Explore topic-wise InterviewSolutions in Current Affairs.

In the above passage, there are blanks, each of which has been numbered. Against a blank, five words have been suggested, one of which fits the blank appropriately. Find out the appropriate word for blank 3.

If $y=\left(\frac{ax+b}{cx+d}\right)$, then $2\frac{dy}{dx}.]\frac{d^{3}y}{d{x}^3}$ is equal to

Three groups of children contain 3 girls and one boy, 2 girls and 2 boys, one girl and 3 boys. One child is selected at random form each group. What is the chance that the three selected consist of 1 girl and 2 boys?

If $ta{n}^{-1}x+ta{n}^{-1}y=\frac{\pi }{4}$ where $xy$ < 1, find the value of $x+y+xy$.

Match the functions with their corresponding derivatives.

On the set of positive rationals, a binary operation $\ast$ is defined by $a\ast b=\frac{2ab}{5}.$ If $2\ast x=3^{-1}$ then $x=$

If a + b +c = 0, then the equation $3a{x}^2+2bx+c=0$ has, in the interval (0, 1)

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm, is

${lim}_{x\to 0}\frac{e^x-1+sinx}{x}$

If a point P (3,- 4, 5) lies on the plane which passes through the intersection of two planes x-3y+4z =0 & 2x+y+6z+7=0 then the equation of this plane is -

Matrix $A=\left[\begin{array}{ccc}x& 3& 2\\ 1& y& 4\\ 2& 2& z\end{array}\right]$. If $xyz=60$ and $8x+4y+3z=20$, then $A\left(adjA\right)$ is equal to

${lim}_{x\to 0}\frac{1-cos5x}{1-cos6x}$

The vector equation of the plane passing through the origin and the line of intersection of the planes $\overrightarrow{r}\cdot \overrightarrow{a}=\lambda$ and $\overrightarrow{r}\cdot \overrightarrow{b}=\mu$ is

Using mathematical induction prove that $\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$ for all positive integers n.

The $\underset{x\to \frac{\pi }{2}}{lim}\{2x\tan x-\frac{\pi }{\cos x}\}$ is:

Write the set $\{\frac{1}{2},\frac{2}{5},\frac{3}{10},\frac{4}{17},\frac{5}{26},\frac{6}{37},\frac{7}{50}\}$ in the set -builder form.

Show that A intersection B is equal to A intersection C need not imply B=C

If the Imaginary part of $\frac{(2z+1)}{(iz+1)}$ is -2, then the locus of the point representing z in the complex plane is:

Find the ratio in which the line segment joining the points (2, 4, 5) and (3, -5, 4) is divided by the yz-plane.

If $y=(1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...\infty )$show that$\frac{dy}{dx}=y.$

(i) In any $\Delta ABC$, prove that $\frac{sin(B-C)}{sin(B+C)}=\frac{b^2-c^2}{a^2}$

(ii) Prove that $cosAcos({60}^{\circ }-A)cos({60}^{\circ }+A)=\frac{1}{4}cos3A$

Or

Find the value of

$\left(i\right)tan\frac{13\pi }{12}$

$\left(ii\right)sin{360}^{\circ }$

$\left(iii\right)cos{18}^{\circ }$

Find the equation of the parabola whose focus is (5,2) and having vertex at (3,2).

Solve the following quadratics $x^2-2x+2=0$

Prove that :

$\sqrt{\frac{1-cos2\theta }{1+cos2\theta }}=tan\theta$

Prove that the product of n geometric means between two quantities is equal to the nth power of a geometric means of those two quantities.

The vertex of the parabola $(y+a{)}^2=8a(x-a)$ is

$cos\frac{\pi }{7}$. $cos\frac{3\pi }{7}$. $cos\frac{5\pi }{7}$ are the roots of the equation $8x^3-4x^2-4x+1=0$. Then the value of $sin\frac{\pi }{14}.sin\frac{3\pi }{14}.sin\frac{5\pi }{14}$ is

Answer the following as true or false:
(i) a and -a are collinear.
(ii) Two collinear vectors are always equal in magnitude.
(iii) Two vectors having same magnitude are collinear.
(iv) Two collinear vectors having the same magnitude are equal.

$\text{In in any}\Delta ABC,\frac{b+c}{12}=\frac{c+a}{13}=\frac{a+b}{15},\text{then prove that}\frac{cosA}{2}=\frac{cosB}{7}=\frac{cosC}{11}.$

Shortest distance (in units) between the two parabolas $y^2=x-2,x^2=y-2$ is

$\int \frac{2+sin2x}{1+cos2x}{e}^{x}dx.$

Find sum to n terms :

3¹+3²+3³......

The range of $k$ for which the equation $k\cos x-3\sin x=k+1$ has a solution is

In an examination, 20 questions of true-false typer are asked. Suppose a students tosses a fair coin to determine his answer to each question. If the coin falls heads, he answer true, if it falls tails, he answer false. Find the probability that he answers atleast 12 questions correctly,

$ta{n}^{-1}\left(tan\frac{3\pi }{4}\right)$

In a certain code, 'BELIE' is written as 'AFKJD'. How would 'SELDOM' be written in that code?

On the set Z of integers define a relation R by a R b if $|a-b|\le 3$.Then R is

The coefficient of $a^8{b}^4{c}^9{d}^9$ in $(abc+abd+acd+bcd{)}^{10}$ is

Prove that: $\frac{1}{9!}+\frac{1}{10!}+\frac{1}{11!}=\frac{122}{11!}$

The number of zero’s at the end of 2007! Is

$A=\left[\begin{array}{ccc}1& 1& 2\\ 0& 2& 1\\ 1& 0& 2\end{array}\right]and{A}^3=(aA-I)(bA-I)$, where a, b are integers and I is a $3\times 3$ unit matrix then value of (a + b) is equal to

There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answeres are there to this question?