Explore topic-wise InterviewSolutions in Current Affairs.

Set of values of $a$ for which both the roots of the quadratic polynomial $f\left(x\right)=a{x}^2+(a-3)x+1$ lie on one side of the $y-$axis is

The equation of the circle passing through three points $(1,0),$ $(-1,0)$ and $(0,1),$ is

If 5 P(4,n)= 6 P (5,n-1), find n.

If $25$ blankets are distributed among $5$ persons then the probability that each person gets odd number of blankets is

The
coefficients of the (r
– 1)^th,
r^th
and (r +
1)^th
terms in the expansion of

(x
+ 1)ⁿ
are in the ratio 1:3:5. Find n
and r.

The co-ordinates of the point on y-axis which is equidistant from the points A(3, 1) and B(1, 5) is:

If $\int \frac{{\sin }^{3}x}{{\cos }^{5}x}dx=\frac{\left(f\right(x){)}^4}{4}+C$ and $\int \left(f\right(x){)}^{5}dx=\frac{\left(f\right(x){)}^4}{4}-\frac{\left(f\right(x){)}^2}{2}+\ln |g(x)|,$ then $g\left(\frac{\pi }{3}\right)=$

(where $C$ is integration constant)

$\begin{array}{ccc}\text{Function}& \text{Domain}& \text{Range}\\ \text{(i) sinx}& \text{(P) R}& \text{(L) [-1, 1]}\\ \text{(ii) cos x}& \text{(Q) R-n}\pi & \text{(M) R}\\ \text{(iii) tan x}& \text{(R) R- {(2n+1)}}& \text{(N)}(-\infty ,\text{-1]}\cup \text{[1,}\infty )\\ \text{(iv) cosec x}& & \\ \text{(v) sec x}& & \\ \text{(vi) cot x}& & \end{array}$

How many of the following are matched correct?

(i) -P-L, (ii) -P-L, (iii)-R-M, (iv) -Q-N, (v) -R-N, (vi) -Q-M

If $f\left(x\right)=sin\left\{\right[x+5]+\{x-\{x-\{x\left\}\right\}\left\}\right\}$ for $xϵ(0,\frac{\pi }{4})$ is invertible, where {.} and [.] represent fractional part and greatest integer functions respectively, then $f^{-1}\left(x\right)$ is

Let $f\left(x\right)=x+\ln x-x\ln xx\in (0,\infty )$

${\int }_0^2\left(\right[x{]}^2-\left[x^2\right])dx$ is equal to

Integrate the rational functions.
$\int \frac{x^3+x+1}{x^2-1}dx.$

If $\alpha$ is a root of equation $(2\sin x-\cos x)(1+\cos x)={\sin }^{2}x$, $\beta$ is a root of equation $3{\cos }^{2}x-10\cos x+3=0$ and $\gamma$ is a root of equation $1-\sin 2x=\cos x-\sin x;0\le \alpha ,\beta ,\gamma \le \frac{\pi }{2},$ then $\sin \alpha +\sin \beta +\sin \gamma$ can be equal to

If $sec\theta +tan\theta =k,cos\theta =$

There are 3 bags which are known to contain 2 white and 3 black, 4 white and 1 black, and 3 white and 7 black balls, respectively. A ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black ball is

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5

State true or false: (give reason for your answer)

(i) A and B are mutually exclusive

(ii) A and B are mutually exclusive and exhaustive

(iii)

(iv) A and C are mutually exclusive

(v) A and are mutually exclusive

(vi) are mutually exclusive and exhaustive.

The real solutions of $|x^2+4x+3|+2x+5=0$ is/are

For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the $\text{1st}$ exam is $p$. If he fails in one of the exams, then the probabiliy of his passing in the next exam is $\frac{p}{2}$, otherwise it remains the same. Then the probability that he will qualify, is

Choose the correct multiplication equation for these daisy flowers.

Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane.

If $xcos\theta =ycos(\theta +\frac{2\pi }{3})=zcos(\theta +\frac{4\pi }{3})$, prove that $xy+yz+zx=0$

If $f\left(x\right)=2\left[x\right]+\cos ([-\pi ]x)$, where $[.]$ represents greatest integer function, then

Find
the matrix X
so that

Possible integral value(s) of m for the equation $sinx-\sqrt{3}cosx=\frac{4m-6}{4-m}$ can be valid for some $xϵ[0,2\pi ]$, is

Evaluate: ${\int }_0^{\frac{\pi }{2}}\frac{si{n}^{2}x}{sinx+cosx}dx.$

OR

Evaluate: ${\int }_{-1}^2(e^{3x}+7x-5)dx$ as a limit of sums.

Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3,3) and directrix is 3x-4y=2.Find also the length of the latus-rectum.

The local bus service has $2$ lines of buses that start together at $8\text{a.m.}$ Buses on line A leave after every $20$ minutes while Buses on line B leave after every $15$ minutes. In a day, how many times do buses on both line A and B leave together between $7\text{a.m.}$ and $10\text{p.m.}$?​

The equation of the line(s) passing through the intersection of the lines $4x-3y-1=0$ and $2x-5y+3=0$ and equally inclined to the axis is/are

The $n^{\text{th}}$ term in the expansion of ${\log }_e\left(\frac{4}{3}\right)$ is

For what values of x does the absolute value of x-1 equals to 2?

The equation of the plane passing through the lines $\frac{x-4}{1}=\frac{y-3}{1}=\frac{z-2}{2}$ and $\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5},$ is

Write the sum of the series : $1^2-2^2+3^2-4^2+5^2-6^2+...+(2n-1{)}^2-(2n{)}^2$

Median of Mode, Mean, Median of data 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5 is