Explore topic-wise InterviewSolutions in .

Number of tangents to $y^2=2x$ through $(1,2)$ is

Simplify $\frac{(1-x-X^2+x^3)}{(1-x{)}^2}$

Why is log(Kp_{​​​​​2}/Kp_{​​​​​1}) negative when Kp2<Kp1?

If f(x) = x + 2, what is f(-3)?

From $(0,0),$ a tangent is drawn to the curve $y=e^x.$ Then the area bounded by the tangent, $y=e^x$ and $y-$axis is

If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -

$f^{\prime }\left(x\right)<0$

$g^{\prime }\left(x\right)=0$

$h^{\prime }\left(x\right)\le 0$

throughout their domains. Then choose the correct option of monotonically decreasing functions -

The value of $\underset{n\to \infty }{lim}[\frac{1}{n^2}{\sec }^2\frac{\pi }{3n^2}+\frac{2}{n^2}{\sec }^2\frac{4\pi }{3n^2}+\frac{3}{n^2}{\sec }^2\frac{9\pi }{3n^2}+\cdots +\frac{1}{n}{\sec }^2\frac{\pi }{3}]$ is

If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

The value of the sum $\sum _{n-1}^{13}(i^n+i^{n+1})$ , where i = $\sqrt{-1}$ equals

Let the straight line $x=b$ divide the area enclosed by $y=(1-x{)}^2$, $y=0$ and $x=0$ into two parts $R_1(0\le x\le b)$ and $R_2(0\le x\le 1)$ such that $R_1-R_2=\frac{1}{4}$ then $b$ equals

Let $f$ be a biquadratic function of $x$ given by $f\left(x\right)=A{x}^4+B{x}^3+C{x}^2+Dx+E,$ where $A,B,C,D,E\in R$ and $A\ne 0.$ If $\underset{x\to 0}{lim}{\left(\frac{f(-x)}{2x^3}\right)}^{\frac{1}{x}}=e^{-3},$ then

If the middle term in the expansion of ${(\frac{x}{2}+2)}^8$is $1120$; then $x\in R$ is equal to

If p, q, r are in A.P. and are positive, the roots of the quadratic

equation p $x^2$ + qx + r = 0 are all real for ___.

Using mathematical
induction prove that
for
all positive integers n.

The slope of tangent at $(1,1)$ to the curve $x=t^2+4t+1$ and $y=2t^2+3t+1$ is

What is the maximum value of the given expression and the corresponding value of x, if x takes only real values?

$p\left(x\right)=289-(x-17{)}^2$

In $△ABC,$ if $A,B$ and $C$ represent the angles of a triangle, then the maximum value of $\cos A+\cos B+\cos C$ is

Among all sectors of a fixed perimeter, choose the one with maximum area. Then the angle at the center of this sector (i.e., the angle between the bounding radii) is

A root of the equation

$17x^2+17x\tan [2{\tan }^{-1}\left(\frac{1}{5}\right)-\frac{\pi }{4}]-10=0$ is

Solve the following system of equations in R.
$\frac{|x-2|-1}{|x-2|-2}\le 0$

If $U_n=\left|\begin{array}{ccc}n& 1& 5\\ n^2& 2N+1& 2N+1\\ n^3& 3N^2& 3N+1\end{array}\right|$ and $\sum _{n=1}^N{U}_n=\lambda \sum _{n=1}^N{n}^2,$ then the value of $\lambda$ is

Find the sum to n terms of the series whose n^th terms is given by (2n – 1)²

If the sum of an infinite GP $a,ar,a{r}^2,a{r}^3,...$ is $15$ and the sum of the squares of its each term is $150,$ then the sum of $a{r}^2,a{r}^4,a{r}^6,...$ is

1. 4

Find the
intervals in which the following functions are strictly increasing or
decreasing:

(a) x²
+ 2x − 5 (b) 10 − 6x − 2x²

(c) −2x³
− 9x² − 12x + 1 (d) 6 −
9x − x²

(e) (x
+ 1)³ (x − 3)³

English is a language that contains words from many other languages. This inclusiveness is one of the reasons it is now a world language, for example:

petite – French

kindergarten – German

capital – Latin

democracy – Greek

bazaar – Hindi

Find out the origin of the following words.

Tycoon, tulip, logo, bandicoot, barbecue, veranda, robot, zero, ski, trek

The general solution of the differential equation $\frac{dy}{dx}+2y=e^{-2x}$ is

The (n+1)th term from the end in the expansion of $(2x-\frac{1}{x}{)}^{3n}$ is:

Consider the following grammar:

$S\to FR$

$R\to {}^{\ast }S|\epsilon$

$F\to id$



In the predictive parser table, M, of the grammar the entries M[S, id] and M[R, $] respectively