Explore topic-wise InterviewSolutions in Current Affairs.

If $\frac{{\cos }^{4}A}{{\cos }^{2}B}+\frac{{\sin }^{4}A}{{\sin }^{2}B}=1$, then which of the following is/are correct?

Give an example of two functions $f:N\to Z$ and $g:Z\to Z$ such that gof is injective but g is not injective.

Find gof and fog, if
$\left(i\right)f\left(x\right)=8x^3$ and $g\left(x\right)=x^{\frac{1}{3}}$.

If tangents are drawn to the ellipse $x^2+2y^2=2$ at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinates axes lie on the curve :

Let A and B be two sets. Show that the sets $A\times B$ and $B\times A$ have an element in common if the sets A and B have an element in common.

If the area (in sq. units) of the region $\left\{\right(x,y):y^2\le 4x,x+y\le 1,x\ge 0,y\ge 0\}$ is $a\sqrt{2}+b,$ then $a-b$ is equal to :

The coefficients $a,b\text{and}c$ of the quadratic equation, $a{x}^2+bx+c=0$ are obtained by throwing a dice three times. The probability that this equation has equal roots is :

If f and g are continuous on [0, a] and satisfy f(x) = f(a - x) and g(x) + g(x - a) = 2, then ${\int }_0^{a}f\left(x\right)g\left(x\right)\mathrm{dx}$is equal to

If the vertices of a hyperbola be at $(-2,0)$ and $(2,0)$ and one of its foci be at $(-3,0),$ then which one of the following points does not lie on this hyperbola

If a,b,c,d,e,f are in AP then e - c is equal to what?

For two finite disjoint sets $A$ and $B$, if the number of elements in power set of $A$ is $224$ more than the number of elements in power set of $B$, then the number of elements present in either of the sets is

If the normal at $P$ to the hyperbola $x^2-y^2=4$ meets the axes in $G$ and $g$ and $C$ is centre of the hyperbola, then

If one of the vertices of the square, inscribed in the circle $|z-1|=2$, is $2+\sqrt{3}i$, then other vertices of the square are

The corner points of the feasible region determined by the system of linear constraints are $(0,10),(5,5),(25,20)$ and $(0,30)$. Let $Z=px+qy$, where $p,q>0$. Condition on $p$ and $q$ so that the maximum of $Z$ occurs at both the points $(25,20)$ and $(0,30)$ is

Solution set for the inequality $\frac{5}{4}{\sin }^{2}x+{\sin }^{2}x\cdot {\cos }^{2}x>\cos 2x$ is

The area bounded by $y=x^2,$ $y=[x+1],$ $x\le 1$ and the $y$-axis, where $[.]$ represents the greatest integer function, is

If the $4^{\text{th}}$ term in the expansion of ${(ax+\frac{1}{x})}^n$ is $\frac{5}{2}$, then

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice.
Write the sample space for this experiment.

A survey of people in a given region showed that $20\%$ were smokers. The probability of death due to lung cancer, given that a person smoked, was $10$ times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is $0.006$, what is the probability of death due to lung cancer given that a person is a smoker?

The probability of men getting a certain disease is $\frac{1}{2}$ and that of women getting the same disease is $\frac{1}{5}$. The blood test that identifies the disease gives the correct result with probability $\frac{4}{5}$. Suppose a person is chosen at random from a group of $30$ males and $20$ females, and the blood test of that person is found to be positive. What is the probability that the chosen person is a man?

If $(x^2+y^2{)}^2=xy$ Find $\frac{dy}{dx}$.

OR If x = $a(2\theta -sin2\theta )$ and y = a $(1-cos2\theta )$, find $\frac{dy}{dx}$ when $\theta =\frac{\pi }{3}$.

Let X={1,2,3} and Y ={4,5}. Find whether the following subsets of $X\times Y$ are functions from X to Y or not.
(iii) h={(1,4),(2,5),(3,5)}

Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

On Railways there are 15 stations.The number of tickets required in order that it may be possible for a passenger to book from every station 2 every other is what?

Let f: R → R be defined as f(x) = 10x + 7. Find the function g: R → R such that g o f = f o g = 1_R.

For what minimum value of n is [(1+I)/(1-i)]ⁿ real?

√x+5+√x+21=√6x+40

If $f\left(x\right)$ is defined on $(-1,1)$ , then the domain of $g\left(x\right)=f\left(e^x\right)+f\left({\log }_e|x|\right))$ is

The number of ordered pairs $(x,y)$ of real numbers that satisfy the simultaneous equations
$x+y^2=x^2+y=12$ is

Find the domain of the function:

f(x)= 1/(√x²-1)

The eccentricity of the ellipse represented by the equation $25x^2+16y^2-150x-175=0$ is

If two tangents from the point $(\alpha ,\beta )$ to the parabola $y^2=4x$ be such that the slope of one tangent is double of the other than

acosφ=bcosθ

Show that

atanθ+btanφ=(a+b) tan (θ+φ) ÷2

The solution of inequality $\frac{5-2x}{3}\le \frac{x}{6}-5$ is

Differentiate the following functions with respect to x :

$\frac{3^x}{x+tanx}$

A function: R ⟶ R satisfies the equation f(x) f(y) -f(xy) = x+ y ∀ x, y ∈ R and f(1) > 0, then

$\omega$ is a cube root of unity, $\omega \ne 1$.

Match the following.

(1) ${\omega }^{99}$ (p) - 1

(2) 1 + ${\omega }^{33}$ + ${\omega }^{66}$ (q) 0

(3) 1 + ${\omega }^{14}$ + ${\omega }^{28}$ (r) 3

(4) ${\omega }^4$ + ${\omega }^5$ + ${\omega }^6$ (s) 1

Find the locus of the point P if $A{P}^2-B{P}^2=18$. Where $A\equiv (1,2,-3)anaB\equiv (3,-2,1)$