Explore topic-wise InterviewSolutions in Current Affairs.

The graph of $f\left(x\right)=||x-1|-1|$ is

Let $PQ$ be a focal chord of the parabola $y^2=4ax$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y=2x+a,a>0$.
If chord $PQ$ subtends an angle $\theta$ at the vertex of $y^2=4ax$, then tan $\theta$ is equal to

In a $△ABC$ , if $\tan A\tan B=3$, then the value of $\frac{\cos C}{\cos A\cos B}$ is

Which of the following function(s) has/have point of inflection?

If $a,b,c$ are the sides opposite to angles $A,B,C$ of a triangle $ABC,$ respectively and $\angle A=\frac{\pi }{3},b:c=\sqrt{3}+1:2,$ then the value of $\angle B-\angle C$ is

If the normal at the point $P(a{p}^2,2ap)$ meets the parabola at $Q(a{q}^2,2aq)$ such that the lines joining the origin to $P$ and $Q$ are at right angle, then

Find the value of x, if

Given, $\left|\begin{array}{cc}2& 3\\ 4& 5\end{array}\right|=\left|\begin{array}{cc}x& 3\\ 2x& 5\end{array}\right|$

${\int }_0^2{e}^{x}dx$

The point on x-axis equidistant from (5, 4) and (–2, 3) is ____ .

$Ifx=co{s}^3\theta ,y=si{n}^3\theta then\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}=$

The locus of the centre of the circle which cuts $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2,$ is

The value of $2{\cot }^{-1}\frac{1}{2}-{\cot }^{-1}\frac{4}{3}$ is

If $\alpha ,\beta ,\gamma$ are the roots of equation $x^3-6x^2+11x-6=0$, then find the equation whose roots are ${\alpha }^2+{\beta }^2,{\beta }^2+{\gamma }^2,{\gamma }^2+{\alpha }^2$ is

If $x-y=\frac{1}{3}$ and ${\cos }^2\left(\pi x\right)-{\sin }^2\left(\pi y\right)=\frac{1}{2}$, then $(x,y)$ can be

Perpendicular distance of the point (3, 4, 5) from the y-axis, is [MP PET 1994, Pb. CET 2002]

Determine whether the given planes are parallel or perpendicular and in case they are neither, find the angle between them.

2x+y+3z-2=0 and x-2y+5=0

Which one of the following hold good?

The coefficient of variance is $60$ and standard deviation is $24,$ then Arithmatic mean is

The value of ${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$ is

If the points (0, 1, 2), (2, –1, 3) and (1, –3, 1) are the vertices of a triangle, then the triangle is

Find the integrals of the functions.
$\int ta{n}^{3}2xsec2xdx.$

If $\sqrt{(1-x^{2n})}+\sqrt{(1-y^{2n})}=a(x^n-y^n)$, then $\sqrt{\left(\frac{1-x^{2n}}{1-y^{2n}}\right)}\frac{dy}{dx}$ is equal to

Statement 1 : If two lines are perpendicular, then product of their slopes is –1.
Statement 2: If the product of slopes of two lines is –1, then these lines will be perpendicular.

What is the difference between locus and equation?

In a traingle $ABC,2a^2+4b^2+c^2=4ab+2ac,$ then numerical value of $\cos B$ is equal to

Find the equations of the tangent and normal to the parabola $y^2=4$ ax at the point $(a{t}^2,2at).$

The number of 5 digit numbers can be made from the digits 0,1,2,3,4,5 if repetition is not allowed is ___

The value of $\underset{-\frac{\pi }{2}}{\overset{\frac{\pi }{2}}{\int }}\frac{x^2\cos x}{1+e^x}dx$ is equal to

Arguments of Z = $\frac{(2+i)}{[4i+(1+i{)}^2]}$ is :

If a, b, c are the roots of x³ - x² - 2004 = 0. Then the value of is equal to

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

Two squares are chosen at random on a chessboard. The probability that they have a side in common is

Given standard equation of ellipse,
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$,
with eccentricity $e$
Match the following
$\begin{array}{cc}\text{a) Focus}& i\left)\right(ae,0)\\ \text{b) Directrix}& ii\left)\right(a,0)\\ \text{c) Eccentricity}& iii)x=\frac{a}{e}\\ \text{d) Vertices}& iv\left)\right(-ae,0)\\ & v)x=\frac{-a}{e}\\ & vi)\sqrt{1-\frac{b^2}{a^2}}\end{array}$

The number of different words that can be formed using all the letters of the word 'APPLICATION' such that two vowels never come together, is

The magnitude of $-\sqrt{4}$ is

The number of divisors of 9600 including 1 and 9600 are

The integer
${}^{\prime }{k}^{\prime }$, for which the inequality $x^2–2(3k–1)x+8k^2–7>0$ is valid for every $x$ in $R$ is :