Explore topic-wise InterviewSolutions in .

Let p : Kiran passed the examination,

q : Kiran is sad

The symbolic form of a statement "It is not true that Kiran passed therefore he is sad' is

The mean and the median of the following ten numbers in increasing order

$10,22,26,29,34,x,42,67,70,y$

are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

$A(3,2,0),B(5,3,2),C(-9,6,-3)$ are three points forming a triangle. If AD, the bisector of $\angle BAC$ meets BC in D, then coordinates of D are _____

C is a circle centered at O. $P{T}_1$ and $P{T}_2$ are the tangents drawn from a point P outside the circle to the circle. Then which of these is the most appropriate relation.

which of the following is true, if A is an invertible square matrix :-

$\frac{d}{dx}\left[ta{n}^{-1}\left(\frac{cosx+sinx}{cosx-sinx}\right)\right]=$

A and B are two sets such that $A\subset B$. Find the value of $A\cup B.$

If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio $r$ is ___.

How many graphs on n labeled vertices exist which have at least $(n^2-3n)/2$ edges?

$\underset{x\to 0}{lim}\frac{1-cosxcos2xcos3x}{si{n}^{2}2x}$ is equal to

Evaluate the following limit:
$\underset{x\to 0}{\text{lim}}\frac{\text{cos x}}{\pi -x}$

A set contains $(2n+1)$ elements. Then the number of subsets of the set which contains at most $n$ elements is

If $\forall n\in N,(1+x+x^2{)}^n=a_0+a_{1}x+a_2{x}^2+......+a_{2n}{x}^{2n}where{a}_1{a}_2.....a_{2n}\in Z$
and $a_0^2-a_1^2+a_2^2-a_3^2+.....+a_{2n}^2=k{a}_n$ then k=

For the following data, mean of x is found to be 7.3. The missing frequency is
x : 5 6 7 8 9
f : 4 6 12 - 8

Let $n\left(A\right)=m$ and $n\left(B\right)=n.$ Then, the total number of non-empty relations that can be defined from $A$ to $B$ is .

If $A=\left[\begin{array}{cc}1& 0\\ \frac{1}{2}& 1\end{array}\right]$ and $B=\left[b_{ij}\right]$ is a matrix such that $A^n-A^2+I=B$ (where $n\in N$). If $2(b_{21}+b_{22})=7$ then, $n$ is

If $a_1,a_2,a_3$ and $a_4$ are the coefficients of four consecutive terms in the expansion of $(1+x{)}^n,$ prove that $\frac{a_1}{a_1+a_2}+\frac{a_3}{a_3+a_4}=\frac{2a_2}{a_2+a_3}.$

If $x^2+y^2+\sin y=4,$ then the value of $\frac{d^{2}y}{d{x}^2}$ at the point $(-2,0)$ is :

If z be a complex number satisfying $z^2$ + z + 1 = 0. Find the value of $\left|z\right|$.

For a circle of radius $r=2m$, the angle subtended by an arc of length $\frac{\pi }{2}m$ will be

A bowl of soap water is at rest on a table in the dining compartment of a train, if the acceleration of the train is $\frac{g}{4}$ in forward direction, the angle made by its surface with horizontal is

What impression would you form of a state where the King was 'just and placid'?

$r^{th}$ term in the expansion of $(a+2x{)}^n$ is

In what ratio, the line joining (-1,1) and (5,7) is divided by the line x+y=4?

Solution set of $lo{g}_3(x^2-2)<lo{g}_3(\frac{3}{2}\left|x\right|-1)$ is

If $x$ satisfies $|x-1|+|x-2|+|x-3|\ge 6$, then

If k is scalar $(k\ne 0)$, I is an identity matrix and A is a square matrix . Then which among the following will always be a scalar matrix.

The sum to $n$ terms of the series $\frac{1}{(1+x)(1+3x)}+\frac{1}{(1+3x)(1+5x)}+\frac{1}{(1+5x)(1+7x)}+\dots \dots$, where $n>5,x\ge 2$ is

Let $a,b$ and $c$ be in G.P. with common ratio $r,$ where $a\ne 0$ and $0<r\le \frac{1}{2}$. If $3a,7b$ and $15c$ are the first three terms of an A.P., then the $4^{th}$ term of this A.P. is :

The complex numbers sinx+icos2x and cosx-isin2x are conjugate to each other for

If |x|<1, then the sum of the series

1 + 2x + 3$x^2$ + 4$x^3$ + ........., ∞ will be

If $x,2y,3z$ are in A.P. where the distinct numbers $x,y,z$ are in G.P, then the common ratio of G.P. is

If A = {a, b, c} then the number of proper subsets of A are:

In a shelf there are $2$ different physics books and $3$ different chemistry books. The number of ways in which a student can select a physics book or chemistry book is:

Find the sum of all two-digit numbers which when divided by 4 yield 1 as remainder.

The sum of an infinite geometric series is $3$. When the common ratio of the series is doubled, then the sum becomes $5$. The first term of the series is

Match the following

Given $\sin A=\frac{2}{3}\text{and}\sin B=\frac{1}{4}$

$A$ and $B$ are acute angles.

$\begin{array}{cc}\left(1\right)\sin (A+B)& \left(p\right)\frac{2\sqrt{15}-\sqrt{5}}{2+5\sqrt{3}}\\ \left(2\right)\cos (A-B)& \left(q\right)\frac{55}{144}\\ \left(3\right)\tan (A-B)& \left(r\right)\frac{2\sqrt{15}+\sqrt{5}}{12}\\ \left(4\right)\sin (A+B)\sin (A-B)& \left(s\right)\frac{5\sqrt{3}+2}{12}\end{array}$

The locus of the point of intersection of any two perpendicular tangents to the parabola $x^2-6x+16y+41=0$ is

If $2\cos \alpha =x+\frac{1}{x},2\cos \beta =y+\frac{1}{y}$ then $\frac{x^{10}}{y^{12}}-\frac{y^{12}}{x^{10}}=$

A parallelogram is cut by two sets of m lines parallel to its sides as shown. The number of parallelograms thus formed is_______.

Let $y=f\left(x\right)$ is a positive function which satisfies equation $\sqrt{y^2+2x}+\sqrt{y^2-2x}=2x^2,\text{then}\frac{dy}{dx}$ is

Let $z$ be a complex number such that $|z-2+i|\le 2$. If $m$ and $M$ denote the least and the greatest value of $|z|$ respectively, then the value of $m^2+M^2$ is