Explore topic-wise InterviewSolutions in Current Affairs.

Find the equation of the normal to the circle $x^2+y^2-6x-8y-24=0$ at the point (4, 6).

A committee of 12 is to be formed from 9 women and 8 men in which at least 5 women have to be included in a committee. Then the numbers of committees in which the women are in majority and men are in majority are respectively.

If A = {x: x is a prime number}

B = {x: x is an odd natural number}

Then A ∩ B is

The function $12x^5-45x^4+40x^3+6$ has a minimum at

The equation of the circle which touches all the sides of the square with sides $y=3,x=6,y=7$ and $x=10$ is $x^2+y^2+2gx+2fy+c=0$. Find the value of $g+f+c$

The sum of real roots of the equation $(x-1)(x-2)(3x-1)(3x-2)=8x^2$ is

Let $\alpha$ and $\beta$ ($\alpha <\beta$) be roots of the quadratic equation $a{x}^2+bx+c=0.$ If 0 < a < c and a + c = b, then which of the following statement(s) is/are correct?

If arg(z) <0, then arg (-z)-arg(z)=

If the function f(x) = $\frac{\sqrt{4+x}-2}{x},x\ne 0$ , is continuous at x = 0, the f(0) =

Let $a,b,c$ be real numbers such that $a+b+c<0$ and the quadratic equation $a{x}^2+bx+c=0$ has imaginary roots. Then

If P(A) = 0.5, P(B) = 0.4 and P(A $\cup$ B) = 0.8, then P(A – B) =

Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.

Consider the following two statements :
$Statementp:$
The value of $\sin {120}^{\circ }$ can be derived by taking $\theta ={240}^{\circ }$ in the equation $2\sin \frac{\theta }{2}=\sqrt{1+\sin \theta }-\sqrt{1-\sin \theta }$
$Statementq:$
The angles $A,B,C$ and $D$ of any quadrilateral $ABCD$ satisfy the equation $\cos \left(\frac{1}{2}\right(A+C\left)\right)+\cos \left(\frac{1}{2}\right(B+D\left)\right)=0$
Then the truth values of $p$ and $q$ are respectively:

Find the equation of the parabola whose focus is the point (2,3) and directrix is the line x-4y+3=0.Also,find the length of its latus-rectum.

Construct a quadratic in x such that A.M. of its roots in A adn G.M. is G.

The sum of the squares of the lengths of the chords intercepted on the circle, $x^2+y^2=16$ by the lines, $x+y=n;n\in N$, where $N$ is the set of all the natural numbers, is :

Check whether the following ststement are true or not :

(i) p : If x and y are odd integers, then x + y is an even integer.

(ii) q : If x, y are integers such that xy is even, then at least one of x and y is an even integer.

The number of diagonals that can be drawn by joining the verticles of an octagon is

If $tanA=\frac{3}{4},cosB=\frac{9}{41},$ where $\pi <A<\frac{3\pi }{2}$ and $0<B<\frac{\pi }{2},$ find $tan(A+B)$.

Write the number of elements in the power set of null set.

The value of $\underset{x\to 2}{lim}\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}$ is

The sum of infinite terms of a G.P. is x and on squaring the each term of it, the sum will be y, then the common ratio of this series is

Equation of the plane containing the line $x+2y+3z-4=0=2x+y-z+5$ and perpendicular to the plane $5x+3y-6z+8=0$ is

The distance between two parallel chords each of length 10 units is 24 units. Then the Radius of the Circle is

A chain of length ‘L’ and mass ‘M’ is placed on a smooth surface. The length BA = L - b. When the end A reaches B, the velocity of the chain is

The value of $\frac{1-{\tan }^2(\frac{\pi }{4}-A)}{1+{\tan }^2(\frac{\pi }{4}-A)}$ is
where $A\in [0,\frac{\pi }{2}]$

The equation of auxiliary circle of the ellipse $16x^2+25y^2+32x-100y=284$ is

The locus of the points representing complex number $z=x+iy$ for which $|z+5{|}^2-|z-5{|}^2=10$ is

If $z$ is a complex number satisfying $z-12=i(9-2\overline{z}),$ then the value of $z+\overline{z}$ is

Without changing the direction of the axes, the origin is transferred to the point $(2,3)$. Then the equation $x^2+y^2–4x–6y+9=0$ changes to

In how many ways can $17$ persons depart from railway station in $2$ cars and $3$ autos, given that $2$ particular persons depart by same car ($4$ persons can sit in a car and $3$ persons can sit in an auto)?

Let P, Q, R, S and T are five sets about the quadratic equation
(a – 5)$x^2$ – 2ax + (a – 4) = 0, a $\ne$ 5 such that
P : All values of ‘a’ for which the product of roots of given quadratic equation is positive.
Q : All values of ‘a’ for which the product of roots of given quadratic equation is negative.
R : All values of ‘a’ for which the product of real roots of given quadratic equation is positive.
S : All values of ‘a’ for which the roots of given quadratic are real.
T : All values of ‘a’ for which the given quadratic equation has complex roots.

Let A = {1, 2, 3}, B = {2, 3, 4}, then which of the following is a function from A to B ?

If the equation $|sinx{|}^2+|sinx|+b=0$ has two distinct roots in $[0,\pi ]$, then the number of integers in the range of b is/are equal to

For a real number $x,$ let $\left[x\right]$ denote the largest integer less than or equal to $x,$ and let $\left\{x\right\}=x–\left[x\right].$ The number of solutions $x$ to the equation $\left[x\right]\left\{x\right\}=5$ with $0\le x\le 2015$ is

Examine if Rolle's theorem is applicable to any of the following functions. Can you say something about the converse of Rolle's theorem from these example ?

(i) $f\left(x\right)=\left[x\right]forxϵ[-2,2]$

If 0 is the origin and A is (a,b,c), then find the direction cosines of the line OA and the equation of plane through A at right angle OA.

Let A and B be square matrices of the order 3 $\times$ 3. Is $(AB{)}^2=A^2{B}^2$ ? Give reasons.

Find the area of the region bounded by the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$.