Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\int \frac{x^3\sin ({\tan }^{-1}{x}^4)}{1+x^8}dx$ is equal to

${lim}_{x\to 0}\frac{(1-cos2x)sin5x}{x^{2}sin3x}=$

The domain of definition of $f\left(x\right)=\sqrt{x-3-2\sqrt{x-4}}-\sqrt{x-3+2\sqrt{x-4}}$ is

${lim}_{x\to 5}\frac{x^3-125}{x^2-7x+10}$

$N={144}^{255}+{192}^{255}$ then N is divisible by

$\text{In}\Delta ABC,\text{if a = 18, b = 24 and c = 30 and}\angle C={90}^{\circ },\text{find sin A, sin B and sin C.}$

$x-2\le \frac{5x+8}{3}$

$5^{2n+2}-24n-25$ is divisible by 576 for all n $ϵ$ N.

${lim}_{x\to 0}\frac{x^2}{sin{x}^2}$

Find the sixth term in the expansion $(y^{1/2}+x^{1/3}{)}^n$, if the binomial coefficient of the third term from the end is 45.

In the XY plane two points A(2,2) and B(7,7) are taken. R is the region in the first quadrant which consists of points C such that triangle ABC is an acute angled triangle. The closest integer to the area of the region R is

The value of $\cos {50}^{\circ }+\cos {70}^{\circ }+\cos {170}^{\circ }$ is

Negation of the statement $\sim p\to (q\vee r)$ is

If A and B are any two different square matrices of order n with A – B is non-singular $A^3=B^3$ and A(AB) = B(BA) , then

Find the value of:

p + q + 3r, when p = 1, q = 5, r = 2.

Let $Z$ be a complex number and $\overline{Z}$ denotes the conjugate of $Z$. If $2Z-3\overline{Z}=\frac{-27+23i}{1+i}$, then which of the following is/are correct?

In each of the following find the equation of the hyperbola satisfying the given conditions.:

$\left(i\right)vertices(\pm 2,0),foci(\pm 3,0)$

$\left(ii\right)vertices(0,\pm ,5),foci(0,\pm ,8)$

$\left(iii\right)vertices(0,\pm ,3),foci(0,\pm ,5)$

$\left(iv\right)vertices(\pm 5,0),transverseaxis=8$

$\left(v\right)foci(0,\pm 13),conjugateaxis=24$

$\left(vi\right)foci(\pm 3\sqrt{5}),thelatus-rectum=8$

$\left(vii\right)foci(\pm ,4,0),thelatus-rectum=12$

$\left(viii\right)vertices(0,\pm 6),e=\frac{5}{3}.$

$\left(ix\right)foci(0,\pm \sqrt{1}0),passingthrough(2,3)$

$\left(x\right)foci(0,\pm 12),latus-rectum=36$

Write the value of ${lim}_{x\to 0^{+}}\left[x\right].$

The mid-points of the sides of a triangle ABC are given by (-2, 3, 5), (4, -1, 7) and (6, 5, 3). Find the coordinates of A, B and C.

If $a,c,b$ are three terms of a geometric progression, then the line $ax+by+c=0$

Which of the following relations are equivalent?

The converse of the contrapositive of the conditional statement $\sim p\to q$ is

If one die is thrown twice, then what will be the probability of getting 9 as sum of the two outcomes? (Given that the outcome on the die is 5 in the first throw.)

For $\left(i\right)A=\left[\begin{array}{cc}cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{array}\right]$, verify that A'A=I.

For (ii)$A=\left[\begin{array}{cc}sin\alpha & cos\alpha \\ -cos\alpha & sin\alpha \end{array}\right]$, verify that A'A=I.

Find the equation of the plane with an intercept 3 on the Y-axis and parallel to ZOX- Plane.

For x, y, z $ϵ(0,\frac{\pi }{2}),$ let x, y, z be first three consecutive terms of an arithmetic progression such that cos x + cox y + cos z = 1 and sin x + sin y + sin z = $\frac{1}{\sqrt{2}}$, then which of the following is/are correct?

The random variable X has a probability distribution P(X) of the following form, where k is some number
$\{\begin{array}{c}K,ifX=0\\ 2k,ifX=1\\ 3k,ifX=2\\ 0,ifotherwise\end{array}$

Determine the value of k

$\{\begin{array}{c}K,ifX=0\\ 2k,ifX=1\\ 3k,ifX=2\\ 0,ifotherwise\end{array}$

If the coefficients of 2nd, 3rd and 4th terms in the expansion of $(1+x{)}^{2n}$ are in AP, show that $2n^2-9n+7=0$

Total number of prime number(s) between $288$ and $300$ is

If $f\left(x\right)=x^2$, find $\frac{f(1,1)-f\left(1\right)}{\left(1.1\right)-1}$

Prove that : $\frac{tan\theta }{sec\theta -1}$ - $\frac{tan\theta }{sec\theta +1}$ = 2 cot$\theta$

$\underset{x\to \infty }{lim}{\left(\frac{x+2}{x+1}\right)}^{x+1}$ is

The conditions for y=ax⁴+bx³+cx²+dx+e to have points of inflection is

A)b²-4ac>0 B)3b²-8ac=0

^{C)3b2 -8ac>0} D) 3b²-8ac<0

Let A and B be two sets such that n(A)=20, n(AUB)=42, n(AintersectionB)=4.

Find i) n(B)

ii) n(A-B)

iii) n(B-A)

Vijay wrote 4 different letters to send to 4 different addresses. For each letter, he prepared one envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, in how many ways can we put the letters so that only two of the letters goes to the right envelopes?

What's the equation of tangent to the parabola $y^2=4ax$ having a slope 'm'.

If exactly two integers lie between the roots of the equation $x^2+ax-1=0$, then possible integral value(s) of $a$ is (are)

Find the number of solutions of $lo{g}_{10}x–x=0$.