Explore topic-wise InterviewSolutions in Current Affairs.

A point on the curve is said to be an extremum it it is a local minimum (or) a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is .....

Let two lines be intersecting at $(4,3)$ and angle between them is ${45}^{\circ }.$ If the slope of one line is $2,$ then the equation of the other line can be

A pole is 100 m high. The angle of elevation of its top from a point 100 [sq root (3)] m away from its base is ___.

Find the integral of $\sqrt{x^2+a^2}$ with respect to $x$ and evaluate $\int \sqrt{16x^2+25}dx$.

The books of Ram and Bharat showed that the capital employed on 31.12.2002 was Rs. 5,00,000 and the profits for the last 5 years: 2002 Rs. 40,000; 2003 Rs. 50,000; 2004 Rs. 55,000; 2005 Rs. 70,000 and 2006 Rs. 85,000. Calculate the value of goodwill on the basis of 3 yr purchase of the average super profits of the last 5 yr assuming that the normal rate of return is 10%.

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

Prove that

sin^​6 A + cos^{​​​​6} A = 1 - 3 sin^{​​​​2} A cos^{​​​​2} A

$\int \sqrt{1+sinxdx}$

is
a square matrix, if

(A)
m < n

(B) m
> n

(C) m
= n

(D) None
of these

Let a, b, c be the sides of a triangle whose perimeter is $p$ and area is $A$, then

A five letter word is to be formed such that the letters appearing in the odd positions are taken from the unrepeated Letters of the word MATHEMATICS whereas the letters which occupy even places are taken from amongst the repeated letters. Then number of such words is

Consider the curve $\sin x+\sin y=1$, lying in the first quadrant , then
$\begin{array}{cccc}& \text{List- I}& & \text{List-II}\\ \text{(I)}& \underset{x\to \pi /2}{lim}\frac{d^{2}y}{d{x}^2}=& \text{(P)}& 0\\ \text{(II)}& \underset{x\to 0^{+}}{lim}{x}^{3/2}\frac{d^{2}y}{d{x}^2}=& \text{(Q)}& 1\\ \text{(III)}& \underset{x\to 0^{+}}{lim}{x}^2\frac{d^{2}y}{d{x}^2}=& \text{(R)}& \frac{1}{\sqrt{2}}\\ \text{(IV)}& \underset{x\to \pi /2}{lim}\frac{dy}{dx}=& \text{(S)}& \frac{1}{2\sqrt{2}}\\ & & \text{(T)}& \sqrt{2}\\ & & \text{(U)}& 3\end{array}$

Which of the following is the only CORRECT combination?

The equation of the common tangent to the curves $y^2=8x$ and $xy=-1$ is

If the line $\frac{x}{a}+\frac{y}{b}=1$ intersects the curve
$5x^2+5y^2+5bx+5ay-9ab=0$ at $P$ and $Q$ such that $\angle POQ={90}^{\circ },$ where $O$ is the origin, then the value of $\frac{a}{b}$ is

Suppose $a,b$ denotes the distinct real roots of the quadratic polynomial $x^2+20x-2020$ and suppose $c,d$ denotes the distinct complex roots of the quadratic polynomial $x^2-20x+2020.$

Then the value of $ac(a-c)+ad(a-d)+bc(b-c)+bd(b-d)$ is

In a G.P., the first term and common ratio is $a$ and $r$ respectively. If $S_n$ denotes the sum of $n$ terms and $U_n=\sum _{n=1}^n{S}_n$, then $r{S}_n+(1-r)U_n$ is equal to

If two sides of a triangle are roots of the equation $x^2-7x+8=0$ and the angle between these sides is ${60}^{\circ }$ then the product of inradius and circumradius of the triangle is

The area (in sq. units) bounded by the curves $y=x^2$ and $y=\frac{2}{1+x^2}$ is

A normal chord $AB$ of a parabola $y^2-12x=0$ subtends a right angle at the vertex of the parabola. If the point of intersection of the normals drawn at $A$ and $B$ is $(p,q)$, then the value of $\frac{p^2}{q^2}$ is

If $f\left(x\right)=\left({\log }_{e}x\right|$, then

If $\frac{|x-2|}{x-2}\ge 0$ ,then

Find in degrees the angle subtended at the centre of a circle of a diameter 50 cm by an arc of length 11 cm.

Given that ${\log }_{10}2=0.3010$, the number of digits in the number ${2000}^{2000}$ is

If the line $2x+\sqrt{6}y=2$ is tangent to the hyperbola $x^2-2y^2=4$ then the point of contact is.

Find the equation of the line passing through (1, 2) and (3, 6) using the determinant.