Explore topic-wise InterviewSolutions in Current Affairs.

Through the vertex $O$ of the parabola $y^2=4ax$ a perpendicular is drawn to any tangent meeting it at $P$ and the parabola at $Q$. Then $OP\cdot OQ=$

Focal chord to $y^2=16xistangentto(x-6{)}^2+y^2=2$ then the possible values of the slopes of this chord(s),are

Let ${\Delta }_1$=$\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$ and
${\Delta }_2=\left|\begin{array}{ccc}{\alpha }_1& {\beta }_1& {\gamma }_1\\ {\alpha }_2& {\beta }_2& {\gamma }_3\\ {\alpha }_3& {\beta }_3& {\gamma }_3\end{array}\right|$, and ${\Delta }_1\times {\Delta }_2$ can be expressed as the sum of $n$ determinants, then $n=$

Find the following integrals.
$\int (2x^2+e^x)dx.$

Let $z$ be a complex number satisfying $z+z^{-1}=1$. A possible value of $n$ when $z^n+z^{-n}$ is minimum, is

If 10 distinct objects are distributed among 3 persons find the chance of a particular person having more than 5 of them.

Given that n numbers of A.Ms are inserted between two sets of numbers $a,2b$ and $2a,b$ where $a,b\in R.$
Suppose further that the $m^{th}$ means between these sets of numbers are same, then the ratio $a:b$ equals

If A + B = 90${}^0$ and cos B = $\frac{3}{5}$, then the value of sin A is -

Find the value of p so that the lines $\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}and\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles

One extremity of a focal chord of the parabola $y^2=16x$ is A(1,4). Then the length of the focal chord at A is

Seven people leave their bags outside a temple and returning after worshiping picked one bag each at random.In how many ways atleast one and atmost three of them get their correct bags?

Let the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$, between vectors $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi }{4}$ and between vectors $\overrightarrow{c}$ and $\overrightarrow{a}$ is $\frac{\pi }{3}$. The angle, the vector $\overrightarrow{a}$ makes with the plane containing vectors $\overrightarrow{b}$ and $\overrightarrow{c}$, is

The statement $(p\Rightarrow \sim p)\wedge (\sim p\Rightarrow p)$ is a:

$\underset{x\to 0}{lim}\frac{(27+x{)}^{\frac{1}{3}}-3}{9-(27+x{)}^{\frac{2}{3}}}\text{equals}$ :

If $l_i^2+m_i^2+n_i^2=1$ for $i=1,2,3$ & $l_i{l}_j+m_i{m}_j+n_i{n}_j=0$ for $i,j\in \{1,2,3\}$ and $i\ne j$ and $\Delta =\left|\begin{array}{ccc}{l}_1& m_1& n_1\\ l_2& m_2& n_2\\ l_3& m_3& n_3\end{array}\right|,$ then

The equation formed by decreasing the roots of the quadractic equation $a{x}^2+bx+c=0$ by $1$ is $2x^2+8x+2=0$, then which of the following statement(s) is/are true?

While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

A (3, 4), B (0, 0) and C (3, 0) are vertices of $△ABC.$ If ‘P’ is a point inside $△ABC,$ such that $d(P,BC)\le mind(P,AB),d(P,AC),$ then the maximum of $d(P,BC)$ is $\left(d\right(P,BC)$ represents distance between P. and BC)

Evaluate: $\int \frac{(x+3)e^x}{(x+5{)}^3}dx$

The general solution of the equation ${\sin }^3\theta \cos \theta -{\cos }^3\theta \sin \theta =\frac{1}{4}$is

An equation of the curve satisfying $xdy-ydx=\sqrt{x^2-y^2}dx$ and y(1) = 0 is

The point $(2t^2+2t+4,t^2+t+1)$ lies on the line x + 2y = 1 for

The solution of $\frac{dy}{dx}=\frac{ax+b}{cy+d}$ represents a parabola if

If $z=\frac{1+i\sqrt{3}}{2i(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3})},$ then

${lim}_{x\to 0}\frac{x^2-tan2x}{tanx}$

Let $f\left(n\right)$ denote the $n^{th}$ term of the sequence $3,6,11,18,27,...$ and $g\left(n\right)$ denote the $n^{th}$ term of the sequence $3,7,13,21,...$ . Let $F\left(n\right)$ and $G\left(n\right)$ denote the sum of $n$ terms of the above sequences, respectiveley. $\underset{n\to \infty }{lim}\frac{f\left(n\right)}{g\left(n\right)}=$

Differentiate the following functions with respect to x :

$3^x+x^3+3^3$

If the equations $x^2+3x+5=0$ and $a{x}^2+bx+c=0;a,b,c\in N$ have a common root, then the least possible value of $a+b+c$ is

Derivative of $y=(sinx{)}^2$ with respect to x will be equal to

Total numbers of terms in the expansion of $(3x-y+2z{)}^{10}$ is :

The centres of the circles $x^2+y^2=1,x^2+y^2+6x-2y=1and{x}^2+y^2-12x+4y=1$ are

If $\tan 2\alpha \cdot \tan \beta =1$ and $\tan \alpha \cdot \tan \gamma =1$ then

If a, b, c be three real numbers of the same sign then the value of $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ lies in the interval

The number of ways one can choose a set of distinct positive integers, each smaller than or equal to $20,$ such that there sum is odd

A vertex of an equilateral triangle is (2, 3) and the equation of the opposite side is x + y = 2. Find the equation of the other sides of the triangle.

If the range of discrete data of n observations is zero, then

The length of the perpendicular from the origin to a line is 7 and the perpendicular makes an angle of ${150}^{\circ }$ with the positive direction of x-axis. Find the equation of the line

Let $P(x,y)$ is a point where $x$ satisfies $x^2-|x|-6=0$ and $y$ satisfies $y^2+|y|-6=0$, if $A(1,1)$, then $\sum (PA{)}^2$ is

The foot of the perpendicular drawn from the origin, on the line, $3x+y=\lambda (\lambda \ne 0)$ is $P$. If the line meets $x$-axis at $A$ and $y$-axis at $B$, then the ratio $BP:PA$ is :

Find the image of :

(i) (-2, 3, 4) in the yz-plane.

(ii) (-5, 4, -3) in the xz-plane.

(iii) (5, 2, -7) in the xy-plane.

(iv)(-5, 0, 3) in the xz-plane.

(v)(-4, 0, 0) in the xy-plane.

Are the points A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5), the vertices of a right-angled triangle ?

The number of integral values of $\lambda$ for which the equation $x^2+y^2+\lambda x+(1-\lambda )y+5=0$ is the equation of a circle whose radius cannot exceed 5, is

Statement: A man must be wise to be a good wrangler. Good wranglers are talkative and boring.

Conclusions:

I. All the wise-persons are boring.

II. All the wise-persons are good wranglers.

The solution set of $x\ge \frac{1}{x}$ is

Are the following sets equal ?

A = {x : x is a letter in the word reap},

B = {x : x is a letter in the word paper},

C = {x : x is a letter in the word rope}

In a box, there are $20$ cards out of which $10$ are labelled as $A$ and remaining $10$ are labelled as $B$. Cards are drawn at random, one after the other and with replacement, till a second $A$-card is obtained. The probability that the second $A$ -card appears before the third $B$-card is :