Explore topic-wise InterviewSolutions in Current Affairs.

The value of ${\int }_2^3\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}.dx$ is equal to

Prove that:

${(cos\alpha +cos\beta )}^2+{(sin\alpha +sin\beta )}^2=4co{s}^2\left(\frac{\alpha -\beta }{2}\right)$

If the coefficients of (2r+1)th term and (r+2)th terms in the expansion of $(1+x{)}^{43}$ are equal, find r.

If $cos(A+B)sin(C-D)=cos(A-B)sin(C+D),provethattanAtanBtanC+tanD=0$

Find the equation of the circle having (1, -2) as its centre and passing through the intersection of the lines 3x + y = 14, and 2x + 5y = 18.

If $f\left(x\right)=(x-a{)}^2(x-b{)}^2$, find $f(a+b)$.

In any $\Delta$ ABC, $2R^2$ sin A sin B sin C is equal to

Two cards are drawn one by one without replacement from a pack of $52$ cards. The probability that the second card is of higher rank than the first card is
(rank in increasing order can be taken from ace to king)

If $19$th term of a non-zero A.P. is zero, then its ($49$th term) : ($29$th term) is :

The cofficient of $x^9$ in the polynomial given by $\sum _{r=1}^{11}(x+r)(x+r+1)(x+r+2).......(x+r+9)$ is

Given that x and y are in inverse proportion, and $y_1$, $y_2$ are values of y corresponding to the values x1, x2 of x respectively. Which of the following is correct?

If $tan\theta =-\frac{1}{\sqrt{5}}$ and $\theta$ lies in the IV quadrant, then the value of $cos\theta$ is

$\int e^x{\left(\frac{1-x}{1+x^2}\right)}^2$dx

If $A{P}^2-B{P}^2=18$, where A ≡ (1, 2, –3) and B ≡ (3, –2, 1). Then the locus of point P is

A manufacturer has $600$ liters of an $12\%$ acid solution. The number of liters of a $30\%$ acid solution to be added to it so that acid content in the resulting mixture will be more than $15\%$ but less $18\%$ is in the interval

If for a real number $y,\left[y\right]$ is the greatest integer less than or equal to $y$, then value of the integral $\underset{\frac{\pi }{2}}{\overset{\frac{3\pi }{2}}{\int }}\left[2\sin x\right]dx$, is

The shaded region shown in fig. is given by the inequation

If the integral of the function $\sin \left(80x\right){\sin }^{78}x$ is $\frac{\sin ax{\sin }^{b}x}{c}+D,$ where $a,b,c\in R$ and $D$ is the constant of integration, then the value of $a+b+c$ is equal to

A man takes a step forward with probability $0.3$ and backwards with probability $\mathrm{0.7.}$ Then the probability that at the end of $15$th step, he is one step away from the starting point is ${}^{15}{C}_a\times b^a.$ The value of $a+100b$ is

If the line $y=b$ divides the region bounded by the curves $y=x^2$ and $y=9$ into regions of equal area, then the value of $b$ is

If A is a square matrix such that $A(Adj.A)=\left[\begin{array}{ccc}4& 0& 0\\ 0& 4& 0\\ 0& 0& 4\end{array}\right],$ then $\frac{|adj(adj.A)|}{|adj.A|}$ is equal to

If the circles $x^2+y^2-4x-6y-12=0$ and $5(x^2+y^2)-8x-14y-32=0$ touch each other then their point of contact is

Write the following in the simplest form,

$ta{n}^{-1}\left(\sqrt{\frac{1-cosx}{1+cosx}}\right),x<\pi$

$\sqrt{5}$ is a/an ___ number

|sin x| is not differentiable at the points

$y=co{s}^{-1}\left(\frac{sinx+cosx}{\sqrt{2}}\right),-\frac{\pi }{4}<x<\frac{\pi }{4}$

Find $\frac{dy}{dx}$

Choose the correct answer in the following question:
The point on the curve $9y^2=x^3$, where the normal to the curve makes equal intercepts with the axes is

(a) $(4,\pm \frac{8}{3})$ (b) $(4,\frac{-8}{3})$
(c) $(4,\pm \frac{3}{8})$ (d) $(\pm 4,\frac{3}{8})$

If angle theta is equal to 45 degrees can we substitute the value and continue with our solution

If the standard deviation of the numbers $2,3,a,$ and $11$ is $3.5,$ then which of the following is true

Let $E$ denote the set of letters of the English alphabet, $V=\{a,e,i,o,u\}$, and $C$ be the complement of $V$ in $E$. Then, the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

|x-2| + |x-3| =1 Solve

Let a function be f(x)=0

This will be the equation of the x axis

Integral of f(x) will be the area under the curve f(x) and the x axis. Since f(x) and x axis coincide , area under them will be 0. But antiderivative of 0 is a constant. ( derivative of a constant is 0 so anti derivative of 0 is a constant)

Is there something wrong in the in this statement? Is yes , give reason, if no give reason

Out of 6 objects n are of one type and the rest are diff type each. If the total number of arrangements of these objects is equal to 30, what is the value of n?

If a line in the ZX-plane makes an angle 30^o with Z-axis, the direction cosines of this line are:

The sum of the sigits in the unit place of all numbers formed with the help of 3,4,5,6 taken all at a time is

For the equation $3x^2+px+3=0$ , p > 0, if one root is the square of the other then value of P is

The solution of the initial value problem e^dy/dx = x + 1, y(0) = 3 is:

The number of values of $\theta$ in the interval $(-\frac{\pi }{2},\frac{\pi }{2})$ such that $\theta \ne \frac{n\pi }{5}forn=0,\pm 1,\pm 2$ and $tan\theta =cot5\theta$ as well as $sin2\theta =cos4\theta$ is___

The number of real solutions of the equation $x^2+3|x|+2$ =0 is:

If in a $△ABC,si{n}^{3}A+si{n}^{3}B+si{n}^{3}C=3sinAsinBsinC$ then the value of the determinant
$\left[\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right]$ is

The Second Derivative Test for finding local maxima, local minima fails if

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three unit vectors such that $\overrightarrow{a}\cdot \overrightarrow{b}=\overrightarrow{a}\cdot \overrightarrow{c}=0$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi }{3},$ then the value of $|\overrightarrow{a}\times \overrightarrow{b}-\overrightarrow{a}\times \overrightarrow{c}|$ is

If $\tan \theta +\sin \theta =m$ and $\tan \theta -\sin \theta =n,$ then which of the following relation between $m,n$ is correct?

The general solution of the equation $\tan 5\theta =\cot 3\theta$ is given by