Explore topic-wise InterviewSolutions in Current Affairs.

Show that the tangents to the curve y
= 7x³ + 11 at the points where x = 2 and x
= −2 are parallel.

The value of $\underset{n\to \infty }{lim}(\frac{1}{2n+1}+\frac{1}{2n+2}+\cdots +\frac{1}{6n})$ is

Write the value of ${\sum }_{r=1}^6{}^{56-r}{C}_3+{}^{50}{C}_4.$

In a right angled triangle, medians drawn from the acute angles make an angle of $\theta$ which each other and L is the length of the hypotenuse. Then the area of the triangle is equal to:

A square of side length $a$ units lies above the $x-$axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha (0<\alpha <\pi /4)$ with the positive direction of $x-$axis. The equation of its diagonal not passing through the origin is

A mirror and a source of light are situated at origin and a point on $OX,$ respectively. A ray of light from the source strikes the mirror and reflected. If the direction ratios of the normal to the plane are $1,-1,1,$ then the direction cosines of the relected ray are

If $\sin \theta =\left(\frac{z-1}{i}\right),$ where $z=x+iy,$ $\theta$ represents an angle of a triangle, then

Let $x_1,x_2,.....x_n$ be values taken by a variable X and $y_1,y_2,.....y_n$ be the values taken by a variables Y such that $y_i=a{x}_i+b,i=1,2,.....,n.$ Then.

Which of the following is a correct representation of $3\times \frac{1}{4}?$

Using differentials, find the approximate value of each of the following up to 3 places of decimal ?
$\sqrt{25.3}$

$\sqrt{49.5}$

$\sqrt{0.6}$

$(0.009{)}^{\frac{1}{3}}$

$(0.999{)}^{\frac{1}{10}}$

$(15{)}^{\frac{1}{4}}$

$(26{)}^{\frac{1}{3}}$

$(255{)}^{\frac{1}{4}}$

$(82{)}^{\frac{1}{4}}$

$(401{)}^{\frac{1}{2}}$

$(0.0037{)}^{\frac{1}{2}}$

$(81.5{)}^{\frac{1}{4}}$

$(3.968{)}^{\frac{3}{2}}$

$(32.15{)}^{\frac{1}{5}}$

Let $F\left(\alpha \right)=\left[\begin{array}{ccc}cos\alpha & -sin\alpha & 0\\ sin\alpha & cos\alpha & 0\\ 0& 0& 1\end{array}\right]$, where $\alpha ϵR.$

Then $\left[F\right(\alpha ){]}^{-1}$ is equal to

Let
and.
Verify that

The values of $x$ satisfying $x^{{\log }_{5}x}>5$ lie in the interval

Count the number of triangles in given figure.

In a right angled triangle ABC (right angled at B), find the value of tan A × tan C.

A particle starts at the origin and moves $1$ unit horizontally to the right and reaches $P_1$, then it moves $\frac{1}{2}$ unit vertically up and reaches $P_2$, then it moves $\frac{1}{4}$ unit horizontally to right and reaches $P_3$, then it moves $\frac{1}{8}$ unit vertically down and reaches $P_4$, then it moves $\frac{1}{16}$ unit horizontally to right and reaches $P_5$ and so on. Let $P_n=(x_n,y_n)$ and $\underset{n\to \infty }{lim}{x}_n=\alpha$ and $\underset{n\to \infty }{lim}{y}_n=\beta .$ Then $(\alpha ,\beta )$ is

The equations of the lines through $(-1,-1)$ and making angle ${45}^{\circ }$ with the line $x+y=0$ are given by

Let $f\left(x\right)=x^2+\frac{1}{x^2}$ and $g\left(x\right)=x-\frac{1}{x},$ $x\in R-\{-1,0,1\}.$ If $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)},$ then the local minimum value of $h\left(x\right)$ is :

Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2.3 + 2.3.4 + … + n(n + 1) (n + 2) =

The point of intersection of diagonals of the parallelogram formed by the lines 3x−2y+5=0, x+3y-5=0, 3x−2y+11=0 and x+3y+3=0 is

Angle between tangents drawn to $x^2+y^2-2x-4y+1=0$ at the points where it is cut by the line $y=2x+c,is\frac{\pi }{2}$ then

1. 2

The equation to the hyperbola having its eccentricity equal to 2 and the distance between its foci equal to 8, is

If the curve $x^2+2y^2=2$ intersects the line $x+y=1$ at two points $P$ and $Q,$ then the angle subtended by the line segment $PQ$ at the origin is:

If $cot(\alpha +\beta )=0$, then write the value of $sin(\alpha +2\beta )$.

If the function $f\left(x\right)=\left[\frac{(x-3{)}^2}{a}\right]\sin (x-3)+a\cos (x-3)$ is continuous in $[4,8]$, then the range of $a$ is
($[.]$ denotes the greatest integer function)