Explore topic-wise InterviewSolutions in .

The value of $a=-\lambda -\frac{\pi }{\mu }$, such that $x^2+ax+si{n}^{-1}(x^2-4x+5)+co{s}^{-1}(x^2-4x+5)=0$ has atleast one solution. Then $\lambda +\mu$ is equal to

The area bounded by the curve $y=\sin x$ and $y=\cos x$ in between $x=0$ and $x=\frac{\pi }{2}$ is

The line 4x-3y=-12 is the tangent at point A(-3,0) and the line 3x+4y=16 is the tangent at the point B(4,1) to a circle. The equation of circle is .

$\begin{array}{ccc}\text{Column I}& \text{Column II}& \text{Column III}\\ \text{P)}\overline{\text{v}}={\text{v}}_0\hat{\text{i}}& 1)\overline{\text{E}}={\text{E}}_0\hat{\text{k}}& \text{i)}\overline{\text{B}}={\text{B}}_0(\hat{\text{i}}+\hat{\text{j}})\\ \text{Q)}\overline{\text{v}}={\text{v}}_0(\hat{\text{i}}+\hat{\text{j}})& 2)\overline{\text{E}}={\text{E}}_0\hat{\text{i}}& \text{ii)}\overline{\text{B}}={\text{B}}_0\hat{\text{k}}\\ \text{R)}\overline{\text{v}}={\text{v}}_0\hat{\text{j}}& 3)\overline{\text{E}}=\text{0}& \text{iii)}\overline{\text{B}}=0\\ \text{S)}\overline{\text{v}}=0& 4)\overline{\text{E}}={\text{E}}_0(\hat{\text{i}}+\hat{\text{j}})& \text{iv)}\overline{\text{B}}={\text{B}}_0\hat{\text{j}}\end{array}$

Which of the following combinations should be true for the particle to travel along a parabolic path?

The value of the limit $\underset{x\to \infty }{lim}(\sqrt{x^2+x}-x)$ is equal to

If $\sin x+{\sin }^{2}x=1$, then
${\cos }^{12}x+3{\cos }^{10}x+3{\cos }^{8}x+{\cos }^{6}x+2{\cos }^{4}x+{\cos }^{2}x-2=$

If the vectors $\overrightarrow{AB}=3\hat{i}+4\hat{k}$ and $\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}$ are the sides of a triangle $ABC$, then the length of the median through $A$ is :

If $z_1,z_2,z_3$ are the vertices of a triangle in argand plane such that $|z_1-z_2|=|z_1-z_3|,$ then $\arg (\frac{2z_1-z_2-z_3}{z_3-z_2})$ is

$\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three vectors having magnitudes 1, 1 and 2 respectively. If $\overrightarrow{a}\times (\overrightarrow{a}\times \overrightarrow{c})+\overrightarrow{b}=0$ , then the acute angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ is

The points whose position vectors are $60i+3j,40i-8j$ and $ai-52j$ collinear, if

At what points in the interval [0, 2π],
does the function sin 2x attain its maximum value?

Let R be the set of all real numbers and let f be a function R to R such that that $f\left(x\right)+(x+\frac{1}{2})f(1-x)=1$ for all x $ϵ$ R.Then 2f(0)+3f(1)is equal to

Write
the general term in the expansion of (x²
– y)⁶

A man decides to throw a party but forgets to print the invitation cards. So he decided to give a particular code to every guest which they have to speak on arrival. When the first guest arrived the watchman said 12 and the guest said 6 and was allowed. For the second guest the watchman said 6 and the guest replied as 3 and he was allowed. For the third guest the watchman said 8 and the guest said 4 but the guest wasn't allowed. What code must the guest say in order to enter the party?

If A and B are two given sets, then $A\cap (A\cap B{)}^{\prime }$ is equal to

ABCD is a rectangle with vertex A(0,0) as shown in below figure where P and Q are midpoints of sides CD and BC respectively. If C =(5,6) then find the coordinates of P and Q.

There are n letters and n addressed envelopes. The probability that all the letters are not kept in the right envelope, is

Line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

If the tangents at P and Q in the parabola meet in T, then which of the following statements are correct.

1. TP and TQ subtends equal angle at the focus S

2. $S{T}^2$ = SP.SQ

Analyze the given table:





The correct equation for the given table is .

If $\frac{dy}{dx}-y=y^2(\sin x+\cos x)$ with $y\left(0\right)=1$, then the value of $y\left(\pi \right)$ is

If circle $x^2+y^2-6x-10y+c=0$ does not touch (or) intersect the coordinates axes and the point $(1,4)$ is inside the circle, then the range of $c$ is

Let $f:[1,1]\to R$ be a function defined by
$f\left(x\right)=\{\begin{array}{cc}{x}^2\left|\cos \frac{\pi }{x}\right|& \text{for}x\ne 0,\\ 0& \text{for}x=0.\end{array}$
The set of points where $f$ is $not$ differentiable is

There are $3$ bags A, B and C. Bag A contains $1$ Red and $2$ Green balls, bag B contains $2$ Red and $1$ Green balls and bag C contains only one Green ball. One ball is drawn from bag A and put into bag B then one ball is drawn from bag B and put into bag C and finally one ball is drawn from bag C and put into bag A. When this operation is completed, probability that bag A contains $2$ Red and $1$ Green balls, is -

The sum $1+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\cdot \cdot \cdot +\frac{1^3+2^3+3^3+\cdot \cdot \cdot +{15}^3}{1+2+3+\cdot \cdot \cdot +15}-\frac{1}{2}(1+2+3+\cdot \cdot \cdot +15)$ is equal to :

Let $\alpha$ and $\beta$ are two real roots of the equation $(k+1){\tan }^{2}x-\sqrt{2}\lambda \tan x=1-k,$ where $k\ne -1$ and $\lambda$ are real numbers. If ${\tan }^2(\alpha +\beta )=50,$ then the value of $\lambda$ is