Explore topic-wise InterviewSolutions in Current Affairs.

$Iff:(0,\infty )\to (0,\infty )$ satisfy

$f\left(xf\right(y\left)\right)=x^2{y}^2(a\in R)$, then

Number of solutions of 2 $f\left(x\right)=e^x$ is

If the points $A,B,C,D$ are collinear and $C,D$ divide $AB$ in the ratios $2:3\text{and}-2:3$ respectively, then the ratio in which $A$ divides $CD$ is:

By using the concept of equation of a line, prove that the three points (-2, -2), (8, 2) and (3, 0) are collinear.

On which of the following lines lies the point of intersection of the line, $\frac{x-4}{2}=\frac{y-5}{2}=\frac{z-3}{1}$ and the plane, $x+y+z=2$?

Find the effective resistance between $\text{A}$ & $\text{B}$.

Let $f\left(x\right)=\frac{1}{\sqrt{4-x^2}}+{\log }_{10}(x^3-x).$ Then the domain of $f$ is

If $z^3+(3+2i)z+(-1+ia)=0$ has one real root, then the value of ${}^{\prime }{a}^{\prime }$ lies in the interval

$(a\in R)$

The value of $\Delta =\left|\begin{array}{ccc}2a_1{b}_1& a_1{b}_2+a_2{b}_1& a_1{b}_3+a_3{b}_1\\ a_1{b}_2+a_2{b}_1& 2a_2{b}_2& a_3{b}_2+a_2{b}_3\\ a_1{b}_3+a_3{b}_1& a_3{b}_2+a_2{b}_3& 2a_3{b}_3\end{array}\right|$ is:

The angle between the planes represented by $2x^2-6y^2-12z^2+18yz+2zx+xy=0$ is

The equation of the plane passing through $(3,4,-1)$ and parallel to the plane $2x-3y+5z-7=0$ is

If ${}^n{C}_{12}={}^n{C}_8$, then n =

A straight line is equally inclined to all the three coordinate axes. Then the acute angle made by the line with the $y$-axis is:

If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$, respectively, then the value of its ${11}^{\text{th}}$ term is :

${lim}_{x\to 0}\frac{\sqrt{1+x}-1}{x}$ 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

Equation of the parabola whose axis is y = x, distance from origin to vertex is $\sqrt{2}$ and distance from origin to focus is $2\sqrt{2},$ is (Focus and vertex lie in Ist quadrant) :

In a class of 100 students, there are 70 boys whose average marks in Mathematics are 75. If the average marks of the complete class is 72, then average marks of girls is

By
giving a counter example, show that the following statements are not
true.

(i) p:
If all the angles of a triangle are equal, then the triangle is an
obtuse angled triangle.

(ii) q:
The equation x²
– 1 = 0 does not have a root lying between 0 and 2.

If A and G be A.M. and
G.M., respectively between two positive numbers, prove that the
numbers are.

Let $T_n=(n^2+1)n!$ and $S_n=T_1+T_2+T_3+\cdots +T_n.$ If $\frac{T_{10}}{S_{10}}=\frac{a}{b},$ where $a$ and $b$ are relatively prime natural numbers, then the value of $(b-a)$ is

The value of $\left\{\frac{2^{4n}}{15}\right\},n\in N$ is

(where {.} represents fractional part function)

Which of the following inequality is always true in the interval $(0,\frac{\pi }{2})$

Write the least value of $co{s}^2\theta +se{c}^2\theta .$

If $\frac{x^2}{f\left(4a\right)}+\frac{y^2}{f(a^2-5)}=1$ represents an ellipse with major axis as y-axis and f is a decreasing function, then