Explore topic-wise InterviewSolutions in Current Affairs.

Let $\text{A}=\{4,6,8,10\},\text{B}=\{3,4,5,6,7\}$, and $f:\text{A}\to \text{B}$ be defined by $f\left(x\right)=\frac{1}{2}x+1$, then which of the following options is correct, if we represent $f$ by a set of ordered pairs?

The locus of the foot of perpendicular drawn from the centre of the ellipse $x^2+3y^2=6$ on any tangent to it is:

If the coordinates if the vertex and focus of a parabola re (-1,1) and (2,3) respectively,then write the equation of its directrix.

The number of intersection points of the function $f\left(x\right)=cosx$ and $y=1/3$ in :

$\left(a\right)x\in (0,3\pi )$

$\left(b\right)x\in [-3\pi ,2\pi ]$ are respectively:

The sum of an infinite number of terms of a G.P. is $20$, and the sum of their squares is $100$, then the common ratio is

From a well-shuffled deck of $52$ cards, $9$ cards are taken out one by one with replacement. Then the probability that out of $9$ cards, $5$ cards are spades, is

If $A^{\prime }\subset B,$ then $(A\cap B^{\prime }{)}^{\prime }=$

Equation of the locus of all points such that the difference of its distances from $(-3,-7)$ and $(-3,3)$ is $8$ units is

The value of $\cot \left({\sum }_{n-1}^{23}{\cot }^{-1}(1+{\sum }_{n=1}^{23}2k)\right)$ is

The greatest possible number of points of intersection of 8 straight lines and 4 circles is________.

A line passes through $(2,2)$ and has $x$-intercept and $y$-intercept as $\alpha \text{units}$ and $\beta \text{units}$ respectively. It makes a triangle of area $A$ with co-ordinate axes. Then the quadratic equation whose roots are $\alpha$ and $\beta$ is :

($\alpha >0,\beta >0$)

If $3-\frac{x^2}{12}\le f\left(x\right)\le 3+\frac{x^3}{9}$ for all $x\ne 0$,

Tangent are drawn to the hyperbola $\frac{x^2}{9}-\frac{y^2}{4}=1$, parallel to the straight line $2x-y=1$. The points of contact of the tangents on the hyperbola are

Question 4 (i)

State whether the following are true or false. Justify your answer.

(i) sin (A + B) = sin A + sin B.

Number of solution(s) of ${\log }_2({4.3}^x-6)-{\log }_2(9^x-6)=1,$ is-

1. 2

The value of $\underset{-1}{\overset{1}{\int }}{x}^2{e}^{\left[x^3\right]}dx,$ where $\left[t\right]$ denotes the greatest integer $\le t$ ,is :

Let $f\left(x\right)=(1-x{)}^{2}si{n}^{2}x+x^2$ for all $x\in R$. Consider the statements:

P: There exists some $x\in R$ such that $f\left(x\right)+2x=2(1+x^2).$

Q:There exists some $x\in R$ such that $2f\left(x\right)+1=2x(1+x).$

Then

The sum of first $8$ terms of the series $3,6,12,24,\dots$ is

If $Z=\frac{7+i}{3+4i}$, then value of $z^{14}$ is

Prove the following,

$2ta{n}^{-1}\left(\frac{1}{2}\right)+ta{n}^{-1}\left(\frac{1}{7}\right)=ta{n}^{-1}\left(\frac{31}{17}\right)$

Which of the following is not a function?

The values of 'm' for which $(m-2)x^2+8x+(m+4)$ > 0 $\forall$ x $ϵ$ R, are

If $A$ is a symmetric matrix and $B$ is a skew- symmetrix matrix such that $A+B=\left[\begin{array}{cc}2& 3\\ 5& -1\end{array}\right],$ then $AB$ is equal to :

The true set of values of $a$ for which the inequality $\underset{a}{\overset{0}{\int }}(3^{-2x}-2\cdot 3^{-x})dx\ge 0$ is true, is

If line $y=2x+\frac{1}{4}$ is tangent to $y^2=4ax$ then a is equal to