Explore topic-wise InterviewSolutions in Current Affairs.

For $x>0,$ which of the following is correct

Show that
if
f and g are defined as
and

Show that the line $\frac{x}{a}+\frac{y}{b}=1$ touches the curve y = $b.e^{-\frac{x}{a}}$ at the point where the curve intersects the axis of Y.

The range of $f\left(x\right)=2x^2-3x+2$ if $x\in [0,2]$ is

If Q gets fewer coins than R, then which one of the following is not necessarily true?

The numbers $1,2,\mathrm{3....},n$ are arranged in random order. The probability that the digits $1,2,\mathrm{3.....},k(k<n)$ appear as neighbours in that order is

A line through $P(3,4)$ cuts the lines $x=6$ and $y=8$ at $L$ and $M$ respectively. $Q$ is a variable point on the line such that $\frac{1}{PQ}=\frac{1}{PL}+\frac{1}{PM}$ then the locus of $Q$ is

The expression $\sim (\sim p\to q)$ is logically equivalent to :

${lim}_{x\to 0}\frac{2sin{x}^{\circ }-sin2x^{\circ }}{x^3}$

Consider the system of linear equations

$-x+y+2z=0$

$3x-ay+5z=1$

$2x-2y-az=7$

Let $S_1$ be the set of all $a\in R$ for which system is inconsistent and $S_2$ be the set of all $a\in R$ for which the system has infinitely many solutions. If $n\left(S_1\right)$ and $n\left(S_2\right)$ denote the number of elements in $S_1$ and $S_2$ respectively, then

Find the equation of the circle whose centre is (3, -1) and which cut-off an intercept of length 6 from the line $2x-5y+18=0$.

Let $f:R\to R:f\left(x\right)=x^2$ and $g:R\to R:g\left(x\right)=2x+1$. Find

(i) $(f+g)\left(x\right)$

(ii) $(f-g)\left(x\right)$

(iii) $\left(fg\right)\left(x\right)$

(iv) $\left(\frac{f}{g}\right)\left(x\right)$

The number of words that can be formed by the letters of $SOURCE$ is

If a tangent is drawn to the parabola $y^2=4x$ through the point $(-2,1)$ then the points of contact is/are

A curve is represented parametrically by $x=t+e^{at}$ and $y=-t+e^{at},t\in R$ and $a>0$. Then, the curve touches the $x-$ axis at

Exhaustive values of $x$ satisfying the equation $|x^4-x^2-12|=|x^4-9|-|x^2+3|$ is -

A fair coin is tossed $100$ times. The probability of getting tails $1,3,....49$ times is

If $a_0,a_1,a_2,............,a_{n-1}$ are nth roots of unity, then $a_k$ = cos $\frac{2k\pi }{n}$ + i sin $\frac{2k\pi }{n}$ where $0\le k\le n-1$.

Also then Value of $2^{n-1}$sin$\left(\frac{\pi }{n}\right)$sin$\left(\frac{2\pi }{n}\right)$.........sin$\left(\frac{n-1}{n}\pi \right)$is

In a class of 100 students, 12 students drink only milk and 5 students drink only coffee and 8 students drink only Tea. Other report says 30 students take both coffee and tea, 25 students take milk and tea and 20 students take only milk and coffee. 10 students drink all the three. Find the number of students who do not drink anything.

The equation of the ellipse whose extremities of minor axis are $(3,1)$ and $(3,5)$ and eccentricity is $\frac{1}{2},$ is

If $A\times B\subseteq C\times D\text{and}A\times B\ne \varphi$, then which of the following is/are must be true?

If P is a point on the hyperbola $16x^2-9y^2=144$ whose foci are $S_{1}and{S}_2,thenP{S}_1\sim P{S}_2=$

In $\Delta ABC,$ if $a=7,b=8,c=9,$ then the distance (in units) from the vertex $B$ to the centroid is

If the vector $\overrightarrow{b}$ is collinear with $\overrightarrow{a}=(2\sqrt{2},-1,4)$ and $|\overrightarrow{b}|=10,$ then

The value of $\tan \left(\frac{11\pi }{12}\right)$ is

For any two sets A and B, $A\cap (A\cup B)=$

Write the area of the triangle formed by the coordinate axes and the line $sec\theta -tan\theta )x+(sec\theta +tan\theta )y=2.$

Length of the interval $(-3,-2)$ is