Explore topic-wise InterviewSolutions in Current Affairs.

If $x^m{y}^n=(x+y{)}^{m+n}$ then $\frac{dy}{dx}$ is equal to

Let $S$ be the set of all right angled triangles with integer sides forming consecutive terms of an arithmetic progression. The number of triangles in $S$ with perimeter less than $30$ is

If $sin(B+C-A),sin(C+A-B),sin(A+B-C)$ are in A.P., then cot A, cotB, cotC are in

The root of the equation, $(x^2+1{)}^2=x(3x^2+4x+3),$ are given by

What are the number of lattice points present in

1.FCC

2.BCC

3.SIMPLE CUBIC

A man saved Rs. 16500 in ten years. In each year after the first he saved Rs. 100 more than he did in the receding year. How much did he save in the first year?

Let A = {$xϵZ:0\le x\le 12$ }. Show that

R = {(a,b) : a, b $ϵA,|a-b|$ is divisible by 4} is an equivalence relation.

Find the set of all elements related to 1. Also write the equivalence class [2].

OR Show that the function $f:R\to R$ defined by $f\left(x\right)=\frac{x}{x^2+1}\forall xϵR$ is neither one-one nor onto. Also, if $g:R\to R$ is defined as g(x) = 2x-1, find fog(x).

If the expansion of $\frac{1}{(1-ax)(1-bx)}=a_0+a_{1}x+a_2{x}^2+\cdots +a_n{x}^n+\cdots$, then $a_n$ is (where $a\ne b,|ax|,|bx|<1$)

If a unit vector $\hat{a}$, makes angles $\frac{\pi }{3}$ with $\hat{i},\frac{\pi }{4}$ with $\hat{j}$ and an acute angle $\theta$ with $\hat{k}$, then find $\theta$ and hence the components of a.

Match $\text{List I}$ with $\text{List II}$ and select the correct answer using the code given below the lists :

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=ab+bc+ca,\text{then}& \text{(P)}& △ABC\text{is an equilateral triangle}\\ \text{(B)}& \text{In a}△ABC,\text{if}{a}^2+2b^2+c^2=2bc+2ab,\text{then}& \text{(Q)}& △ABC\text{is a right angled triangle}\\ \text{(C)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=\sqrt{2}a(b+c),\text{then}& \text{(R)}& △ABC\text{is a scalene triangle}\\ \text{(D)}& \text{In a}△ABC,\text{if}{a}^2+b^2+c^2=ca+\sqrt{3}ab,\text{then}& \text{(S)}& A={90}^{\circ },B={45}^{\circ },C={45}^{\circ }\end{array}$

Which of the following is the only CORRECT combination?

Solve the differential equation
$y{e}^{\frac{x}{y}}dx=(x{e}^{\frac{x}{y}}+y^2)dy(y\ne 0)$

Differentiate the following questions w.r.t. x.

$cos(logx+e^x).$

$\int \sqrt{2ax-x^2}dx=$

Differentiate it with respect to x

( x^2 + R^2 )^3/2

Which of the following equation(s) ($t$ being the parameter) represents a hyperbola?

A project manager estimates that a project will take x hours to complete, where x > 100. The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes y hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time?

Evaluate: $\underset{x\to \frac{\pi }{2}}{lim}\frac{tan2x}{x-\frac{\pi }{2}}$

The area (in square units) of the region bounded by the curve $x=y^2\text{and}x=3-2y^2$ is

P,Q,R and S are four points with the position vectors, $3\overrightarrow{i}-4\overrightarrow{j}+5\overrightarrow{k},4\overrightarrow{k},-4\overrightarrow{i}+5\overrightarrow{j}+\overrightarrow{k}\text{and}-3\overrightarrow{i}+4\overrightarrow{j}+3\overrightarrow{k}$ respectively. Then the line PQ meets the line RS at the point

If both $\theta$ and $\varphi$ are acute angles such that $\sin \theta =\frac{1}{2}$ and $\cos \varphi =\frac{1}{3}$, then $(\theta +\varphi )$ belongs to

Mean Value Theorem states

$\underset{n\to \infty }{lim}\sum _{r=1}^{n}co{t}^{-1}(r^2+\frac{3}{4})$ is

Equation of the tangent to $y^2=8x$ which is parallel to x-y+3=0 is

If ${\log }_{10}7=0.8451$ and ${\log }_{10}11=1.0414$, then the number of digits in ${77}^{100}$ is

The coefficient of $x^2{y}^3$ in the expansion of $(1-x+y{)}^{20}$ is

Two players toss 4 coins each. The probability that they both obtain the same number of heads is

A ship travels downstream from point A to a point B in 2 hours and upstream in 3 hours. Then the time taken by log of wood to cover the distance from A to B is

A) 5h. B) 9h. C) 12h. D) 1h.

Explain in detail.

There are 4 boys and 4 girls to sit in row randomly. What is the chance that all the girls do not sit together?

If $x^2$ - ( a - 3)x + a = 0 has atleast one positive root then :

Let $p,q$ be integers and let $\alpha ,\beta$ be the roots of the equation, $x^2-x-1=0,$ where $\alpha \ne \beta .$ For $n=0,1,2,....,$ let $a_n=p{\alpha }^n+q{\beta }^n.$

FACT: If $a$ and $b$ are rational numbers and $a+b\sqrt{5}=0.$ then $a=0=b.$

$a_{12}=$

Let $A$ and $B$ be two non-null events such that $A\subset B.$ Then, which of the following statements is always correct?

The chord of the curve $y=x^2+2ax+b$, joining the points where $x=\alpha$ and $x=\beta$, is parallel to the tangent to the curve at abscissa $x=$

Study the following information carefully and answer the questions below.

A team of five is to be selected from amongst five boys A, B, C, D and E and four girls P, Q, R and S. Some criteria for selection are—

Unless otherwise stated, these criteria are applicable to all questions below.

Q64. If two of the members have to be boys, the team will consist of:

If f(0)=0 and that 'f' is differentiable at x = 0, and ‘k’ is a positive integer. Then ${lim}_{x\to 0}\frac{1}{x}\left[f\right(x)+f\left(\frac{x}{2}\right)+f\left(\frac{x}{3}\right)+\dots \dots +f\left(\frac{x}{k}\right)]$

Points (a,a,c),(1,0,1) and (c,c,b) are collinear if

If $z$ is a complex number, then the number of solution(s) for the equation $z^2=\overline{z}$ is

The integral $\underset{\pi /6}{\overset{\pi /4}{\int }}\frac{dx}{\sin 2x({\tan }^{5}x+{\cot }^{5}x)}$ equals :

The two curves $x^3-3x{y}^2+2=0and3x^{2}y-y^3-2=0$