Explore topic-wise InterviewSolutions in Current Affairs.

Prove $x=(2n\pi +\frac{\pi }{2})$ or $x=2n\pi$, where $n\in I$.

Consider $f:1,2,3\to$ {a,b,c}given by f(1)=a, f(2)=b and f(3)=c. Find the $(f^{-1}{)}^{-1}$ of $\left(f^{-1}\right)$ . Show that $(f^{-1}{)}^{-1}=f.$

Let A = {{1, 2, 3}, {4, 5}, {6, 7, 8 }}. Determine whch of the following is true or false :

(i) 1 $ϵ$ A (ii) {1, 2, 3} $\subset$ A (iii) {6, 7, 8} $ϵ$ A (iv) {{4, 5}} $\subset$ A (v) $\varphi$ $ϵ$ A

One vertex of the equilateral triangle with centriod at origin and one side as $x+y-2=0$ is

If f(x) = $\frac{x}{x^2+1}$ , then $f\circ f\left(2\right)$

The number of solutions of $\sin x=\frac{|x|}{10}$ is

$\frac{1}{x-1}\le 2$

Find ${lim}_{x\to -\frac{5}{2}}\left[x\right].$

${lim}_{x\to 1}\frac{\sqrt{x^2-1}+\sqrt{x-1}}{\sqrt{x^2-1}},x>1$

1+(1+2)+(1+2+3)+(1+2+3+4)+...

If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by atmost $4,$ then the range of $b$ is

The equation of tangent to the parabola $y^2=x$ at point $(4,2)$ is

Find the image of the point $(2,1)$ with respect to the line mirror $x+y-5=0.$

$\text{If}z=1-cos\theta +isin\theta ,\text{then}|z|=$

$e^{x-y}=x^y,then\frac{dy}{dx}=$

If two sides of a triangle are the roots of $x^2-7x+8=0$ and the angle between these sides is $\frac{\pi }{3},$ then the product of inradius and circumradius of the triangle is

An urn contains 25 balls of which 10 balls bear a mark X and the remaining 15 bear a mark Y. A ball is drawn at random from the urn, its mark note down and it is replaced. If 6 balls are drawn in this way, find the probability that

atleast one ball will bear Y mark

Show that the function given by $f\left(x\right)=3x+17$ is strictly increasing on R.

Compute the following:
$\left(i\right)\left[\begin{array}{cc}a& b\\ -b& a\end{array}\right]+\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$

$\left(ii\right)\left[\begin{array}{cc}{a}^2+b^2& b^2+c^2\\ a^2+c^2& a^2+b^2\end{array}\right]+\left[\begin{array}{cc}2ab& 2bc\\ -2ac& -2ab\end{array}\right]$

$\left(iii\right)\left[\begin{array}{ccc}-1& 4& -6\\ 8& 5& 16\\ 2& 8& 5\end{array}\right]+\left[\begin{array}{ccc}12& 7& 6\\ 8& 0& 5\\ 3& 2& 4\end{array}\right]$

$\left(iv\right)\left[\begin{array}{cc}co{s}^{2}x& si{n}^{2}x\\ si{n}^{2}x& co{s}^{2}x\end{array}\right]+\left[\begin{array}{cc}si{n}^{2}x& co{s}^{2}x\\ co{s}^{2}x& si{n}^{2}x\end{array}\right]$

Given an example of a map
(iii) which is neither one-one nor onto.

The value of definite integral ${\int }_{-1}^2\left(x^3-x\right|\mathrm{dx}$ is

Two tailors, A and B,earn Rs 300 and Rs 400 per day respectively.A can stitch 6 shirts and 4 pairs of trousers while B can stitch 10 shirts and 4 pairs if trousers per day.To find how many days should each of them work and if it is desired to produce at least 60 shirts and 32 pairs of trousers at a minimum labour cost,formulate this as an LLP.

A factory produces bulbs. The probability that any one bulb is defective is $\frac{1}{50}$ and they are packed in 10 boxes. From a single box, find the probability that

(i) None of the bulbs is defective.

(ii) Exactly two bulbs are defective.

