Explore topic-wise InterviewSolutions in Current Affairs.

Show that the given differential equation is homogeneous and then solve it.

$x^2\frac{dy}{dx}=x^2-2y^2+xy$

Integrate the following functions w.r.t. x.

$\int \frac{1}{x\sqrt{ax-x^2}}dx$

If $\frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y+i}{3-i}=i$, then values of $x$ and $y$ are

In a group of 500 persons, 300 take tea, 150 take coffee, 250 take cold drinks, 90 take tea and coffee, 110 take tea and cold drinks, 80 take coffee and cold drink, 30 none of them. Find the no. of persons who take all the three drinks.

Four identical condensers each of capacity of 6 $\mu$ F are connected in the form of a square. Across one of the diagonals of the square a condenser of capacity 3 $\mu$ F is connected. The resultant capacitance of the combination across that diagonal will be

Set of values of $\alpha$ for which the point $(\alpha ,1)$ lies inside the curves $c_1:x^2+y^2-4=0$ and $c_2:y^2=4x$ is

For $2\le r\le n,\left(\begin{array}{c}n\\ r\end{array}\right)+2\left(\begin{array}{c}n\\ r-1\end{array}\right)+\left(\begin{array}{c}n\\ r-2\end{array}\right)$ is equal to

In the solution to this question the total number of outcomes is given as 3^12 , but since the balls are identical won't there be many repetations. I feel the total number of outcomes should be 14C2 using the dash and ball method

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Value of the definite integral ${\int }_{-3}^1\left(2\right(t+1{)}^5-5(t+1{)}^3+t+3)dt$ is equal to -

The area between the parabolas $y^2=4ax,x^2=4ay$ is

Find the value of ' a ' and ' b ' if 5+2√3 / 7+4√3 = a+b√3

The sum to infinite terms of the series $cose{c}^{-1}\sqrt{10}+cose{c}^{-1}\sqrt{50}+cose{c}^{-1}\sqrt{170}+......+cose{c}^{-1}\sqrt{(n^2+1)(n^2+2n+2)}$ is

Let A be the set of first ten natural numbers and let R be a relation in A defined by (x, y) $ϵ$ R is and only if x + 2y = 10. Which of the following is false?

Number of positive integral solutions of the equation $xyz=90$ is

If the quadratic expression
$a{x}^2+(a-2+3^{\sqrt{{\log }_{3}5}}-5^{\sqrt{{\log }_{5}3}})x+(5^{{\log }_{5}3}-3^{{\log }_{3}5})$ is negative for exactly two integral values of $x$, then the possible value(s) of $a$ is/are

$Ify=co{s}^{-1}\left(\frac{1-x^2}{1+x^2}\right),0<x<1,then\frac{dy}{dx}=$

The sum of an infinite geometric series is $512$ and sum of first $n$ terms is $510$ ($n>1$) . If the inverse of its common ratio is an integer then which of this following can not be the second term of the series?

The length of latus rectum of parabola $4y^2+3x+3y+1=0$ is

How to geometrically prove that $\cos (x+y)=\cos x\cos y-\sin x\sin y$

If A, B, C are points (1, 0, 4) (0, -1, 5) and (2, -3, 1) respectively, then the coordinates of the foot of the perpendicular drawn from A to the line BC are

The function f (x) = x³ – 8 on [1, 2] is

Let $z_1$ and $z_2$ be roots of the equation $z^2+pz+q=0$ where the coefficients $p$ and $q$ may be complex numbers. Let $A$ and $B$ represent $z_1$ and $z_2$ in the complex plane, If $\angle AOB=\theta \ne 0$ and $OA=OB$ where $O$ is the origin, then $p^2$ is

If $\omega \ne 1$ is a cube root of unity and $\left|\begin{array}{ccc}x+{\omega }^2& \omega & 1\\ \omega & {\omega }^2& 1+x\\ 1& x+\omega & {\omega }^2\end{array}\right|=0$, then value of x is

The number of straight lines joining 8 points on a circle is______.

If the distance between the points P(a, 2, 1) and Q (1, -1, .1) is 5 units, find the value of a.

Find the geometric means of the following pairs of numbers.

(i) 2 and 8

(ii) $a^{3}b$ and $a{b}^3$

(iii) - 8 and - 2

For a system of Linear Equations to have infinite solutions , the ratio of the coefficients in standard form of ax + by + c= 0 must be

Total number of $6$ digit numbers that can be formed, having the property that every succeeding digit is greater than the preceding digit, is equal to

X, Y and Z are partners dealing in manufacturing paper bags. They share profits and losses in the ratio of 5 : 3 : 2. They admitted S for $\frac{2}{10}$th share. S is a single parent (Mother) of a girl child. On the admission of S, Z declared that he does not want to change his profit share and wants to retain his original share. Find out the new profit sharing ratio of X, Y and Z.

If $(1+x)(1+x^2)(1+x^4)\dots (1+x^{128})=\sum _{r=0}^n{x}^r,$ then $n$ is equal to

If $A,$ $B$ and $C$ are the angles of a non-right angled triangle $ABC,$ then the value of $\left|\begin{array}{ccc}\tan A& 1& 1\\ 1& \tan B& 1\\ 1& 1& \tan C\end{array}\right|$ is equal to

Sum of n terms of the series $\sqrt{2}+\sqrt{8}+\sqrt{32}+...$ is

If $P$ is a point on the parabola $y=x^2+4$ which is closest to the straight line $y=4x-1,$ then the co-ordinates of $P$ are

If $\int$$\frac{{sec}^{2}x-2010}{{sin}^{2010}x}$ dx = $\frac{f\left(x\right)}{{sin}^{2010}x}$ + c, then f ($\frac{\pi }{3}$) =

(1+tan²A) (1+1/tan²A) = 1/sin²A-sin⁴A

If $\int \frac{3+2\cos x}{(2+3\cos x{)}^2}dx=\frac{f\left(x\right)}{2+3\cos x}+C$, where $C$ is a constant of integration, then $f\left(x\right)$ is

Each morning, John jogs at 6 miles per hour and rides a bike at 12 miles per hour. His goal is to jog and ride his bike a total of at least 9 miles in less than 1 hour. If John jogs j miles and rides his bike b miles, which of the following systems of inequalities represents John’s goal?

If $A$ and $B$ are two matrices such that $AB=B$ and $BA=A$, then $A^2+B^2$ equals