Explore topic-wise InterviewSolutions in Current Affairs.

Show that the line through the points (1, -1, 2), (3, 4, -2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

The transverse axis of a hyperbola is double the conjugate axes. Whats the eccentricity of the hyperbola

Find the equation of a circle with centre (h, k) and touching both the axes.

What's the equation of tangent on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ at the point $(4\sqrt{2},3)?$

If $2\le x\le 9,$ then $x$ can be represented on the number line by

If ${\overline{x}}_1$ and ${\overline{x}}_2$ are the means of two distributions such that ${\overline{x}}_1<{\overline{x}}_2$ and $\overline{x}$ is the mean of the combined distribution, then

Tangent is drawn to ellipse $\frac{x^2}{27}+y^2=1at$
$(3\sqrt{3}cos\theta ,sin\theta )$ $(where,\theta \in (0,\frac{\pi }{2}))$.
Then, the value of $\theta$ such that the sum of intercepts on axes made by this tangent is minimum, is

A coin is tossed twice. If the second throw results in a tail, a die is thrown. Deseri the sample space for this experiment.

If the axes are shifted to $(-2,-3)$ and then rotated through $\frac{\pi }{4}$ in anticlockwise direction, then transformed equation of $x^2-y^2+2x+4y=0$ is

Column - 1 contains definitions of various functions f(x) in terms of real parameter 'a'.

Column - 2 contains information about the coefficient of $x^2$ in the binomial expansion of f(x) for small numerical values of x.

Column - 3 contains the corresponding value of 'a'.

$\begin{array}{cccccc}& \text{Column 1}& & \text{Column 2}& & \text{Column 3}\\ \text{(I)}& f\left(x\right)=\frac{a(2-3x)}{(1-2x)(2+x)},|x|<\frac{1}{2}& \text{(i)}& \frac{1}{4}& \text{(P)}& 10\\ \text{(II)}& f\left(x\right)=\sqrt{\frac{1+2x}{4-x}},|x|<1& \text{(ii)}& \frac{1}{64}& \text{(Q)}& 4\\ \text{(III)}& f\left(x\right)=\frac{1}{\sqrt{1-ax}}-\sqrt{1+ax},|x|<\frac{1}{a}& \text{(iii)}& 10& \text{(R)}& \frac{1}{4}\\ \text{(IV)}& f\left(x\right)=\frac{a(1-x)}{1+x+x^2+x^3},|x|<1& \text{(iv)}& 4& \text{(S)}& \sqrt{8}\end{array}$

What of the following options is the only INCORRECT combination ?

Form the differential equation of the family of hyperbolas having foci on X-axis and centre at origin.

Let $\ast$ be the binary operation on N given by $a\ast b=LCM$ of a and b.
(i)Is $\ast$ commutative?

Evaluate the following definite integrals as limit of sums.
${\int }_0^4(x+e^{2x})dx.$

Question 2 (iii)
Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.
(iii) a = 4, d = - 3

Out of four number in a sequence,first three are in GP with first term 2 and last three are in AP with common difference 12. Find the common ratio, if the number are positive.

Which of the following statements is/are correct?

1. The radical axis of two circles is the locus of points whose power with respect to the two circles is equal.

2. The common point of intersection of the radical axes of three circles taken two at a time called the radical center of three circles.

If a complex number $z$ satisfies $|2z+10+10i|\le 5\sqrt{3}-5,$ then the least principle argument of $z,$ is

Find the number of integers satisfying the condition $|x-3|$$>$ 5 and $|x+1|$ $\le$ 4

If $\sqrt{1-c^2}=nc-1$ for all permissible values of $c$ and $n,$ and $z=e^{i\theta },$ then $\frac{c}{2n}(1+nz)(1+\frac{n}{z})$ is equal to

If $z_1$ and $z_2$ are two non zero complex numbers, satisfying the equation $\arg \left({\overline{z}}_1\right)=\arg \left(z_2\right),$ then which of the following is/are true

A ={x:x <-N,x <3}and B={y:(y^2)-3y+2=0}

Show they are equal or not

a person sitting on the top of a tall building is dropping balls at regular intervals of one second . find the position of the 3rd , 4th and the 5th ball when the 6th ball is dropped

a positive number is 5 times another number . if 21 is added to both the numbers than 1 of the new number becomes twice the other new number . what are the the nubers?

The general solution of $\frac{dy}{dx}-\frac{y}{x}=\frac{y^2}{x^2}$ is

With usual notification $C_0^2-C_1^2+C_2^2-....-C_{11}^2=$

Numbers formed using the digits $1,2,3,4,5$ (without repetition) that are greater than $20000$ are

If $1,lo{g}_9(3^{1-x}+2)lo{g}_3({4.3}^x-1)$ are in A.P., then x equals

The complete solution set of the inequality $[co{t}^{-1}x{]}^2-6[co{t}^{-1}x]+9\le 0,$ where $[.]$ denotes greatest integer function is

A circle having its centre at (2, 3) is cut orthogonally by the parabola $y^2=4x$. The possible intersection point(s) of these curves, can be

Let $f,f^{{}^{\prime }},f^{\prime \prime }$ be continuous in $[0,\ln 2]$ and $f\left(0\right)=0$, $f^{\prime }\left(0\right)=3$, $f\left(\ln 2\right)=6$, $f^{\prime }\left(\ln 2\right)=4$ and $\underset{0}{\overset{\ln 2}{\int }}{e}^{-2x}f\left(x\right)dx=3$, then $\underset{0}{\overset{\ln 2}{\int }}{e}^{-2x}{f}^{\prime \prime }\left(x\right)dx$ is -

Number of solution(s) of the equation $x^2-5x\text{sgn}(x^2-9)+6=0$ is
(Here, $\text{sgn}$ denotes the signum function)

The equation of the circle passing through the origin and cutting intercepts of length 3 and 4 units from the positive axes, is

Let $f\left(x\right)={\int }_0^{1}t|t-x|dt,xϵR$
The minimum value of f(x) is

The expression $(2+\sqrt{2}{)}^4$ has value, lying between

The area of the region $\left\{\right(x,y):\frac{2}{1+x^2}\ge y\ge x^2\}$ is (in sq. units):

If a, b c are in HP then the expression $a(b-c)x^2$ + b(c-a)x + c(a-b)

Number of distinct terms in the expansion of $(x+y+z+w{)}^{50}$ is equal to

${lim}_{x\to i}\frac{1+cosx}{ta{n}^{2}x}$