Explore topic-wise InterviewSolutions in Current Affairs.

For some $\alpha ϵR,$ if $\frac{\alpha -x}{px}=\frac{\alpha -y}{qy}=\frac{\alpha -z}{rz}$ and p,q,r are in A.P., then

For the differential equation $xy\frac{dy}{dx}=(x+2)(y+2),$ find the equation of the curve passing through the point (1, -1).

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)

Find the equation of
the circle passing through the points (4, 1) and (6, 5) and whose
centre is on the line 4x + y = 16.

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition) ?

Suppose that the three quadratic equations $a{x}^2-2bx+c=0,$ $b{x}^2-2cx+a=0$ and $c{x}^2-2ax+b=0$ all have only positive roots. Then $a^3+b^3+c^3$ is equal to

lf $I_1=\underset{0}{\overset{1}{\int }}{2}^{x^2}dx,I_2=\underset{0}{\overset{1}{\int }}{2}^{x^3}dx,I_3=\underset{1}{\overset{2}{\int }}{2}^{x^2}dx$ and $I_4=\underset{1}{\overset{2}{\int }}{2}^{x^3}dx$ then which of the following is/are TRUE?

If the value of the integral $\underset{0}{\overset{5}{\int }}\frac{x+\left[x\right]}{e^{x-\left[x\right]}}dx=\alpha e^{-1}+\beta ,$ where $\alpha ,\beta \in R,5\alpha +6\beta =0,$ and $\left[x\right]$ denotes the greatest integer less than or equal to $x;$ then the value of $(\alpha +\beta {)}^2$ is equal to:

Evaluate

Using the
property of determinants and without expanding, prove that:

If one of the diameters of the circle, given by the equation, $x^2+y^2-4x+6y-12=0$, is a chord of a circle S, whose centre is at (–3, 2), then the radius of S is:

If the equation $x^3+px+q=0(p<0)$ has three distinct real roots, then

If $a,b,c>0,a^2=bc$ and a + b + c = abc, then least value of $a^4+a^2+7$ is $‘{\alpha }^{\prime }$, the value of $\alpha -16$ is___

1. 3

   
   

If $f\left(x\right)$ is an even function and satisfies the relation $x^{2}f\left(x\right)-2f\left(\frac{1}{x}\right)=g\left(x\right),$ where $g\left(x\right)$ is an odd function, then $f\left(5\right)$ equals

Define a continuity of a function of a point.find all the points of discontinuity of defined f (x)=|x|-|x-1|

If $A_1,A_2,...A_n$ are vertices of regulr polygen of $n$ sides, inscribed in circle of radius $r$, whose cnetre is origin $O$, any $P$ is any point on the $arc{A}_n,A_1$ such that $\angle PO{A}_1=\theta$. The value of sum of lenghts of the lines joining $P$ to the angluar points of the polygen is

Let $(x,y)\in Q_1,2x\le y$ be such that

${\sin }^{-1}\left(ax\right)+{\cos }^{-1}\left(y\right)+{\cos }^{-1}\left(bxy\right)=\frac{\pi }{2}.$

Match the statements in Column I with the locus in Column II.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \left(A\right)& \text{If}a=1\text{and}b=0,\text{then}(x,y)& \left(p\right)& \text{lies on part of the circle}{x}^2+y^2=1\\ \left(B\right)& \text{If}a=1\text{and}b=1,\text{then}(x,y)& \left(q\right)& \text{lies on part of the curve represented by}(x^2-1)(y^2-1)=0\\ \left(C\right)& \text{If}a=1\text{and}b=2,\text{then}(x,y)& \left(r\right)& \text{lies on part of the line}y=x\\ \left(D\right)& \text{If}a=2\text{and}b=2,\text{then}(x,y)& \left(s\right)& \text{lies on part of the curve represented by}(4x^2-1)(y^2-1)=0\end{array}$

The domain of the function $f\left(x\right)=\sqrt{({\log }_{0.2}x{)}^3+({\log }_{0.2}{x}^3\left)\right({\log }_{0.2}0.0016x)+36}$ is

If $f^{\prime }\left(x\right)=\frac{1}{1+x^2}$ for all $x$ and $f\left(0\right)=0,$ then

In the expansion of ${(3^{5x/4}+3^{-x/4})}^n$ the sum of binomial coefficient is $64$. If the term with greatest binomial coefficient exceeds the third term by $(n-1),$ then the number of value(s) of $x$ is

The locus of the point, the chord of contact of tangents from which to the circle $x^2+y^2=a^2$ subtends a right angle at the centre is a circle of radius

If $(1+x{)}^n=C_0+C_{1}x+\cdots +C_n{x}^n,$ then the value of $\sum _{r=0}^n\sum _{s=0}^n{C}_r{C}_s$ is equal to

1. 4

The minimum value of $3sin\theta +4cos\theta$ is