Explore topic-wise InterviewSolutions in Current Affairs.

Show that the function given by $f\left(x\right)=sinx$ is
strictly increasing in $(0,\frac{\pi }{2})$

strictly decreasing in $(\frac{\pi }{2},\pi )$

neither increasing nor decreasing in $(0,\pi )$

If $5\sqrt{5}\times 5^3÷5^{-3/2}=5^{a+2}$, the value of a is

The quadrant in which sin θ is negative and tan θ is positive is

1. undefined

Let $f\left(x\right)=(x+1{)}^2-1,(x\ge -1)$. Then the set $S=\{x:f(x)=f^{-1}(x\left)\right\}$. is

Let 2 sin a + 3 cos b = 3 and 3 sin b + 2 cos a = 4 then

For the given graph of a quadratic equation as shown $y=a{x}^2+bx+c,$

If the coefficient of $(2r+4{)}^{th}$ and $(r-2{)}^{th}$ terms in the expansion of ($1+x{)}^{18}$ are equal, then r =

If $\alpha$ and $\alpha$ are two points on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and the chord joining these two points passes
through the focus (ae, 0) then e $cos\frac{\alpha -\beta }{2}$

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that OP.OQ + OR.OS = OR.OP + OQ.OS = OQ.OR + OP.OS Then the triangle PQR has S as its

find the value of $\underset{x\to \infty }{lim}\frac{2x^3-3x^2+5x+6}{7x^2+8x+15}$

If the entries in a $3\times 3$ determinant are either $0$ or $1,$ then the greatest value of their determinant is

If the direction cosines of a variable line in two adjacent positions be l, m, n and l + a, m + b, n + c and the small angle between the two positions be $\theta$, then :

If the ratio of sum of $p$ terms to $q$ terms of an A.P. is $\frac{p^2+p}{q^2+q}$, then the ratio of $p^{th}$ term to $q^{th}$ term is equal to

Match the column

$\begin{array}{cc}\text{Equation}& \text{Name of the curve}\\ \text{1)}{x}^2-2x-y-3=0& \text{P) Circle}\\ \text{2)}{x}^2+3xy+2y^2-x-4y-6=0& \text{Q) Parabola}\\ \text{3)}{x}^2+y^2-20=0& \text{R) Ellipse}\\ \text{4)}7x^2+7y^2+2xy+10x-10y+7=0& \text{S) Hyperbola}\\ \text{5)}6x^2-xy-y^2-23x+4y+15=0& \text{T) Pair of straight lines}\end{array}$

Find the last two digits of the number $(17{)}^{10}$.

Let $I_1=\underset{0}{\overset{1}{\int }}\frac{e^{x}dx}{1+x}$ and $I_2=\underset{0}{\overset{1}{\int }}\frac{x^{2}dx}{e^{x^3}(2-x^3)}$, then $\frac{I_1}{I_2}$ is equal

Circle $C_1:x^2+y^2=16$ intersects another circle $C_2$ of radius $6$ in such a manner that their common chord is of maximum length and has slope equal to $\frac{1}{2}.$ Then the co-ordinates of the centre of the circle(s) $C_2$ is (are)

The domain of $f\left(x\right)=\sqrt{\frac{1-|x|}{|x|-2}}$ is

Suppose the direction cosines of two lines are given by $al+bm+cn=0$ and $fmn+gln+hlm=0$ where $f,g,h,a,b,c$ are arbitrary constants and $l,m,n$ are direction cosines of the line. On the basis of the above information the given lines will be perpendicular if:

${\int }_{\frac{-\pi }{4}}^{\frac{\pi }{4}}\frac{dx}{1+cos2x}$ is equal to

Prove the following by using the principle of mathematical induction for all n ∈ N:

If $\begin{array}{c}R\left(t\right)=\left[\begin{array}{cc}cost& sint\\ -sint& cost\end{array}\right]\end{array}$

then R(s).R(t) =

If 5^x-3 ×3^2x-8 = 225

Then, x=?

Find the vector
equation of the line passing through the point (1, 2, − 4) and
perpendicular to the two lines:

1. 0

If a curve $y=f\left(x\right)$ passes through the point $(1,2)$ and satisfies $x\frac{dy}{dx}+y=b{x}^4,$ then for what value of $b,$ $\underset{1}{\overset{2}{\int }}f\left(x\right)dx=\frac{62}{5}$ ?

If four of eight vertices of a regular octagon are chosen at random, then the probability that the quadrilateral formed is a rectangle(not a square), is

$\left(i\right)$ Show that the matrix $A=\left[\begin{array}{ccc}1& -1& 5\\ -1& 2& 1\\ 5& 1& 3\end{array}\right]$ is a symmetric matrix.

$\left(ii\right)$ Show that the matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ -1& 0& 1\\ 1& -1& 0\end{array}\right]$ is a skew-symmetric matrix.