Explore topic-wise InterviewSolutions in Current Affairs.

There is a line and a parabola $y^2=4x$ on the xy plane. The line intersects the parabola at only 1 point. If one of the point lying on this line is (105,1) ,then which among the following points would also lie on the line.

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

The number of ways in which $20$ different white balls and $19$ different black balls be arranged in a row, so that no two balls of the same colour come together is

What is the inverse of the matrix $\left[\begin{array}{cc}-3& 2\\ 5& -1\end{array}\right]$

The ratio in which a point $P(2,3)$ divides the line segment joining $A(-2,-7)$ and $B(4,8)$ is

If the equations $x^2+bx+c=0and{x}^2+cx+b=0(b\ne c)$ have a common root, then :

Give the components of M3 measure of money supply.

The value of k for which the lines $kx+y=6$ and $2x-5y=1$ are perpendicular to each other is

Two tangents are drawn from a point with abscissa 25, to the ellipse $24x^2+25y^2=600$ with foci at $S_1$ and $S_2$. The points of contact of the tangents are $A$ and $B.$ If the distance of $A$ from $S_1$ is $\frac{60}{13}$ units, then

Three ships A, B and C sail from England to India. If the ratio of their arriving safely are 2 : 5, 3 : 7 and 6 : 11 respectively then the probability of all the ships for arriving safely is
[Pb. CET 2000]

Starting at (0,0), an object moves in x-y plane via a sequence of steps, each of length 1 unit. Each step is left, right, up or down, all the four being equally likely. The probability that object reaches (2,2) in exactly 4 steps is

If $a^2,b^2,c^2$ are in A.P. prove that $\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}$ are in A.P.

Find the coefficient of a4 in the product $(1+2a{)}^4(2-a{)}^5$ using binomial theorem.

Find the value of ${}^{1000}{C}_{500}+{}^{1000}{C}_{501}$

If $\int \frac{\cos x}{{\sin }^{3}x(1+{\sin }^{6}x{)}^{2/3}}dx=f\left(x\right)(1+{\sin }^{6}x{)}^{1/\lambda }+c$, where $c$ is a constant of integration, then $\lambda f\left(\frac{\pi }{3}\right)$ is equal to :

The mean of $5$ observation is $6$ and the varience is $\mathrm{6.80.}$ If three of the five observation are $8,5$ and $10.$ Then the remaining two observation are

In a triangle ABC the value of $\angle A$ is given by 5 cos A+3=0, then the equation whose roots are sin A and tan A will be

Find the A.M. between:
(i) 7 and 13
(ii) 12 and -8
(iii) $(x-y)$ and $(x+y)$

What part of speech is the underlined word?

Both were sentenced to 40 years in prison.

Using properties of determinants prove the following questions.

$\left|\begin{array}{ccc}3a& -a+b& -a+c\\ -b+a& 3b& -b+c\\ -c+a& -c+b& 3c\end{array}\right|=3(a+b+c)(ab+bc+ca)$.

Two finite sets A and B are said to be equivalent, if n(A)=n(B),
Equal sets are always equivalent, But, equivalent sets need not be equal.

The sub-tangent at any point of the curve $x^m{y}^n=a^{m+1}$ varies as

x2-kx+k,+2

Write the sample space for the experiment of tossing a coin four times.

The greatest value of $c\in R$ for which the system of linear equations
$x-cy-cz=0cx-y+cz=0cx+cy-z=0$
has a non-trivial solution, is :

If the complex number $z$ satisfies $z+\sqrt{2}|z+1|+i=0$, then $z$ is :

Find the nth term of the following series $2+5x+8x^2+11x^3+......$

Find the value of expression ${\sum }_{i=1}^n{\sum }_{j=1}^i{\sum }_{k=1}^{j}6.$

The line 2x+3y=6, 2x+3y=8 cut the X-axis at a A,B respectively. A line L=o drawn through the point (2,2) meets the X-axis at C in such a way that abscissae of A,B,C are in arithmetic progression. Then the equation of the line L is

The inequality $\frac{x}{3}\ge \frac{5x-2}{3}-\frac{7x-4}{5}$ holds true for $x$ in the interval

Complete values of $a$ for which the equation $|x-1|+|x-2|+x-a>0$ has two solutions, is

Differentiate each of the following from first principles :

$\left(i\right)ta{n}^{2}x$

$\left(ii\right)tan(2x+1)$

$\left(iii\right)tan2x$

$\left(iiv\right)\sqrt{tanx}$

The value of the $\underset{x\to 0}{lim}\frac{\sin \left(\pi {\cos }^2\right(\pi {\cos }^{2}x\left)\right)}{x^2}$ is equal to

$\int \frac{dx}{x(logx-2)(logx-3)}=f\left(x\right)+cthenf\left(x\right)=$

In $△ABC$, if $\cos B\cos C+\sin B\sin C{\sin }^{2}A=1$, then

The sum to $n$ terms of the series $\frac{1}{(1+x)(1+3x)}+\frac{1}{(1+3x)(1+5x)}+\frac{1}{(1+5x)(1+7x)}+\dots \dots$, where $n>5,x\ge 2$ is

1. undefined
2. undefined
3. undefined
4. undefined