Explore topic-wise InterviewSolutions in Current Affairs.

Find whether the following functions are one-one or many-one and into or onto if $f:D\to R$ where D is a domain.
i) $f\left(x\right)=\frac{3x^2}{4\pi }-cos\pi x$

If $r,k,p\in W$, then $\sum _{r+k+p=10}{}^{30}{C}_r{\cdot }^{20}{C}_k{\cdot }^{10}{C}_p$ is

If $\alpha ,\beta$ are roots of the equation $x^2-\alpha (x+1)-c=0,\text{the write value of (1+}\alpha \text{)(1+}\beta \text{).}$

The rate of growth of bacteria in culture is proportional to the number of bacteria present and the bacteria count is $1000$ at the initial time $t=0$.

The number of bacteria has increased by $20\%$ in $2hours$. If the population of bacteria is $2000$ after $\frac{k}{{\log }_e\left({\displaystyle \frac{6}{5}}\right)}hours$, then${\left(\frac{k}{{\log }_{e}2}\right)}^2$ is equal to

A variable line has intercepts $e$ and $e^{\prime }$ on the coordinate axes, where $\frac{e}{2}$ and $\frac{e^{\prime }}{2}$ are the eccentricities of a hyperbola and its conjugate hyperbola respectively. The value of $r$ for which the line always touches the circle $x^2+y^2=r^2$ is

Which of the following matrix/matrices is/are invertible?

If y= cos(1-x) find dy by dx

If $\int \frac{\sin 2x}{\sin 5x\sin 3x}dx=\frac{1}{3}\log |\sin 3x|-\frac{1}{5}\log |f\left(x\right)|+C$, then $f\left(x\right)$ is

Differentiate the following functions with respect to x :

$\frac{x^2+1}{x+1}$

Evaluate the determinants.

$\left|\begin{array}{ccc}2& -1& -2\\ 0& 2& -1\\ 3& -5& 0\end{array}\right|$

Prove that:

(sin 3A + sin A) sin A + (cos 3A - cos A) cos A = 0

Find the equations of the tangent and normal to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ at the point $(x_0,y_0)$.

Find the value of x, y and z from the following equations:
$\left(iii\right)\left[\begin{array}{c}x+y+z\\ x+z\\ y+z\end{array}\right]=\left[\begin{array}{c}9\\ 5\\ 7\end{array}\right]$

$ifx=\sqrt{a^{si{n}^{-1}t}},y=\sqrt{a^{co{s}^{-1}t}},thenshowthat\frac{dy}{dx}=-\frac{y}{x}.$

Differentiate each the following from first principles :

$\left(i\right)\frac{2}{x}$

$\left(ii\right)\frac{1}{\sqrt{x}}$

$\left(iii\right)\frac{1}{x^3}$

$\left(iv\right)\frac{x^2+1}{x}$

$\left(v\right)\frac{x^2-1}{x}$

$\left(vi\right)\frac{x+1}{x+2}$

$\left(vii\right)\frac{x+2}{3x+5}$

$\left(viii\right)k{x}^n$

$\left(ix\right)\frac{1}{\sqrt{3-x}}$

$\left(x\right)x^2+x+3$

$\left(xi\right)(x+2{)}^3$

$\left(xii\right)x^3+4x^2+3x+2$

$\left(xiii\right)(x^2+1)(x-5)$

$\left(xiv\right)\sqrt{2x^2+1}$

$\left(xv\right)\frac{2x+3}{x-2}$

[5]is a scalar matrix of order

Equation of the circle whose radius is 3 and which touches the circle $x^2+y^2-4x-6y-12=0$ internally at the point $(-1,-1)$, is

Choose the correct answer in the following.

Area of the region bounded by the curve $y^2=4x,$ Y - axis and the line y = 3 is

(a) $2$ (b) $\frac{9}{4}$

(c) $\frac{9}{3}$ (d) $\frac{9}{2}$

Prove that $ta{n}^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)=\frac{\pi }{4}+\frac{1}{2}co{s}^{-1}{x}^2.$

Without changing the direction of coordinate axes, origin is transferred to (h, k), so that the linear (one degree)

terms in the equation $x^2+y^2-4x+6y-7=0$ are eliminated. Then the point (h, k) is

The value of k, for which $(cosx+sinx{)}^2+ksinxcosx-1=0$ is an identity, is

$cose{c}^{2}Aco{t}^{2}A-se{c}^{2}Ata{n}^{2}A-(co{t}^{2}A-ta{n}^{2}A)(se{c}^{2}A+cose{c}^{2}A-1)$ is equal to

Three six faced fair dice are rolled together. The probability that the sum of the numbers appearing on the dice is 8, is

Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.

The distance of the point (1, 3, -7) from the plane passing through the point (1, -1, -1) having normal perpendicular to both the lines
$\frac{x-1}{1}=\frac{y+2}{-2}=\frac{z-4}{3}$ and $\frac{x-2}{2}=\frac{y+1}{-1}=\frac{z+7}{-1}$, is

If the sum of the squares of deviations for 10 observations taken from their mean is 2.5, then write thevalue of standard deviation.

Prove that : $A\subseteq B,B\subseteq CandC\subseteq A\Rightarrow A=C$.

The solution of the equation ${[sinx+cosx]}^{1+sin2x}=2,-\pi \le x\le \pi$ is

Differentiate given problems w.r.t.x.

$(5x{)}^{3cos2x}$

Integrate the following functions.
$\int \frac{1}{\sqrt{x^2+2x+2}}dx.$

The minimum and maximum value of $y=\frac{x^2-x+4}{x^2+x+4}$ will be and respectively.

State which part of speech is the underlined word.

He has been absent from school since last Tuesday.

If $b{x}^2+acx+b^{2}c=0$ and $c{x}^2+abx+b^{2}c=0$ have a common root (where $a,b,c$ are non zero distinct real numbers), then which of the following is/are correct?

In an objective paper, there are two sections of $10$ questions each. For "section $1$", each question has $5$ options and only one option is correct and "section $2$" has $4$ options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "section $1$" is $1$ and in "section $2$" is $3.$
(There is no negative marking)
If a canidate attempts only two questions by guessing, one from "section $1$" and one from "section $2$", the probability that he scores in both questions is

If A, B, C be the angles of a triangle, then which of the following hold good?

If $\alpha ,\beta \gamma ,ϵ(0,\frac{\pi }{2}),then\frac{sin(\alpha +\beta +\gamma )}{sin\alpha +sin\beta +sin\gamma }is$

Let $f:R\to R$ be a function such that $f(x+y)=f\left(x\right)+f\left(y\right)+x^{2}y+x{y}^2$ $\forall x,y\in R$. If $\underset{x\to 0}{lim}\frac{f\left(x\right)}{x}=1$, then $f\left(x\right)$ is

The sum of the slopes of the tangents to the parabola $y^2=8x$ drawn from the point (–2, 3) is

For a acute $△ABC$, the value of $\frac{\cos (A+B)}{\cos C}$ is