Explore topic-wise InterviewSolutions in Current Affairs.

If centre of circles $x^2+y^2=25$ and $x^2+y^2-4x+9y+3=0$ are the endpoints of the diameter of a circle $S$, then equation of the circle $S$ is

If $a,b,c$ be three unequal positive quantities in H.P., then

If $P\left(A\right)=\frac{6}{11},P\left(B\right)=\frac{5}{11}andP(A\cup B)=\frac{7}{11},$ find
$P\left(\frac{A}{B}\right)$

Prove that the curves $x=y^2$ and xy=k cut at right angle if $8k^2=1$.

Parametric form of a straight line passing through $(4,5)$ and making an angle ${60}^{\circ }$ with $x$-axis in the positive direction is
(where $\lambda$ be any parameter)

A point on the curve $y=x^2+x$, where the tangent is parallel to the chord joining the points (0, 0) and (1, 2) is .

Let f(x) be a function such that $f\text{'}\left(x\right)={\log }_{1/3}\left({\log }_3\left(\sin x+a\right)\right]$. If f(x) is decreasing for all real values of x, then .

Range of the function f(x)= x^{​​​​​​2}​​​​​ - x - 6 ÷ x - 3 is?

(1+cosx) (1+sinx) = 5/4 Find a)(1-cosx) and b)(1-sinx)

What is the eccentricity of a hyperbola if a chord joining 2 points given by parameters $\alpha$ and $\beta$ also passes through the focus. [Given :$\alpha +\beta =p,\alpha -\beta =q]$

For $x\in R$, the range of $f\left(x\right)=\frac{2^x-1}{2^x+1}$ is

tanA+tan(60+A)+tan(60-A)=3tan3A

a, b, c, d $\in R^{+}$ such that a, b, and c are in A.P. and b,c and, d are in H.P., then

I. $x^2-365=364$

II. $y-\sqrt{324}=\sqrt{81}$

The number of solutions of the equation x/100=sinx

A) 63

B)32

C) 33

D) 0

The value of $\underset{n\to \infty }{lim}\frac{\pi }{6n}[{\sec }^2\left(\frac{\pi }{6n}\right)+{\sec }^2(2\cdot \frac{\pi }{6n})+\cdots +{\sec }^2\left(\right(n-1\left)\frac{\pi }{6n}\right)+\frac{4}{3}]$ is

In the binomial expansion of the (1+x)ⁿ the coefficient of fifth ,sixth and the seventh terms are in A.P . find all value of n for which this can happen

The number of solutions of the equation $x^3$ + $x^2$ + 4x + 2sinx = 0 in 0 ≤ x ≤ 2$\pi$

Find point local maxima for the function f(x)=x³ +x² +x+1

For which of the following functions. Rolle’s theorem can be applied in the given interval

$e_1$ and $e_2$ are the eccentricities of two conics S and $S^1$. If ${e_1}^2+{e_2}^2$ = 3 then both S and $S^1$ can be

Area of the region bounded by the curve y² = 2y - x and y-axis is:

One of the sides of a triangle is divided into segments of $4$ and $6$ units by the point of tangency of the inscribed circle which has radius $2\sqrt{2}$ units, then the largest side of triangle is -

We are given M urns, numbered 1 to M and n balls (n < M) and P(A) denote the probability that each of the urns numbered 1 to n, will contain exactly one ball.

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \left(a\right)& \text{If the balls are different and any number of balls can go to any urn then P(A)}=\underset{–}{}& \left(p\right)& \frac{1}{{}^M{C}_n}\\ \left(b\right)& \text{If the balls are identical and any number of balls can go to any urn then P(A)}=\underset{–}{}& \left(q\right)& \frac{1}{{}^{(M+n-1)}{C}_{M-1}}\\ \left(c\right)& \text{If the balls are identical but at most one ball can be put in any box, then P(A)}=\underset{–}{}& \left(r\right)& \frac{n!}{{}^M{C}_n}\\ \left(d\right)& \text{If the balls are different and at most one ball can be put in any box, then P(A)}=\underset{–}{}& \left(s\right)& \frac{n!}{M^n}\end{array}$

$ta{n}^{-1}n+co{t}^{-1}(n+1)$ is equal to

The equations of common tangents to the hyperbolas $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$ are

If the line ax + by + c=0 is a normal to the curve xy=1, then

The number $N=6{\log }_{10}2+{\log }_{10}31$ lies between two successive integers whose sum is equal to

Coefficient of $x^{10}$ in the expansion of $(2+3x)e^{-x}$ is

${lim}_{x\to \frac{\pi }{8}}\frac{cot4x-cos4x}{(\pi -8x{)}^3}$

If one A.M. A and two G.M.s p and q be inserted between two numbers a and b, then which of the following is hold good

If $sinx=co{s}^{2}x,$ then write the value of $co{s}^{2}x(1+co{s}^{2}x$

If $\sum _{i=1}^{\pi }i$ = $\frac{i(i+1)}{2}$, then $\sum _{i=1}^n(3i-2)$ =

If $xsin{45}^{\circ }co{s}^2{60}^{\circ }=\frac{ta{n}^2{60}^{\circ }cosec{30}^{\circ }}{sec{45}^{\circ }co{t}^2{30}^{\circ }}$, then x =

Integrate dx/sinx+√3cosx

If $X=\{4^n-3n-1:n\in N\}$ and $Y=\left\{9\right(n-1):n\in N\}$, where $N$ is the set of natural numbers, then $X\cup Y$ is equal to:

If vertices of a quadrilateral are A (0,0), B(3,4), C(7,7) and D(4,3) then quadrilateral ABCD is

The number of term with integeral coefficients in the expansion of $({17}^{\frac{1}{3}}+{35}^{\frac{1}{2}}x{)}^{600}$ is

Let $f\left(a\right)=g\left(a\right)=k$ and their $n^{th}$ derivatives $f^n\left(a\right)$, $g^n\left(a\right)$ exist and are not equal for some $n$. Further if $\underset{x\to a}{lim}\frac{f\left(a\right)g\left(x\right)-f\left(a\right)-g\left(a\right)f\left(x\right)+g\left(a\right)}{g\left(x\right)-f\left(x\right)}=4$, then the value of $k$ is:

The number of integers x for which x, 10 and 24 are the sides of an acute angled triangle is

If one root of the quadratic equation $a{x}^2-bx-c=0;a,b,c\in R$ is reciprocal of the other, then which one of the following is correct?