Explore topic-wise InterviewSolutions in .

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two non-parallel unit vectors in a plane. If the vectors $(\alpha \overrightarrow{a}+\overrightarrow{b})$ bisects the internal angle between $\overrightarrow{a}$ and $\overrightarrow{b}$, then $\alpha$ is

Question 68

In the following question, state whether the statement is True (T) or False (F):

Some of the factors of $\frac{n^2}{2}+\frac{n}{2}$ are $\frac{1}{2}n$ and (n+1).

A sample of 35 observations has the mean 80 and standard deviation as 4. A second sample of 65 observations from the same population has mean 60 and standard deviation 3. Then the standard deviation of the combined sample is

Let $f\left(x\right)=x^2-px+q,$ p is an odd positive integer and the roots of the equation $f\left(x\right)=0$ are two distinct prime numbers, if $p+q=35$, then the value of $f\left(10\right)\left({\sum }_{r=1}^{10}f\right(r\left)\right)-878$ equal to ___

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time (ii) all letters are used at a time (iii) all letters are used but first letter is a vowel ?

Explain why the tax multiplier is smaller in absolute value than the government expenditure multiplier.

The equation of circle which passes through focus of parabola $x^2=4y$ and touches it at $(6,9)$ is

The total revenue in Rupees received from the sale of $x$ units of a product is given by

$R\left(x\right)=3x^2+36x+5$. The marginal revenue, when

$x=15$ is

If $x^2+6+2i=(y^2-y)i+5x,$ then $(x,y)$ cannot be equal to

The coefficient of $x^{-3}$ in the expansion of ${(x-\frac{m}{x})}^{11}$ is

Let $T$ be the mean life of a radioactive sample. $75\%$ of the active nuclei present in the sample initially will decay in time

If $m$ and $n$ are whole numbers such that $m^n=121,$ the value of $(m-1{)}^{n+1}$ is

If $x=a+\frac{a}{r}+\frac{a}{r^2}+\cdots \infty ,$ $y=b-\frac{b}{r}+\frac{b}{r^2}-\cdots \infty$ and $z=c+\frac{c}{r^2}+\frac{c}{r^4}+\cdots \infty$ for $|r|>1,$ then the value of $\frac{xy}{z}$ is

Real part of $e^{e^{i\theta }}$ is

The area of the triangle formed by the tangent and the normal to the parabola $y^2=4ax$, both drawn at the same end of the latus rectum, and the axis of the parabola is

If the roots of the equation $\frac{x^2+4x}{8x+6}=\frac{k-1}{k+1}$ are equal in magnitude and opposite in sign, then the value of $k$ is

If $a,b,c$ are the sides of a triangle $ABC$ opposite to angles $A,B,C$ respectively and angle $C$ is ${90}^{\circ },$ then $\tan A+\tan B$ is equal to

If x and y
are connected parametrically by the equation, without eliminating the
parameter, find.

Find
if

(i) How many different words can be formed by using all the letters of the word, 'ALLAHABAD'?

In how many of them :

(ii) Both L's do not come together ?

(iii) The vowels occupy the even positions ?

The maximum value of the function $y=2\tan x-{\tan }^{2}x$ over $[0,\frac{\pi }{2}]$ is

If S(3, 4) & S’(9, 12) are two foci of an ellipse. If the foot of perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then eccentricity of the ellipse is

Given that the points A(3, 2, -4), B(5, 4, -6) and C(9, 8, -10) are collinear, the ratio in which B divides $\overline{AC}$ is :

A vector $\overrightarrow{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}(\alpha ,\beta \in R)$ lies in the plane of the vectors, $\overrightarrow{b}=\hat{i}+\hat{j}$ and $\overrightarrow{c}=\hat{i}-\hat{j}+4\hat{k}$. If $\overrightarrow{a}$ bisects the angle between $\overrightarrow{b}$ and $\overrightarrow{c},$ then