$, then x =

$co{s}^{-1}x\{-cos\left(\frac{-13\pi }{6}\right)\}$ is equal to

The ratio in which the line joining the points (a, b, c) and (-a, -c, -b) is
divided by the xy-plane is
[MP PET 1994]

If $f\left(x\right)sinxcosxdx=\frac{1}{2(b^2-a^2)}log\left(f\right(x\left)\right)+c$, then f(x) =

If $3k,k,[k^2-34]$ are the first three terms of a geometric progression, where $k\in R^{+}$ and $[.]$ is the greatest integer function, then the value of $\sum _{r=1}^{10}(r{)}^{k/2}$ is

If $2ta{n}^2\alpha ta{n}^2\beta ta{n}^2\gamma +ta{n}^2\alpha ta{n}^2\beta +ta{n}^2\beta ta{n}^2\gamma +ta{n}^2\gamma ta{n}^2\alpha =1$ (where, $\alpha ,\beta ,\gamma \ne (2n+1)\frac{\pi }{2},\ne n\pi ,nϵI$) then

If $\int \frac{dx}{x^2(x^n+1{)}^{\frac{(n-1)}{n}}}=-\left[f\right(x){]}^{\frac{1}{n}}+C$ then f(x) is

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one in each box, could be placed such that a ball does not go to box of its own colour is