Explore topic-wise InterviewSolutions in Current Affairs.

If $X=\{4^n-3n-1:n\in N\}$ and $Y=\left\{9\right(n-1):n\in N\}$, then $X\cup Y$ is equal to

Miss $X$ takes either tea or coffee at morning break. If she had tea one morning, the probability that she has tea the next morning is $\mathrm{0.4.}$ If she had coffee one morning, the probability that she has coffee the next morning is $\mathrm{0.3.}$ Suppose she has coffee on a Monday morning. The probability that she has tea on the following Wednesday morning, is

The tangent at a point P on $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ cuts one of its directrices in Q. Then PQ subtends at the corresponding focus an angle of

A line $L_1:2x-2y+5=0$ is rotated about its point of intersection with $y-$axis such that $L_1$ becomes $L_2$ and area of the triangle formed by $L_1,L_2$ and $x=4$ is $13\text{sq. unit}$, then $L_2$ will be

If from the point P(a, b, c) perpendicular PL, PM be drawn to YOZ and ZOX planes, then the equation of the plane OLM is

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (–4, 3b, –10) and R (8, 14, 2c), then find the values of a, b and c.

Two finite sets have m and n elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set.Then, the values of m and n are :

Let $A=\{x:x\text{is a root of the equation}{x}^3+2x^2-x-2=0\}$ and $B=\{x:x\text{is a prime divisor of 720}\},$ then $n(A\times B)$ is

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x-y+3z-1=0 and 2x-y+3z+3=0

If $2f\left(sinx\right)+f\left(cosx\right)=x\forall xϵ$ R then range of f(x) is

If $y=\sqrt{\sin x-\sqrt{\sin x-\sqrt{\sin x-.....\infty }}}$ , then $\frac{dy}{dx}=$

The correct matching is

If complex number $z$ satisfies $|z|+z=2+i$, then $z$ is

The value of the limit $\underset{x\to e}{\lim }\frac{\log x-1}{x-e}$ is

The negation of $\sim s\vee (\sim r\wedge s)$ is equivalent to

If [x] denotes the greatest integer $\le$ x, then evaluate ${lim}_{n\to \infty }\frac{1}{n^3}\left\{\right[1^{2}x]+[2^{2}x]+[3^{2}x+.....+\left[n^{2}x\right]\}$

The product of slope of tangents from point $(0,1)$ to circle $x^2+y^2-2x+4y=0$ is:

If the vertices of a variable triangle are $(4,3),(-5\cos \theta ,-5\sin \theta ),\text{and}(5\sin \theta ,-5\cos \theta )$, where $\theta \in R,$ then the locus of its orthocenter is

If $n^{th}$ of a sequence is given by $T_n=2n+1$, then the sum of $4$ terms is

Sum up to $16$ terms of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\dots \dots$ is

If $2^{4n+4}-15n-16,n\in N$ is divided by $225$, then the remainder is

Given 11 points, of which 5 lie on one circle, other than these 5 no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is

If a plane passes through the point (1,1,1) and is perpendicular to the line $\frac{x-1}{3}=\frac{y-1}{0}=\frac{z-1}{4}$ then its perpendicular distance from the origin is

The complex number z which satisfies the condition $\left|\frac{i+z}{i-z}\right|=1$ lies on

If $|3x-5|\le 2$ then

Let $L$ be the line of intersection of planes $\overrightarrow{r}\cdot (\hat{i}-\hat{j}+2\hat{k})=2$ and $\overrightarrow{r}\cdot (2\hat{i}+\hat{j}-\hat{k})=2$. If $P(\alpha ,\beta ,\gamma )$ is the foot of perpendicular on $L$ from the point $(1,2,0)$, then the value of $35(\alpha +\beta +\gamma )$ is equal to

Show
that the following statement is true by the method of contrapositive.

p:
If
x is an integer and x²
is even, then x is also even.

A plane passes through a fixed point (a,b,c). Then the locus of the foot of the perpendicular to it from the origin is