Explore topic-wise InterviewSolutions in Current Affairs.

If sum of all the solutions of the equation $8\cos x(\cos (\frac{\pi }{6}+x)\cos (\frac{\pi }{6}-x)-\frac{1}{2})=1$ in $[0,\pi ]$ is $k\pi ,$ then $k$ is equal to

The number of intersection points of the function $f\left(x\right)=\sin x\&y=0.5\text{in}$

$\left(a\right).x\in (0,3\pi )$

$\left(b\right).x\in [-6\pi ,6\pi ]$ respectively are:

The value of
$\underset{n\to \infty }{lim}(1-\frac{1}{x}+\frac{1}{x^2}-.......n\text{term})$ for all $x\in (-1,1)$ is

If $a^{x-1}=bc,b^{y-1}=ac,c^{z-1}=ab$ such that $x,y,z$ are integers then value of $xy+yz+zx–xyz$ is

Find the coordinates of a point on y-axis which are at a
distance offrom
the point P (3, –2, 5).

Let $P$ be the foot of the perpendicular from focus $S$ of hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ on the line $bx-ay=0$ and let $C$ be the centre of the hyperbola. Then the area of the rectangle whose sides are equal to that of $SP$ and $CP$ is

Which of the following statements are correct?

1 . if sin θ = sin α ⇒ θ = nπ + $(-1{)}^n$α where α ∈ [ - $\frac{\pi }{2}$ , $\frac{\pi }{2}$] n ∈ I

2 . if cos θ = cos α ⇒ 2nπ±α where α ∈ [0,π] n ∈​ I

3 . if tan θ = tan α ⇒ θ = nπ + α where α ∈ (- $\frac{\pi }{2}$ , $\frac{\pi }{2}$ ) n ∈​ I

Determine the distance between the following pair of parallel lines:

(i) $4x-3y-9=0$ and $4x-3y-24=0$

(ii) $8x+15y-34=0$ and $8x+15y+31=0$

(iii) $y=mx+c$ and $y=mx+d$

(iv) $4x+3y-11=0$ and $8x+6y=15$

If $\alpha \text{and}\beta$ are the the root of $x^2-ax+b^2=0$, then ${\alpha }^2+{\beta }^2$ is equal to

A function $y=f\left(x\right)$ satisfies the condition $f^{\prime }\left(x\right)sinx+f\left(x\right)cosx=1,f\left(x\right)$ being bounded when $x\to 0$. if $I={\int }_0^{\frac{\pi }{2}}f\left(x\right)dx,$ then

If the set $S=\{1,2,3,\cdots ,12\}$ is to be partitioned into three sets $A,B,C$ of equal size such that $A\cup B\cup C=S,A\cap B=B\cap C=A\cap C=\varphi$ then the number of ways of partitioning $S$ is :

Maximize Z = 3x + 4y, subject to the constraints are x + y $\le$ 4, x $\ge$ 0 and y $\ge$ 0.

If $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ then the value of the integral $\underset{-\pi /2}{\overset{\pi /2}{\int }}\left[\right[x]-\sin x]dx$ is equal to:

The value of the expression $\tan \frac{\pi }{7}+2\tan \frac{2\pi }{7}+4\tan \frac{4\pi }{7}+8\cot \frac{8\pi }{7}$ is equal to

Which of the following is not equal to $co{s}^3\theta cose{c}^2\theta +cos\theta$ ?

Determine order and degree(if defined)
of differential equation

Let $F_1(x_1,0)$ and $F_2(x_2,0),$ where, $x_1<0$ and $x_2>0$ be the foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{8}=1$ suppose a parabola having vertex at the origin and focus at $F_2$ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.
If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the X-axis at Q then the ratio of area of $\Delta MQR$ to area of the quadrilateral $M{F}_{1}N{F}_2$ is

If $\underset{x\to \infty }{lim}(\sqrt{x^2-x+1}-ax)=b,$ then the ordered pair $(a,b)$ is

Let $\alpha =\frac{-1+i\sqrt{3}}{2}$.

If $a=(1+\alpha )\sum _{k=0}^{100}{\alpha }^{2k}$ and $b=\sum _{k=0}^{100}{\alpha }^{3k}$,

then $a$ and $b$ are the roots of the quadratic equation:

If $\left|\begin{array}{ccc}{x}^n& x^{x+2}& x^{x+4}\\ y^n& y^{n+2}& y^{n+4}\\ z^n& z^{n+2}& z^{n+4}\end{array}\right|=(\frac{1}{y^2}-\frac{1}{x^2})(\frac{1}{z^2}-\frac{1}{y^2})(\frac{1}{x^2}-\frac{1}{z^2})$ then n=

In a survey, it is found that $63\%$ Americans like cheese and $76\%$ like apple. If $x\%$ Americans like both, then

Let $p\left(x\right)=x^2–5x+a$ and $q\left(x\right)=x^2–3x+b$, where a and b are positive integers. Suppose hof(p(x),q(x)) = x – 1 and k(x) = 1cm (p(x), q(x)). If the coefficient of the highest degree term of k(x) is 1, the sum of the roots of (x – 1) + k(x) is.

If the extremities of the diagonal of a square are (1, -2, 3) and (2, -3, 5), then the length of the side is

Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.