Explore topic-wise InterviewSolutions in .

The letters of the word COCHIN are arranged and all the words are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is:

Locus of image of the point $P(h,k)$ with respect to the line mirror which passes through the origin is

If $(x+iy{)}^5=p+iq$, then the value of $\frac{2(y+ix{)}^5}{q+ip}$ is

The solution set of the inequality $\left({\cot }^{-1}x\right)\left({\tan }^{-1}x\right)+(2-\frac{\pi }{2}){\cot }^{-1}x-3{\tan }^{-1}x-3(2-\frac{\pi }{2})>0,$ is

Let $f:R-\{b,c\}\to R,f\left(x\right)=\frac{x-a}{(x-b)(x-c)},b>c$. If $f$ is onto function, then

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x + y = 2$\sqrt{2}$ , then one of them will have its coordinates as

If for positive integers r > 1 n > 1 and the coefficient of $(3r{)}^{th}$ and $(r+2{)}^{th}$ terms in the binomial expansion of $(1+x{)}^{2n}$ are equal, then

If $\alpha =\underset{0}{\overset{1}{\int }}\left(e^{9x+3{\tan }^{-1}}\right)\left(\frac{12+9x^2}{1+x^2}\right)dx$, where ${\tan }^{-1}x$ only principal values, then the value of $({\log }_e|1+\alpha |-\frac{3\pi }{4})$ is

The number of distinct positive real roots of the equation $(x^2+6{)}^2-35x^2=2x(x^2+6)$ is

Determine whether each of the following relations are reflexive, symmetric and transitive:

(iv) Relation R in the set Z of all integers defined as R = {(x, y): x − y is an integer}

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

For any angle $x\in (0,\pi )\cup (\pi ,2\pi ),$



$\text{cosec}x\in [1,\frac{2}{\sqrt{3}}]\text{for}x\in$

A coin is tossed once. Write its sample space

This section contains four questions, each having two matching lists. Choices for the correct combination of elements from List – I and List – II are given as options (A), (B), (C) and (D), out of which one is correct.

$\begin{array}{cccc}& \text{List - I}& & \text{List - II}\\ P.& Z_k=cos\left(\frac{2k\pi }{2016}\right)+isin\left(\frac{2k\pi }{2016}\right)k=1,2,3,....,2015then& 1.& 0\\ & 1-{\sum }_{k=1}^{2015}cos\left(\frac{2k\pi }{2016}\right)=& & \\ Q.& If(a^2-a+k)(11b^2-4b+2)=\frac{9}{2}& 2.& 2\\ & \text{have exactly one ordered pair (a,b) then k =}& & \\ R.& \text{In a triangle ABC, equations of medians}& 3.& 3\\ & \text{AD and BE are 2x + 3y = 6, 3x - 2y = 10 respectively and}& & \\ & \text{AD = 6, BE = 11 and area of triangle ABC is 11K then K =}& & \\ S.& \text{y(x) = a cos lnx + b sin lnx, (x > 0) and}& 4.& 4\\ & \frac{1}{y\left(x\right)}(x^2\frac{d^{2}y\left(x\right)}{d{x}^2}+x\frac{dy\left(x\right)}{dx})+1=& & \end{array}$

Let $f\left(h\right)$ be a function continuous $\forall h\in R-\left\{0\right\}$ such that $f^{\prime }\left(h\right)<0,\forall h\in (-\infty ,0)$ and $f^{\prime }\left(h\right)>0,\forall h\in (0,\infty ).$ If $\underset{h\to 0^{+}}{lim}f\left(h\right)=3,\underset{h\to 0^{-}}{lim}f\left(h\right)=4$ and $f\left(0\right)=5,$ then the image of the point $(0,1)$ about the line, $y\cdot \underset{h\to 0}{lim}f({\cos }^{3}h-{\cos }^{2}h)=x\cdot \underset{h\to 0}{lim}f({\sin }^{2}h-{\sin }^{3}h),$ is

Find the equation for the ellipse that satisfies the given conditions,
Centre at (0, 0), major axis on the y- axis and passes through the points (3,2) and (1, 6).

If trace of the square matrix $A=[a_{ij}{]}_{n\times n}$ is zero, where $a_{ii}=i(i-3),$ then the order of the matrix is

An experiment consists of tossing a coin and then tossing it second time if head occurs.
If a tail occurs on the first toss, then a die is tossed once.
Find the sample space.

If $I_{m,n}=\int {\sin }^{m}x\cdot {\cos }^{n}xdx,$ then which of the following is/are equal to $I_{3,2}$

(where $C$ is integration constant)

Find the anti-derivative (or integral) of the following by the method of inspection.
cos 3x.

1. 11

The number of solution(s) of the equation $\cos x=|x|$ in $[-\frac{3\pi }{2},\frac{3\pi }{2}]$ is

The point of intersection of the tangents at the point P on the ellipse$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and its corresponding point Q on the auxiliary circle, lies on the line

${lim}_{x\to 0}\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{x}$

If $A=(5,0)$ and $B=(0,4)$, then the locus of moving point $P$ such that $|PA{|}^2-|PB{|}^2=9$ is

Range of the function $y=\frac{2^x-2^{-x}}{2^x+2^{-x}}$ is

Differentiate the following functions with respect to $x$ :

$\frac{{10}^x}{\sin x}$

Derivative of $log|x|$ w.r.t. $|x|$ is