Explore topic-wise InterviewSolutions in Current Affairs.

If $\Phi \left(x\right)=\int \frac{dx}{si{n}^{\frac{1}{2}}xco{s}^{\frac{7}{2}}x}$, then $\Phi \left(\frac{\pi }{4}\right)-\Phi \left(0\right)=$

Solution of the differential equation $\frac{dy}{dx}=\frac{x^{2}y}{x^3+y^3}$ is:

(where $C$ is integration constant)

Let $\alpha ,\beta ,\gamma$ be the roots of the equation $x^3-12x^2+44x-48=0.$ If the coordinates of the vertices of a triangle are $A(\alpha ,\frac{1}{\alpha }),$ $B(\beta ,\frac{1}{\beta })$ and $C(\gamma ,\frac{1}{\gamma }),$ then the centroid of the $△ABC$ is

In a circle with centre $O$, suppose $A,P,B$ are three points on its circumference such that $P$ is the mid-point of minor arc $AB$. Suppose when $\angle AOB=\theta$,
$\frac{\text{area}\left(△AOB\right)}{\text{area}\left(△APB\right)}=\sqrt{5}+2,$
If $\angle AOB$ is doubled to $2\theta$, then the ratio is $\frac{\text{area}\left(△AOB\right)}{\text{area}\left(△APB\right)}$ is

The value of the integral $\underset{0}{\overset{\infty }{\int }}\frac{\ln x}{x^2+2x+4}dx$ is equal to

If the coefficient of $x^7$ in $(a{x}^2+\frac{1}{bx}{)}^{11}$ is equal to the coefficient of $x^{-7}$ in $(ax-\frac{1}{b{x}^2}{)}^{11}$, then ab =

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (x² + 1) cos x

Which of the following transformations in order will give $-|(-x)+3|$ from $|x|$?

(1) $f\left(x\right)\to f(-x)$

(2) $f\left(x\right)\to f(x+3)$

(3) $f\left(x\right)\to -f\left(x\right)$

(4) $f\left(x\right)\to f(x-3)$

The coefficient of $x^{53}$ in ${\sum }_{r=0}^{100}{}^{100}{C}_r(x-3{)}^{100-r}{2}^r$ is

Find all points of discontinuity of f,
where f is
defined by

Find the equation of the line on which the length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is ${30}^{\circ }.$

Let $f\left(x\right)=x^2-6x+5$ and $m$ is the number of points of non-derivability of $y=|f\left(|x|\right)|.$ If $|f\left(|x|\right)|=k,k\in R$ has at least $m$ distinct solution(s), then the number of integral values of $k$ is

Let $z$ be a complex number such that $|z|=z+32-24i$. Then $Re\left(z\right)+Im\left(z\right)$ is equal to

Sarah has $6$ apples. If Sarah gives $2$ apples to her friend James, how many apples does Sarah have?

Consider the following arguments.



$S_1:\left\{\right(A\vee B\sim C),(\sim B\to (\sim A\vee C)\left)\right\}\Rightarrow B$



$S_2:\{\sim B\to (P\leftrightarrow R),R\to \sim B,P\to \sim R\}$



Which of the following is true?

Question 4 (xv)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(xv) $1^2,5^2,7^2,73,\dots$

The point of intersection of the tengents to the parabola $y^2=4x$ at the points, where the parameter 't' has the value 1 and 2, is

The probability of happening of two events A and B are 0.25 and 0.50 respectively. If the probability of happening of A and B together is 0.14, then probability that neither A nor B happens is

The number of ordered triples (a,b,c) of positive integers which satisfy the simultaneous equations ab + bc = 44 and ac + bc = 23 is

Which of the following functions are monotonically decreasing functions ?

The value(s) of $x,$ which satisfy the equation $|x-2{|}^2+|x-2|-2=0$ is/are

Two numbers ‘a’ & ‘b’ are chosen from the set of {1,2,3……3n}. In how many ways can these integers be selected such that $a^2-b^2$ is divisible by 3

If $A=\{1,3,5\},B=\{2,4,6\},C=\{1,4\}$ then which of the following is universal set?

A rectangle ABCD, A = (0,0), B = (4, 0), C = (4, 2), D = (0, 2) undergoes the following transformations successively.

(i) $f_1(x,y)\to (y,x)$

(ii) $f_2(x,y)\to (x+3y,y)$

(iii) $f_3(x,y)\to (\frac{x-y}{2},\frac{x+y}{2})$

The final figure will be

If $\int \frac{\tan x}{\sec x+\tan x}dx=I+x+c$ where $c$ is an arbitary constant, then the value of $I$ is

Both the roots of x² - 63x + k = 0 are prime numbers. Then the sum of the digits of k is

If a,b,c be in A.P. and b,c,d be in H.P., then

A point P lies on the line y = 2x in the first quadrant. Another point Q lies on the line y = 3x in the first quadrant. Suppose QP is perpendicular to the line y = 2x and QP = 5. The distance of P from the origin is:

The number of ways in which the time table for Monday can be made if there must be $5$ lessons to be taught that day (Algebra, Geometry, Calculus, Trigonometry, Vector) and topics Algebra and Geometry cannot immediately follow each other are