Explore topic-wise InterviewSolutions in Current Affairs.

The mean of five observations is $5$ and their variance is $9.20$. If three of the given five observations are $1,3$ and $8$, then a ratio of other two observations is :

Area bounded by the curve $x(x^2+P)=y-1$ with $y=1$ is

How is Gaurav’s wife related to Tanya?

The shaded region in the figure is the solution set of the inequations.

A circle touches the $y$-axis at the point $(0,4)$ and passes through the point $(2,0)$. Which of the following lines is not a tangent to the circle?

The radius of an air bubble is increasing at the rate of $2cm/s$. At what rate is the volume of the bubble increasing when the radius is $2cm$?

The minimum distance of the point $(2,-2)$ from the line $y=mx+1$ where $m>0$ is $3$ units. The value of $m$ is

Evaluate the following :

(i) ${}^{14}{C}_3$ (ii) ${}^{12}{C}_{10}$

(iii) ${}^{35}{C}_{35}$ (iv) ${}^{n+1}{C}_n$

The parabola $y^2=px$ passes through the point of intersection of lines $\frac{x}{3}+\frac{y}{2}=1$ and $\frac{x}{2}+\frac{y}{3}=1$ its focus is

In a triangle ABC, $b=\sqrt{3},$ c = 1 and $\angle A={30}^0$, then the largest angle of the triangle is

The degree of the differential equation ${\left(\frac{d^{2}y}{d{x}^2}\right)}^3+{\left(\frac{dy}{dx}\right)}^2+sin\left(\frac{dy}{dx}\right)+1=0$ is
(a) 3
(b) 2
(c) 1
(d) None of these

If $I_n=\underset{\frac{\pi }{4}}{\overset{\frac{\pi }{2}}{\int }}{\cot }^{n}xdx$, then

Let $P\left(x\right)=x^2+bx+c$, where $b$ and $c$ are integers. If $P\left(x\right)$ is a facter of both $x^4+6x^2+25$ and $3x^4+4x^2+28x+5$, then value of $P\left(1\right)$ is -

Using the property of determinants and without expanding.

$\left|\begin{array}{ccc}b+c& q+r& y+x\\ c+a& r+p& z+x\\ a+b& p+q& x+y\end{array}\right|=2\left|\begin{array}{ccc}a& p& x\\ b& q& y\\ c& r& z\end{array}\right|$

let A,B ,C be the sets such thatA∪B=A∪C and A∩B=A∩C .show that B=C

Let $A=\left[\begin{array}{cc}2& 4\\ 3& 2\end{array}\right],B=\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right],$
Find the value of the following:
AB

A stone is dropped into a quiet lake and waves move in circles at the speed of 5 cm/s . At the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing?

The rate of change of volume of a sphere with respect to its surface area when the radius is $4cm$is

A letter is known to have come either from 'TATA NAGAR' or from 'CALCUTTA'. On the envelope, just two consecutive letters TA are visible. what is the probability that the letter came from 'TATA NAGAR' ?

$\frac{d}{dx}\left[ta{n}^{-1}\left(\frac{5x}{1-6x^2}\right)\right]=$

Using the property of determinants and without expanding.
$\left|\begin{array}{ccc}x& a& x+a\\ y& b& y+b\\ z& c& z+c\end{array}\right|=0$

If tan $\theta$ = $\sqrt{\frac{3}{2}}$, the sum of the infinite series
1 + 2(1 - cos$\theta$) + 3(1 - cos$\theta$)${}^2$ + 4(1 - cos$\theta$)${}^3$+........$\infty$ is

The set of the solutions for $\frac{2x-5}{(x-1)(x-7)}\le 0$ is

Find the equation of the circle concentric with the circle $2x^2+2y^2+8x+10y-39=0$and having its area equal to $16\pi$ sq units.

Or

Find the equation of the hyperbola whose conjugate axis is 5 and the distance between foci is 13.

Let f(x) be a polynomial function of degree 2 satisfying $\int \frac{f\left(x\right)}{x^3-1}=ln\left|\frac{x^2+x+1}{x-1}\right|+\frac{2}{\sqrt{3}}ta{n}^{-1}\left(\frac{2x+1}{\sqrt{3}}\right)+c,$ where c is indefinite integration constant.
Let $\int \frac{1-6cosecx}{6+f\left(sinx\right)}d\left(sinx\right)=g\left(x\right)+k,$ where g(x) contains no constant term. Then $\underset{t\to \frac{\pi }{2}}{lim}g\left(t\right)$ is equal to (where k is indefinite integration constant)

How many words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE' ?

A point c in the domain of a function f is called a critical point of f if

Let $x>0$ be a fixed real number. Then the integral $\underset{0}{\overset{\infty }{\int }}{e}^{-t}|x-t|dt$ is equal to

In a $△$ABC, a=1 and the perimeter is six times the A.M of the sines of the angles then measure of $\angle A$ is

If cos $\theta$ = $\frac{3}{5}$ and cos $\varphi$ = $\frac{4}{5}$, where $\theta$ and $\varphi$ are

positive acute angles, then cos $\frac{\theta -\varphi }{2}$ =

In a random survey 250 people participated. Out of 250 people who took part in the survey, 40 people have listened to Pink Floyd. 30 people have listened to Metallica and 20 people have listened to John Denver. If 10 people have listened to all three then find the no. of people who have listened to only Pink Floyd.

If the normal at any given point P on ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets its auxiliary circle at Q and R such that $\angle QOR={90}^{\circ }$, where O is centre of ellipse, then

You have been appointed as a Brand Manager of Ford Motors. The company is to introduce a compact small car in Indian Market. The name of the car is yet to be decided. You have been asked to chair a brainstorming session. Before the suggestions come forward you have to briefly explain the participants as to what constitutes a good brand name with the help of suitable examples.

(i) Identify which of these does branding a component of?

(ii) Explain the features of a good brand name for Ford Motors with suitable examples only in the context of the case study.

let $S$,$S^1$ be the foci of an ellipse. If $\angle BS{S}^1$ = $\theta$,where B is any point on the ellipse. Then its eccentricity is

If $\left|\overrightarrow{a}\right|=10,\left|\overrightarrow{b}\right|=2and\overrightarrow{a}.\overrightarrow{b}=12$, then the value of $|\overrightarrow{a}\times \overrightarrow{b}|=$

The two points A and B in a plane are such that for all points P lies on circle satisfied $\frac{PA}{PB}=k$, then k will not be equal to

The term independent of $x$ in the expansion ${(\frac{\sqrt{x}}{\sqrt{3}}+\frac{\sqrt{3}}{2x^2})}^{10}$ is equal to:

The range of the function $f\left(x\right)=co{s}^2\frac{x}{4}+sin\frac{x}{4},xϵR$ is

If both the roots of the quadratic equation $x^2-2kx+k^2+k-5=0$ are less then 5, then k lies in the Interval

If $3^{x-y}=27,3^{x+y}=243,$ what is the value of $x?$

Show that the function given by $f\left(x\right)=sinx$ is
neither increasing nor decreasing in $(0,\pi )$