Explore topic-wise InterviewSolutions in Current Affairs.

Let $A=\{y:y={\log }_{2}x,x<16,x,y\in N\},B=\{x:x^2-7x+12=0\}$ then $(A\cup B)\times (A\cap B)$ is

Six boys and six girls sit in a row at random. The probability that the boys and girls sit alternatively is

The value of $\tan 6^{\circ }\tan {42}^{\circ }\tan {66}^{\circ }\tan {78}^{\circ }$ is

In the sum fo first n terms of an A.P. is $c{n}^2$ then the sum of squares of these n terms is

A pair of straight lines $x^2-8x+12=0$ and $y^2-14y+45=0$ are forming a square. Co-ordinates of the center of the circle inscribed in the square are

For any complex number $w=c+id$, let $\arg \left(w\right)\in (-\pi ,\pi ]$, where $i=\sqrt{-1}$. Let $\alpha$ and $\beta$ be real numbers such that for all complex numbers $z=x+iy$ satisfying $\arg \left(\frac{z+\alpha }{z+\beta }\right)=\frac{\pi }{4}$, the ordered pair $(x,y)$ lies on the circle $x^2+y^2+5x-3y+4=0$. Then which of the following statements is(are) TRUE?

If two events A and B are such that $P\left(A^C\right)=0.3,P\left(B\right)=0.4,P(A\cap B^C)=0.5$, then find the value of $P\left[\frac{B}{A\cup B^C}\right]$

If $\overrightarrow{r}\cdot \hat{i}=2\overrightarrow{r}\cdot \hat{j}=4\overrightarrow{r}\cdot \hat{k}$ and $|\overrightarrow{r}|=\sqrt{21},$ then vector $\overrightarrow{r}$ is

Find the sum of first 10 terms of the G.P 3, 6, 12, 24___

The number of solution(s) of the equation $x-\frac{7}{x-3}=3-\frac{7}{x-3}$ is

${lim}_{n\to \infty }\frac{(n+2)!+(n+1)!}{(n+2)!-(n+1)!}$

If $A=\left[\begin{array}{cc}9& 1\\ 7& 8\end{array}\right],B=\left[\begin{array}{cc}1& 5\\ 7& 12\end{array}\right],$ then $C$ such that $5A+3B+2C$ is a null matrix, is:

Two parabolas $x^2=4y$ and $y^2=4x$ intersect at two distinct points out of which one of them is origin then the other point will be

The value of $a$ for which the equation $(a^2-a-2)x^2+(a^2-4)x+(a^2-3a+2)=0$ have more than two roots

Find the integrals of the functions.
$\int \frac{cosx-sinx}{1+sin2x}dx.$

The point of inflection for the function $f\left(x\right)=\frac{\ln x}{x}$ is:

In a triangle origin is centroid and all medians are of length $3$ units. If one of the vertex is $(-3,4)$ and $I$ is incentre of the triangle then $GI=$

The three axes OX, OY, OZ determine _______________________.

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord to the circle with centre $(2,1)$, then the equation of the circle is

If a point P divides the line segment joining $A(5,3)$ and $B(10,8)$ in the ratio $3:2$ internally, then point P lies on:



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If $x=Rsin\omega t+R\omega t$ and $y=Rcos\left(\omega t\right)+R$ (where $\omega$ and R are constants), what are x and y components of acceleration when y is minimum?

A particle is in motion along a curve $12y=x^3$. The rate of change of its ordinate exceeds that of abscissa in

The value of the integral $\int \frac{1}{x^4-1}dx$ is

(where $C$ is an arbitrary constant)

Let $g\left(x\right)={\int }_0^{x}f\left(t\right)dt$ where $\frac{1}{2}\le f\left(t\right)\le 1,tϵ[0,1]$ and $0\le f\left(t\right)\le \frac{1}{2}$ for $tϵ(1,2)$, then [IIT Screening 2000]

If for non-zero $x$, $3f\left(x\right)+4f\left(\frac{1}{x}\right)=\frac{1}{x}-10$, then ${\int }_2^{3}f\left(x\right)dx$ is equal to

If $G$ be the geometric mean of $x$ and $y,$ where $x,y>0,$ then the value of $\frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}$ is

If $\overrightarrow{a^1},\overrightarrow{b^1},\overrightarrow{c^1}$ is the reciprocal system of vector triad of $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$, then $(\overrightarrow{a}+\overrightarrow{b})\cdot \overrightarrow{a^1}+(\overrightarrow{b}+\overrightarrow{c})\cdot \overrightarrow{b^1}+(\overrightarrow{c}+\overrightarrow{a})\cdot \overrightarrow{c^1}=$

If $\alpha$ is one of the roots of $x^2+7x+10=0$, then the value of ${\cot }^{-1}\alpha +{\cot }^{-1}\frac{1}{\alpha }$ is equal to

If the plane $2x-y+2z+3=0$ has the distances $\frac{1}{3}$ and $\frac{2}{3}$ units from the planes $4x-2y+4z+\lambda =0$ and $2x-y+2z+\mu =0,$ respectively, then the maximum value of $\lambda +\mu$ is equal to :

Let $I=\underset{0}{\overset{1}{\int }}\sqrt{\frac{1+\sqrt{x}}{1-\sqrt{x}}}$ and $J=\underset{0}{\overset{1}{\int }}\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}.$ Then

The intercept form of the line $3x-4y+12=0$ is