Explore topic-wise InterviewSolutions in Current Affairs.

Show that the line joining (2, -3) and (-5, 1) is parallel to the line joining (7, -1) and (0, 3).

If $\alpha$ is one of the principal solutions which satisfies the equation $1+{\sin }^2\theta =3\sin \theta \cos \theta ,$ then which of the following is not possible?

If $f\left(x\right)=\{\begin{array}{c}2x+b\text{if}x<a\\ x+d\text{if}x\ge a\end{array}$ and $\underset{x\to a}{lim}f\left(x\right)=l,$ then $l$ is equal to

If $\int \frac{x^4+1}{x(x^2+1{)}^2}dx=A\ln |x|+\frac{B}{1+x^2}+C,$ where $C$ is the constant of integration, then $|A+B|$ is equal to

The value of $\underset{n\to \infty }{lim}\frac{1}{n^3}(\sqrt{n^2+1}+2\sqrt{n^2+2^2}+\cdots +n\sqrt{n^2+n^2})$ is

Three groups A, B, C are competing for positions on the Board of Directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is

If A = {1, 2, 3}, B = {4} and C = {5}, then verify that :

(i) $A\times (B\cup C)=(A\times B)\cup (A\times C)$

(ii) $A\times (B\cap C)=(A\times B)\cap (A\times C)$

(iii) $A\times (B-C)=(A\times B)-(A\times C)$

A solid body floating on water has one-fifth of its volume above the surface. It is allowed to float in a liquid of relative density $1.25$, the fraction of the volume that will above the surface of liquid is

If two concentric ellipses be such that the foci of one be on the other and if $\frac{\sqrt{3}}{2}$ and $\frac{1}{\sqrt{2}}$ be their eccentricities. Then angle between their axes is

Show that the points (3, -2), (1, 0), (-1, -2) and (1, -4) are concylic.

If $x^3$ - 1 can be written as $(x-{\alpha }_0)$ $(x-{\alpha }_1)$ $(x-{\alpha }_2)$.Where,${\alpha }_0$,${\alpha }_1$ and ${\alpha }_2$ are the roots of the equation

and $\frac{1}{(3-{\alpha }_0)}$ + $\frac{1}{(3-{\alpha }_1)}$ + $\frac{1}{(3-{\alpha }_2)}$ = $\frac{k}{26}$. Find the value of k.

1. 3

The expression $(\cos 3\theta +\sin 3\theta )+(2\sin 2\theta -3)(\sin \theta -\cos \theta )$ is positive for all $\theta \in R$ in

Locus of mid point of chords of $x^2+y^2+2gx+2fy+c=0$ that pass through the origin, is

The curve y = f(x) is such that the area of the trapezium formed by the coordinate axes, ordinate of an arbitrary point and the tangent at this point equals half the square of its abscissa. The equation of the curve can be

If $\tan \left(\frac{\pi }{2}\sin \theta \right)=\cot \left(\frac{\pi }{2}\cos \theta \right)$, then $\sin (\theta +\frac{\pi }{4})$ can be

Prove the following by using the principle of mathematical induction for all n ∈ N:

The least value of $\alpha \in R$ for which $4\alpha x^2+\frac{1}{x}\ge 1,\text{for all}x>0$, is:

The following bar graph shows different fruits sold in a day by weight. Find the difference in sales between the most popular and least popular fruit.

The domain of $f\left(x\right)=\sqrt{{\log }_x\left(\cos 2\pi x\right)},$ is

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

(where $m$ is an arbitary constant)

Evaluate the determinants

(i)$\left|\begin{array}{ccc}3& -1& -2\\ 0& 0& -1\\ 3& -5& 0\end{array}\right|$

(ii)$\left|\begin{array}{ccc}0& 1& 2\\ -1& 0& -3\\ -2& 3& 0\end{array}\right|$

(iii)$\left|\begin{array}{ccc}3& -4& 5\\ 1& 1& -2\\ 2& 3& 1\end{array}\right|$

(iv)$\left|\begin{array}{ccc}2& -1& -2\\ 0& 2& -1\\ 3& -5& 0\end{array}\right|$

The value of $tan\left(1^{\circ }\right)+tan\left({89}^{\circ }\right)$ is

Let $0<A<B<\pi .$ If $\sin A-\sin B=\frac{1}{\sqrt{2}}$ and $\cos A-\cos B=\sqrt{\frac{3}{2}},$ then the value of $A+B$ is equal to

2 x 3 + 6 = ___

If the acute angles between the pairs of lines $3x^2-7xy+4y^2=0$ and $6x^2-5xy+y^2=0$ be ${\theta }_1$ and ${\theta }_2$ respectively, then

If the sum of the deviations of $50$ observations from $30$ is $50$, then the mean of these observations is:

How many number of terms are their in (a+b+c+d)^n

The
integrating factor of the differential equation.

is

A.

B.

C.

D.