Explore topic-wise InterviewSolutions in Current Affairs.

find the distance between the planes 2x-y+2z=5 and 5x-2.5y+5z=20.

The solution of $(x^2+y^2)dx=2xydy$ is

(where $c$ is integration constant)

If

$\int \frac{5\tan x}{\tan x-2}dx=x+a\ln |\sin x-2\cos x|+k$

then $a$ is equal to

The equation of the reflection of the hyperbola $\frac{(x-4{)}^2}{16}-\frac{(y-3{)}^2}{9}=1$ about the line $x+y-2=0$ is

Let $f:(4,6)\to (6,8)$ be defined by $f\left(x\right)=x+\left[\frac{x}{2}\right]$, where $[.]$ represents the greatest integer function. Then the range of $f$ is

The graph of $y=x\ln x$ is

The ratio of maximum and minimum magnitudes of the resultant of two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ is 3 : 1. Now , $|\overrightarrow{a}|$ is equal to :

The value(s) of $\left[c\right]$ for which the line $y=4x+c$ touches the curve $x^2+16y^2=16$ is/are (where $[.]$ represents greatest integer function)

Let E and F be two independent events. The probability that exactly one of them occurs is $\frac{11}{25}$ and the probability of none of them occurring is $\frac{2}{25}$. If P(T) denotes the probability of occurrence of the event T, then

The probability that a certain beginner at golf gets good shot if he uses the correct club is $\frac{1}{3}$, and the probability of a good shot with an incorrect club is $\frac{1}{4}$. In his bag there are 5 different clubs only one of which is correct for the shot. If the chooses a club at random and takes a stroke, the probability that he gets a good shot is:

The coordinate of the point on y^2 =8x which is closest from x^2 +(y+6)^2 =1 is

Let $\overrightarrow{a}=2\hat{i}+2\hat{j}+\hat{k}$ and $\overrightarrow{b}$ be another vector such that $\overrightarrow{a}\cdot \overrightarrow{b}=14$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+\hat{j}-8\hat{k}$ then the vector $\overrightarrow{b}$ is equal to

Range of the function ${\log }_{0.5}(x^4-2x^2+3)$ is

In a triangle $ABC,\frac{\cos C+\cos A}{c+a}+\frac{\cos B}{b}=$

If the median of $\Delta ABC$ through $A$ is perpendicular to $AB$ then

The value of ${\log }_{\text{cosec}\pi /4}|\cos 2019\pi |$ is

The foot of the perpendicular drawn from the origin, on the line, $3x+y=\lambda (\lambda \ne 0)$ is $P$. If the line meets $x$-axis at $A$ and $y$-axis at $B$, then the ratio $BP:PA$ is :

Find the probability distribution of

number of tails in the simultaneous tosses of three coins

Find the difference in fractions of filled pieces of both below given shapes in its lowest form?

(blue color represents the filled part)

The angle between a pair of tangents drawn from a point P to the circle $x^2+y^2+4x-6y+9si{n}^2\alpha +13co{s}^2\alpha =0is2\alpha$. The equation of the locus of the point P is

A surface $S(x,y)=2x+5y-3$ is integrated once over a path consisting of the points that satissfy $(x+1{)}^2+(y-1{)}^2=\sqrt{2}$. The integral evaluates to

If for a binomial distribution, $\mu =10$ and ${\sigma }^2=5,$ then $P(X>6)$ is

Let $ABC$ be a triangle with sides $a,b,c$ and corresponding angles $A,B,C$ respectively. If angle $A=3B$, then $(a^2-b^2)(a-b)$ is equal to

If an unbiased coin is tossed and two fair dice are rolled at the same time, then what is the probability that head is the outcome and sum of the numbers on the dice is 9?

The normal
at the point (1, 1) on the curve 2y + x² = 3
is

(A) x
+ y = 0 (B) x − y = 0

(C) x
+ y + 1 = 0 (D) x − y = 1

The function $y=f\left(x\right)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^4+2x}{\sqrt{1-x^2}}$ in (-1, 1) satisfying f(0) =0. Then ${\int }_{\frac{-\sqrt{3}}{2}}^{\frac{\sqrt{3}}{2}}f\left(x\right)d\left(x\right)$ is

Let $a_1,a_2,a_3......$ are in G.P and let ${\sum }_{n=1}^{100}{a}_{2n}=\alpha$ and ${\sum }_{n=1}^{100}{\alpha }_{2n-1}=\beta$, such that $\alpha \ne \beta$, then the common ratio is

Find the sum of the following series:
(i) 2 + 5 + 8 + .... + 182
(ii) 101 + 99 + 97 + .... + 47
(iii) $(a-b{)}^2+(a^2+b^2)+(a+b{)}^2+\dots \dots +\left[\right(a+b{)}^2+6ab]$

If roots $\alpha ,\beta$ of the equations $x^2-px+16=0$ satisfy the relation ${\alpha }^2+{\beta }^2=9$, then write the value of P.

Prove the following:

$\text{cos}(\frac{\pi }{4}-x)\text{cos}(\frac{\pi }{4}-y)$$\text{-}sin(\frac{\pi }{4}-x)\text{sin}(\frac{\pi }{4}-y)$ = sin (x+y)

If $tan\theta =x-\frac{1}{4x}$, then sec \theta-tan \theta is equal to

f(x) = sin(x) defined on f: $[\frac{-\pi }{2},\frac{\pi }{2}]$ $\to$ $[-1,1]$ is -

Tangents are drawn to the circle $x^2+y^2=50$ from a point $P$ lying on the $x-$axis. These tangents meet the $y-$axis at points $P_1$ and $P_2$. Possible coordinates of $P$ so that area of $△P{P}_1{P}_2$ is minimum, are