Explore topic-wise InterviewSolutions in Current Affairs.

(i) If ${}^n{P}_4{:}^n{P}_5=1:2$ find n.

(ii) If ${}^{n-1}{P}_3{:}^{n+1}=5:12,$ find n.

If $X=\{1,3,5,7\}$, then which of the following is a function from $X$ to itself?

Number of $4$ digit numbers that can be formed using the digits $0,1,2,3,4,5$ which are divisible by $6$ when repetition of digits is not allowed are

If $\left|\frac{(x^2-x-6)(x-5)}{(x^2+1)(x-4)}\right|=-\frac{(x^2-x-6)(x-5)}{(x^2+1)(x-4)}$, then $x$ lies in

Given that the two curves $\arg \left(z\right)=\frac{\pi }{6}$ and $|z-2\sqrt{3}i|=r$ intersect in two distinct points, then
([r] represents integaral part of $r$)

What is calculus

The value of $y=(0.36{)}^{{\log }_{0.25}(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\dots \infty )}$ is

Let $f:R\to R$ be a continuous function satisfying $f\left(x\right)=\underset{0}{\overset{x}{\int }}f\left(t\right)dt.$ Then the value of $f\left(1\right)$ is

For the expression f(x) = a $x^2$ + bx + c (a > 0), $b^2$ > 4ac always. A real value $x_0$ will lie in between the roots of f(x) if

The values of a for which the equation $2x^2$ - 2(2a +1 ) x + a ( a-1 ) = 0 has

roots $\alpha \&\beta$ satisfying the condition $\alpha$ < a < $\beta$ , are

The value of $\underset{x\to 0}{lim}\left(\right[\frac{100x}{sinx}]+[\frac{99sinx}{x}\left]\right)$,where [.] denotes the greatest integer function, is

The minimum value of f(x) = -2 $x^2$ + 5x + 4 ∀ x $\in$ [0, 3] is __

The inverse of a matrix is defined for

If $A=\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$ then AA' =

The point in the graph of $y=x^2-2x+3$ where it attains the minimum value is

$ta{n}^2\theta +co{t}^2\theta$ is

If $A=\tan 1,B=\tan 2$ and $C=\tan 3,$ then the descending order of $A,B$ and $C$ is

If $y=\cos x^{\circ },$ then $\frac{dy}{dx}=$

The no of ways of selecting atleast one letter from the letters of the word "PROPORTION" is

$\left[\begin{array}{ccc}3& -1& 2\\ -3& 1& 2\\ -6& 2& 4\end{array}\right]$What is the rank of the matrix.

Find the vector and the Cartesian equation of the line that passes through the points (3, -2, -5), (3, - 2, 6).

Let $\ast$ be the binary operation on N given by $a\ast b=LCM$ of a and b.
(i) Find the identity of $\ast$ in N

Integrate the rational functions.
$\int \frac{x}{(x-1)(x-2)(x-3)}dx.$

Choose the correct. answer.
$\int \left(\frac{10x^9+{10}^{x}lo{g}_{e}10}{x^{10}+{10}^x}\right)dx$ equals
$\left(a\right){10}^x+x^{10}+C\left(b\right){10}^x+x^{10}+C\left(c\right)({10}^x-x^{10}{)}^{-1}+C(d)log|{10}^x+x^{10}|+C$

Choose the correct answer in the following questions

Area lying between the curves $y^2=4x$ and y = 2x is

(a) $\frac{2}{3}$ (b) $\frac{1}{3}$

(c) $\frac{1}{4}$ (d) $\frac{3}{4}$

Choose the correct answer in questions

Let A be a square matrix of order $3\times 3$, then $|kA|$ is equal
a) $k|A|$
b) $k^2|A|$
c) $k^3|A|$
d) $3k|A|$

Let a = 1 1 1....1 (55 digits), b=1 +10+10${}^2$ +....+10${}^4$, c =1+10${}^5$+10${}^{10}$+10${}^{15}$+....+10${}^{50}$, then

If in the expansion of ${(\frac{1}{x}+xtanx)}^5$, the ratio of fourth and second term is $\frac{2}{27}{\pi }^4$. Then smallest positive value of x is

The differential equation corresponding to the family of curves $y=cx+c-c^2$ where `c` is a parameter.

Starting at (0,0), an object moves in x-y plane via a sequence of steps, each of length 1 unit. Each step is left, right, up or down, all the four being equally likely. The probability that object reaches (2,2) in exactly 6 steps is

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are ${30}^{\circ }$, ${45}^{\circ }$, and ${60}^{\circ }$ respectively, then the ratio AB:BC is

There are n hose pipes lying on the floor. 2 boys decide to hold the pipe from any 1 of the end. The probability that they end up holding the ends of the same pipe is $\frac{1}{101}$. Find the value of n?

What are the types of the underlined clauses in the sentence?

The fact that Isha didn’t pay attention annoyed her teacher because he was short-tempered.

Which of the following relation in x and y is general solution of the differential equation $\frac{dy}{dx}=y$

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP=2AB$. If $\angle BPC=\beta$ , then $\tan \beta$ is equal to:

The sum of first three terms of a G.P. is $\frac{13}{12}$ and their product is - 1. Find the G.P.

If $A_1,A_2$ be two AM'x and $G_1,G_2$ be two GM's between a and b, then find the value of $\frac{A_1+A_2}{G_1{G}_2}$

If A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, find $n\left[\right(A\times B)$ and $n(A\times B)\cap (B\times A)]$.