If the function f(x) satisfies $\underset{x\to 1}{\text{lim}}\frac{f\left(x\right)-2}{x^2-1}=\pi$, evaluate $\underset{x\to 1}{\text{lim}}$ f(x).

The value of $\underset{x\to 2}{lim}\underset{2}{\overset{x}{\int }}\frac{3t^2}{x-2}dt$ is

If p and q are two statements, then $\sim (p\wedge q)\vee \sim (q\iff p)$ is

The length of the latus rectum of the parabola $3x^2+4y+5+6x=0$ is

Which of the following function is not differentiable at x = 0?

A ring, 10 cm in diameter, is suspended from a point 12 cm above its centre by 6 equal strings attached to its circumference at equal intervals. The cosine of the angle between consecutive strings is

A man is known to speak truth is 75% cases. If he throws an unbiased die and tells his friend that it is a six, then the probability that it is actually a six, is

If y = y(x) and it follows the relation $e^{xy}+ycosx=2$, then which of the following is/are correct?

Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10. The probability that both will qualify the examination, is 0.02. Find the probability that

(i) both Anil and Ashima will not qualify the exam.

(ii) atleast one of them will not qualify the exam.

(iii) only one of them will qualify the exam.

In an A.P. of which 1 is the first term, if the second, tenth and thirty fourth terms form a G.P. then the fourth term of the A.P. is

Let f be a differentiable function satisfying ${\int }_0^x(x+1-y)f\left(y\right)dy=\frac{3x^2-2x^4}{6}\forall x\ge 0.$
Then the value of ${\int }_0^{\frac{1}{2}}\frac{2}{\sqrt{f^{\prime }\left(x\right)+f\left(x\right)+3}}dx$ is equal to

At the point x = 1, the given function $f\left(x\right)=\{\begin{array}{cc}{x}^3-1;& 1<x<\infty \\ x-1;& -\infty <x\le 1\end{array}$ is

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \left(a\right)& \text{If}\frac{a_1}{a_2}=\frac{b_1}{b_2}\text{then}(a_{1}x+b_{1}y+c_1)(a_{2}x+b_{2}y+c_2)& \left(p\right)& \text{a parabola}\\ & +k=0,(k\ne 0)\text{represents}& & \\ \left(b\right)& \text{If}\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\text{then}(a_{1}x+b_{1}y+c_1)(a_{2}x+b_{2}y+c_2)& \left(q\right)& \text{a pair of lines}\\ & +k=0,(k\ne 0)\text{represents}& & \\ \left(c\right)& \text{Locus of a point moving such that its distances from}& \left(r\right)& \text{a straight line}\\ & \text{the point (-13, 7) and the line 17x + 29y + 18 = 0}& & \\ & \text{are always equal}& & \\ \left(d\right)& \text{Locus of a point moving such that the ratio of its}& \left(s\right)& \text{a hyperbola}\\ & \text{distances from the point (3, 11) and the line}& & \\ & \text{14x - 5y + 13 = 0 is always 2}& & \end{array}$

What is the probability that the ${13}^{th}$ days of a randomly chosen month is Friday ?

Among the following, the ion with highest magnetic moment is .

Match each of the sets on the left in the roster form with the same set on the right described in the set -builder form :

(i) {A, P, L, E} (i) { $x:x+5=5,xϵZ$}

(ii) {5, -5} (ii) {x : x is a prime natural number and a divisor of 10}

(iii) {0} (iii) {x : x is a letter of the word "RAJASTHAN"}

(iv) {1, 2, 5, 10} (iv) {x : x is a natural number and divisor of 10}

(v) {A, H, J, R, S T, N} (v) {$x:x^2-25=0$}

(vi) {2, 5} (vi) {x : X is a letter of the word "APPLE"}

The quotient when $1+x^2+x^4+x^6+\cdots +x^{34}$ is divided by $1+x+x^2+x^3+\cdots +x^{17}$

The line 6x + 8y = 48 intersects the coordinate axes at A and B respectively. A line L bisects the area and the perimeter of the triangle OAB where O is the origin.

The line L does not intersect the side ______ of the $△OAB$.