Explore topic-wise InterviewSolutions in .

Let R be a relation over the set $N\times n$ and it is defined by (a, b) R (c, d) $\Rightarrow$ a+ d = b + c. Then, R is

The eccentricity of the hyperbola whose asymptotes are $3x+4y=10$ and $4x-3y=5$ is

If the straight line through the point P (3, 4) makes an angle $\pi /6$ with the x-axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.

If the coefficients of $x^{7}and{x}^8$ in the expansion of ${(2+\frac{x}{3})}^n$ are equal then n =

A boy went to the theatre to watch a movie and found a man who was his relative. The man was the husband of the sister of his mother. How was the man related to the boy?

If ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i=0$, then ${\sum }_{i-l}^{2n}co{s}^{-1}{x}_i$ is

Equation of a plane passing through $\hat{i}+\hat{j}+\hat{k}$ parallel to both $\hat{i}+\hat{j}and\hat{j}+\hat{k}$ can be given by

If $f:Z\to Z$ is defined by $f\left(x\right)=\{\begin{array}{c}\frac{x}{2}\text{if x even}\\ 0\text{if x odd}\end{array}$ then f is

Let $x_1=1and{x}_{n+1}=\frac{4+3x_n}{3+2x_n}forn\le 1$. If $\underset{n\to \infty }{lim}{x}_n$ exists finitely, then the limit is equal to

If $f\left(x\right)=\{\begin{array}{cc}\frac{\sin (p+1)x+\sin x}{x}& ,x<0\\ q& x=0\\ \frac{\sqrt{x+x^2}-\sqrt{x}}{x^{3/2}}& ,x>0\end{array}$ is continuous at $x=0$, then the ordered pair $(p,q)$ is equal to :

How many garlands can be formed using 10 different flowers?

The value of $\underset{\lambda \to 0}{lim}{\left(\underset{0}{\overset{1}{\int }}(1+x{)}^{\lambda }dx\right)}^{1/\lambda }$ is equal to

The solution of the differential equation $\frac{dy}{dx}=\frac{\sin y+x}{\sin 2y-x\cos y}$ is:

(where $c$ is constant of integration)

If $\left[x\right]$ denotes the greatest integers $\le x,$ then find



$\left[\frac{2}{3}\right]+[\left(\frac{2}{3}\right)+\left(\frac{1}{99}\right)]+[\left(\frac{2}{3}\right)+\left(\frac{2}{99}\right)]+\dots \dots +[\left(\frac{2}{3}\right)+\left(\frac{98}{99}\right)]$

Name the octants in which the following points lie:

(i) (5, 2, 3)

(ii) (-5, 4, 3)

(iii)(4, -3, 5)

(iv) (7, 4, -3)

(v) (-5, -4, 7)

(vi)(-5, -3, -2)

(vii) (2, -5, -7)

(viii)(-7, 2, -5)

In a triangle $ABC$, if $|\overrightarrow{BC}|=3,|\overrightarrow{CA}|=5$ and $|\overrightarrow{BA}|=7,$ then the projection of the vector $\overrightarrow{BA}$ on $\overrightarrow{BC}$ is equal to:

In throwing a fair dice, the probability of the event ''a number $\le 3$ turns up'' is

${lim}_{x\to a}\frac{x^n-a^n}{x-a}$ is equal to

If $cosec\theta =\frac{5}{4}$, then find the value of $\frac{(1+\tan \theta )(1-\tan \theta )}{(1+\cot \theta )(1-\cot \theta )}$

Expand:
(1)$(a+2)(a-1)$
(2) $(m-4)(m+6)$
(3) $(p+8)(p-3)$
(4) $(13+x)(13-x)$
(5) $(3x+4y)(3x+5y)$
(6) $(9x-5t)(9x+3t)$
(7) $(m+\frac{2}{3})(m-\frac{7}{3})$
(8) $(x+\frac{1}{x})(x-\frac{1}{x})$
(9) $(\frac{1}{y}+4)(\frac{1}{y}-9)$

What is probability that you spell " ERADICATE" correctly when you hit keyboard alphabet keys randomly?

Let $\overrightarrow{a}=-\hat{i}-\hat{k},\hat{b}=-\hat{i}+\hat{j}$ and $\overrightarrow{c}=\hat{i}+2\hat{j}+3\hat{k}$ be three given vectors. If $\overrightarrow{r}$ is a vector such that $\overrightarrow{r}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{b}$ and $\overrightarrow{r}\cdot \overrightarrow{a}=0,$ then the value of $\overrightarrow{r}\cdot \overrightarrow{b}=$

Angle between the curves $x^{2}y=1-y$ and $x^3=2(1-y)$ is

If $\left|\frac{z_1}{z_2}\right|=1$ and $\arg \left(z_1{z}_2\right)=0,$ then

Phoebe wants to make the smallest $7$ digit number possible using the digits $7,6,9,4,3,0,8$ . A digit can be repeated any number of times.The number formed by Phoebe is:

If $1,\omega ,{\omega }^2,\dots ,{\omega }^{n-1}$ are the $n^{\text{th}}$ roots of unity of $x^n=1,$ then the value of $(5-\omega )(5-{\omega }^2)\dots (5-{\omega }^{n-1})$ is equal to

The complex number $z$ satisfying the equation $|z|=z+1+2i$ is

If $sinA$ and $sinB$ of a $\Delta ABC$ satisfy $c^2{x}^2-c(a+b)x+ab=0$ then the triangle is

The value of ${\cot }^{-1}\frac{5}{\sqrt{3}}+{\cot }^{-1}\frac{9}{\sqrt{3}}+{\cot }^{-1}\frac{15}{\sqrt{3}}+{\cot }^{-1}\frac{23}{\sqrt{3}}+\cdots \infty$ is equal to

The focus and directrix of a parabola are (1,2) and 2x-3y+1=0. Then the equation of the tangent at vertex is