Explore topic-wise InterviewSolutions in Current Affairs.

The number of all the possible triplets $(a_1,a_2,a_3)$ such that $a_1+a_{2}cos\left(2x\right)+a_{3}si{n}^2\left(x\right)=0$ for all x is

The value of $\int \frac{8x+15}{5x+3}dx$ is

(where $C$ is constant of integration)

$\underset{n\to \infty }{lim}\frac{1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^n}}{1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^n}}\text{is equal to}$

The number of straight lines joining 8 points on a circle is

If R = {(x,y) | x $\in$ N, y $\in$ N, x + 3y = 12} then $R^{-1}$ is

The minimum area of triangle formed by the tangents to the ellipse

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and coordinate axes is:

Probability that a random chosen three digit number has exactly 3 factors is

If $x^2-2x+{\log }_{\frac{1}{2}}p=0$ does not have two distinct real roots, then the maximum value of $p$ is

$\text{The limiting value of}{\left(cosx\right)}^{1/sinx}\text{as x}\to 0is$

Solve $x^2-2x+\frac{3}{2}=0$

The value of ${\tan }^{-1}\left(\tan 1\right)+{\tan }^{-1}\left(\tan 2\right)+{\tan }^{-1}\left(\tan 3\right)+{\tan }^{-1}\left(\tan 4\right)$ is

Let a function $f\left(x\right)=x+\cos x$ and $f\left(x\right)=0$ has atleast one real solution, then which of the following is correct

The value of the integral $\int \frac{2}{(1-x)(1+x^2)}dx$ is (where $C$ is integration constant)

A parabola $y=a{x}^2+bx+c$ crosses the x-axis at $(\alpha ,0)(\beta ,0)$ both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is

Solve the given inequality for real x: 3(x – 1) ≤ 2 (x – 3)

Let total revenue received from the sale of $x$ units of a product is given by $R\left(x\right)=12x+2x^2+6.$

Then the marginal revenue is



[2 marks]

Consider the differential equation, $y^{2}dx+(x-\frac{1}{y})dy=0.$ If value of $y$ is $1$ when $x=1,$ then the value of $x$ for which $y=2,$ is:

If $0<x,y<\pi$ and $\cos x+\cos y-\cos (x+y)=\frac{3}{2},$ then $\sin x+\cos y$ is equal to :

If $\alpha ,\beta ,\gamma$ are the angles made by a line with the positive directions of the coordinate axes, then $\frac{\sin \gamma +\cos \beta }{1-\sin \alpha }=$

If $\int \frac{dx}{4x^2-4x-3}=\frac{1}{p}\cdot \ln \left|\frac{2x-q}{rx+1}\right|+C$

If in a certain code, $ZIP$ is written as $33$ and $ZAP$ is written as $41,$ then how will $VIP$ be written?

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through $P(h,k)$, with the lines $y=x$ and $x+y=2$ is $h^2.$ The locus of the point $P$ is

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

Which of the following is/are a polynomial?

Find the centre and radius of the circle x² + y² – 8x + 10y – 12 = 0

Prove that
the line through the point (x₁, y₁)
and parallel to the line Ax + By + C = 0 is A (x
–x₁) + B (y – y₁)
= 0.

Question 6

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

$\begin{array}{ccccccc}Numberofletters& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ Numberofsurnames& 6& 30& 40& 16& 4& 4\end{array}$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.