Explore topic-wise InterviewSolutions in Current Affairs.

Which of the following has most number of divisors ?

$Find\frac{dy}{dx}ify=12(1-cost),x=10(t-sint),-\frac{\pi }{x}<t<\frac{\pi }{2}.$

$Ify=co{s}^{-1}x,thenfind\frac{d^{2}y}{d{x}^2}intermsofyalone.$

If $A=\left[\begin{array}{cc}0& -tan\frac{\alpha }{2}\\ tan\frac{\alpha }{2}& 0\end{array}\right]$ and I is the identity matrix of order 2, show that I + A $=(I-A)\left[\begin{array}{cc}cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{array}\right]$

A box, constructed from a rectangular metal sheet, is $21$ cm by $16$ cm by cutting equal squares of side $x$ cm from the corners of the sheet and then turning up the projected portions. The value of $x$ (in cm) so that volume of the box is maximum is

If $\left|\begin{array}{ccc}a& b+c& a^2\\ b& c+a& b^2\\ c& a+b& c^2\end{array}\right|=0$, where a, b, c are distinct real numbers, then the straight line ax + by + c = 0 passes through the fixed point

1. undefined
2. undefined
3. undefined
4. undefined

The value of $\sin {75}^{\circ }+\cos {75}^{\circ }$ is

Let $f:R\to R$ be a function defined as



$f\left(x\right)=\{\begin{array}{cc}\frac{\sin (a+1)x+\sin 2x}{2x},& \text{if}x<0\\ b,& \text{if}x=0\\ \frac{\sqrt{x+b{x}^3}-\sqrt{x}}{b{x}^{5/2}},& \text{if}x>0\end{array}$



If $f$ is continuous at $x=0,$ then the value of $a+b$ is equal

Evaluate,
when

(i) n
= 6, r
= 2 (ii) n
= 9, r
= 5

Which one of the following functions is strictly bounded?

Let $AD$ be a median of the $△ABC$. If $AE$ and $AF$ are medians of the triangle $ABD$ and $ADC$, respectively, and $AD=m_1,AE=m_2,AF=m_3$, then $\frac{a^2}{8}$ is equal to

The number of solutions of $3^{|x|}(|2-|x||)=1$ is

The areas of triangles formed by a plane with the positive $X,Y;Y,Z;Z,X$ axes respectively are $12,9,6$ square units, then the equation of the plane is

Column Matching:

$$\begin{array}{cc}\text{Column (I)}& \text{Column (II)}\\ \begin{array}{cc}\text{(A)}& \text{In a triangle}△XYZ,\text{let}a,b\text{and}c\text{be the}\\ & \text{lengths of the sides opposite to the angles}\\ & X,Y\text{and}Z,\text{respectively. If}2(a^2-b^2)=c^2\\ & \text{and}\lambda =\frac{\sin (X-Y)}{\sin Z},\text{then possible values}\\ & \text{of}n\text{for which}\cos \left(n\pi \lambda \right)=0\text{is (are)}\end{array}& \text{(P) 1}\\ & \\ \begin{array}{cc}\text{(B)}& \text{In a triangle}△XYZ,\text{let}a,b\text{and}c\text{be}\\ & \text{the lengths of the sides opposite to the}\\ & \text{angles}X,Y\text{and}Z,\text{respectively. If}\\ & 1+\cos 2X-2\cos 2Y=2\sin X\sin Y,\text{then}\\ & \text{possible value(s) of}\frac{a}{b}\text{is (are)}\end{array}& \text{(Q) 2}\\ & \\ \begin{array}{cc}\text{(C)}& \text{In}{R}^2,\text{let}\sqrt{3}\hat{i}+\hat{j},\hat{i}+\sqrt{3}\hat{j}\text{and}\beta \hat{i}+(1-\beta )\hat{j}\\ & \text{be the position vectors of}X,Y\text{and}Z\text{with}\\ & \text{respect to the origin}O,\text{respectively. If the}\\ & \text{distance of}Z\text{from the bisector of the acute}\\ & \text{angle of}\overrightarrow{OX}\text{with}\overrightarrow{OY}\text{is}\frac{3}{\sqrt{2}},\text{then possible}\\ & \text{value(s) of}|\beta |\text{is (are)}\end{array}& \text{(R) 3}\\ & \\ \begin{array}{cc}\text{(D)}& \text{Suppose that}F\left(\alpha \right)\text{denotes the area of the}\\ & \text{region bounded by}x=0,x=2,y^2=4x\\ & \text{and}y=|\alpha x-1|+|\alpha x-2|+\alpha x,\text{where}\\ & \alpha \in \{0,1\}.\text{Then the value(s) of}F\left(\alpha \right)+\frac{8}{3}\sqrt{2}\text{,}\\ & \text{when}\alpha =0\text{and}\alpha =1,\text{is (are)}\end{array}& \text{(S) 5}\\ & \\ & \text{(T) 6}\\ & \end{array}$$
Option $\text{(D)}$ matches with which of the elements of right hand column?

Solution of the differential equation $\left(\frac{dy}{dx}\right)+\left(\frac{y}{x}\right)=y^3$ is:

(where $c$ is integration constant)

The value of $\underset{h\to 0}{lim}2\left\{\frac{\sqrt{3}\sin (\frac{\pi }{6}+h)-\cos (\frac{\pi }{6}+h)}{\sqrt{3}h(\sqrt{3}\cos h-\sin h)}\right\}$ is :

If $f(x-y),f\left(x\right)f\left(y\right)$ and $f(x+y)$ are in A.P. for all $x,y\in R$ and $f\left(0\right)\ne 0$, then

What is the equation of the auxiliary circle of a hyperbola

$\frac{x^2}{16}-\frac{y^2}{9}=1$

Let $f\left(0\right)=0$ and $\underset{0}{\overset{2}{\int }}{f}^{\prime }\left(2t\right)e^{f\left(2t\right)}dt=5$, then the value of $f\left(4\right)$ is:

The middle term(s) in the expansion of ${\left(x+2\right)}^9$is

If $\omega$ is an imaginary cube root of unity, then the value of $(2-\omega )(2-{\omega }^2)+2(3-\omega )(3-{\omega }^2)+...+(n-1)(n-\omega )(n-{\omega }^2)$ is

How many different words with or without meaning can be formed from the letters of the word "BHARAT" ?

If PQ is a double ordinate of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ such that OPQ is an equilateral triangle, O being the centre of the hyperbola. Then the eccentricity e of the hyperbola, satisfies

Find the centre and radius of the circle (x + 5)² + (y – 3)² = 36

Find the equation of the planes that passes through the sets of three points.

(1,1,-1),(6,4,-5) and (-4,-2,3)

(1,1,0),(1,2,1),(-2,2,-1)