Explore topic-wise InterviewSolutions in Current Affairs.

Prove the following,

$3co{s}^{-1}x=co{s}^{-1}(4x^3-3x),xϵ[\frac{1}{2},1]$.

Consider the equation $x^2+2x-n=0$, where n $\in$ [5,100]. Total number of different values of 'n' so that the given equation has integral roots is

If a tangent to the parabola $y^2=4ax$ makes an angle of $\frac{\pi }{3}$ with the axis of symmetry of the parabola, then point of contact(s) is/are

A problem in mathematics is given to $4$ students whose chances of solving individually are $\frac{1}{2},\frac{1}{3},\frac{1}{4}$ and $\frac{1}{5}$. The probability that the problem will be solved at least by one student is

If the function $f\left(x\right)=2x^3-9a{x}^2+12a^{2}x+1[a>0]$ attains its maximum and minimum at $p$ and $q$ respectively such that $p^2=q$, then $a$ is equal to

If the equation $sin\theta =-\frac{1}{2}andtan\theta =\frac{1}{\sqrt{3}}$ then the most common general values of $\theta$ is

If the angle between two lines is $\frac{\pi }{6}$ and slope of one of the lines is $\frac{1}{2}$, then the slope of the other line can be

If $\tan \theta =-\frac{1}{\sqrt{3}},$ then the value of $\theta \in [0,2\pi ]$ for which $\frac{\cos \theta -{\cos }^3\theta }{\tan \theta +2}$ is always positive is

Two perpendicular unit vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $\left[\overrightarrow{r}\overrightarrow{a}\overrightarrow{b}\right]=\frac{5}{4},$ $\overrightarrow{r}\cdot (3\overrightarrow{a}+2\overrightarrow{b})=0$ and $\underset{-2\overrightarrow{r}.\overrightarrow{a}}{\overset{\frac{-4}{3}\overrightarrow{r}.\overrightarrow{b}}{\int }}\frac{x+1}{x^2+1}dx=\frac{\pi }{2}$. Then which of the following is(are) correct ?

Integrate the following functions.
$\int \frac{cosx}{\sqrt{1+sinx}}dx.$

If the tangent at any point on the curve \(x^4 + y^4 = a^4^\) cuts off intercepts p and q on the coordinate axes, the value of $p^{-\frac{4}{3}}+q-\frac{4}{3}$ is

Find the equation of a line passing through (2, 3) and inclined at an angle of ${135}^{\circ }$ with the positive direction of x-axis

The area of a triangle with vertices at $(-4,-1),(1,2)$ and $(4,-3)$ is

The set of all real numbers x for which $x^2-|x+2|+x>0$, is

Two statements p and q are given below.

p: 7 is not greater than 4
q: Paris is in France

Then the statement $\sim (p\vee q)is$

If A is a $3\times 3$ non-singular matrix such that $A{A}^T=A^{T}A$ and $B=A^{-1}{A}^T,$ then $B{B}^T$ is equal to

${lim}_{x\to 4}\frac{x^2-16}{\sqrt{x}-2}$

show that the function defined by f(x) = |cos x | is a continuous function.

Choose the correct answer in the given question.
$\int \sqrt{x^2-8x+7}dx$ is equal to
$\left(a\right)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}+9log|x-4+\sqrt{x^2-8x+7}|+C\left(b\right)\frac{1}{2}(x+4)\sqrt{x^2-8x+7}+9log|x+4+\sqrt{x^2-8x+7}|+C\left(c\right)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}-3\sqrt{2}log|x-4+\sqrt{x^2-8x+7}|+C\left(d\right)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}-\frac{9}{2}log|x-4+\sqrt{x^2-8x+7}|+C$

Prove that :$3si{n}^{-1}x=si{n}^{-1}(3x-4x^3),xϵ[-\frac{1}{2},\frac{1}{2}].$

Find $\frac{dy}{dx}$in the following questions:

$si{n}^{2}x+co{s}^{2}y=1$

Given an example of a relation. Which is
(iii) Reflexive and symmetric but not transitive.

Evaluate sin(π\n)+sin(3π\n)+sin(5π\n)+...to n terms

If $y=\left\{\frac{1-tanx}{1+tanx}\right\},showthat\frac{dy}{dx}=\frac{-2}{(1+sin2x)}$

The value of ${\int }_0^2\left(x^2\right]\mathrm{dx}$ is equal to

If f(x) =x²+kx+1,for all x and if it is an even function, find k.

If tanA/2=±√1-e/1+e*tanB/2

So prove

CosB = cosA-e/1-ecosA

Suppose we are given a point P on the Argand plane represented by the complex number Z,moving anticlockwise along the circle with |z| = 2 from the point of complex number 2 to 2i. If $\omega$ = $\frac{z+1}{z+2}$, then the path described by Q(x,y) which represents the complex number $\omega$ is

Find the number of words that can be formed using all the lettersA, B, C, D, E such that the word always starts with a vowel and repetition of letters is not allowed?

If P is a point on the hyperbola $16x^2-9y^2=144$ whose foci are $S_{1}and{S}_2,thenP{S}_1\sim P{S}_2=$

If $A=\left|\begin{array}{cc}\alpha & 2\\ 2& \alpha \end{array}\right|and|A^3|=125$, then the value of $\alpha$ is

The number of solution of cos$\theta$ + $\sqrt{3}$sin$\theta$ = 5, 0 ≤ $\theta$ ≤ 5$\pi$ is

If ${\int }_0^1\frac{e^{t}dt}{t+1}=a,then{\int }_{b-1}^b\frac{e^{-t}dt}{(t-b-1)}$ is equal to

Let the equations of the perpendicular bisectors of $AB$ and $AC$ in a traingle $ABC$ is $x+y=2$ and $2x-y=10$ respectively. If the coordinates of the point $A(0,10)$, then the equation of the line $BC$ is

Values of 'm' for which both the roots of equation $x^2$ - 2mx + $m^2$ - 1=0 are less than 4 are

The sum of the series $\frac{x}{1-x^2}+\frac{x^2}{1-x^4}+\frac{x^4}{1-x^8}+......$ to infinite terms, if |x| > 1 is

If y=x sin(logx)+xlogx,then $x^2\frac{d^{2}y}{d{x}^2}-x\frac{dy}{dx}+2y$=

The planes x-cy-bz=0, cx-y+az=0 and bx+ay-z=0 pass through a straight line, where a,b,c are non-zero constants. Then the value of $a^2+b^2+c^2+2abc$ is

Solve $ydx-xdy=x^{2}ydx.$