Explore topic-wise InterviewSolutions in .

A $\times$ A $\times$ A has 512 elements. Find the number of elements in A.

For $r=0,1,...,10$, let $A_r,B_r$ and $C_r$ denote, repsectively, the coefficientt of $x^r$ in the expansions of $(1+x{)}^{10},(1+x{)}^{20}$ and $(1+x{)}^{30}$. The ${\sum }_{r=1}^{10}A-r(B_{10}{B}_r-C_{10}{A}_r)$ is equal to

Find the identity of the operation a ${}^{\ast }$ b = $\frac{ab}{4}$

No. Of ways in which 12 identical balls can be put in 5 different boxes in a row, if no box remains empty is

Examine whether the following statements are true or false :

(i) {a, b} $\subset ̸$ {b, c, a}

(ii) {a, e} $\subset$ {x: x is a vowel in the English alphabet}

(iii) {1, 2, 3} $\subset$ {1, 3, 5}

(iv) {a} $\subset$ {a, b, c}

(v) {a} $\in$ {a, b, c}

(vi) {x : x is an even natural number less than 6} $\subset$ {x : x is a natural number which divides 36}

The length of perpendicular drawn from the point (5,4, -1) to the line $\overrightarrow{r}=\hat{i}+\lambda (2\hat{i}+9\hat{j}+5\hat{k})$ is

For any empty set $X,$ the value of $n\left(P\right(P\left(P\right(P\left(P\right(X\left)\right)\left)\right)\left)\right)=$

Sum of the first n terms of the series

$\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+\cdots$ is equal to

The expression $\frac{\tan A}{1-\cot A}+\frac{\cot A}{1-\tan A}$ can be written as :

The team played the two matches successfully.

The equation of the locus of the point of intersection of two normals to the parabola $y^2=4ax$ which are perpendicular to each other is

Let $E,F$ and $G$ be finite sets:

Let $X=(E\cap F)-(F\cap G)$ and

$Y=(E-(E\cap G\left)\right)-(E-F)$

Which one of the following is true?

The coefficient of the term independent of $x$ in the expansion of ${(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}})}^{10}$

The range of $f\left(x\right)=\frac{2x}{2+3x}$ is

Which of the following is a fallacy?

$\frac{d}{dx}\left[lo{g}_a^x\right]$

The centre of the hyperbola 2xy+3x+4y+1=0 is

Find the equation of the bisectors of the angle between the lines represented by $3x^2-5xy+4y^2=0$

$If\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha \end{array}\right]\text{is the square root of second order unit matrix,}Then\alpha ,\beta and\gamma \text{should satisfy the relation}$

$ta{n}^{-1}\left(\frac{1}{3}\right)+ta{n}^{-1}\left(\frac{1}{7}\right)+........+ta{n}^{-1}\left(\frac{1}{n^2+n+1}\right)=$

Find out the missing item x of the following distribution, where arithmetic mean $\left(\overline{X}\right)$ is 11.37

$\begin{array}{cccccccc}X& 5& 7& X& 11& 13& 16& 20\\ \text{Frequency (f)}& 2& 4& 29& 54& 11& 8& 4\end{array}$

The system of linear equations $x+y+z=6,x+2y+3z=10,$

$x+2y+2z=4$ will have

If $si{n}^2$z = 1 + $co{s}^2$ y, find the value of $co{s}^2$ z + $si{n}^2$ y

$f\left(x\right)=\frac{1}{x+|x-1|},g\left(x\right)=\frac{1}{x+|x+1|}$

If $x,|x+1|,|x-1|$ are first three terms of an A.P. then the sum of its first $20$ terms is

Which of the following is an empty set

Which of the following can be an alternate representation of variance, where $x_i$ being the midpoint of class intervals, $f_i$ being frequency of class interval and $\overline{x}$ the mean,N = ${\sum }_{i=1}^n{f}_i$

$1.2+{2.2}^2+{3.2}^3+\cdots +n.2^n=(n-1)2^{n+1}+2.$

The polynomial $x^6+4x^5+3x^4+2x^3+x+1$ is divisible by (where $\omega$ is one of the imaginary cube roots of unity)

If $y\left(x\right)$ is the solution of the differential equation

$(x+2)\frac{dy}{dx}=x^2+4x–9,x\ne –2$

$\text{and}y\left(0\right)=0,\text{then}y(–4)$is equal to :

Find the coefficient of $x^3$ in the expansion of $(1+x+x^2{)}^5$

Find the domain and range of the real function $f\left(x\right)=\frac{1}{1-x^2}$

Let $f:[0,1]\to R$ be such that $f\left(xy\right)=f\left(x\right)\cdot f\left(y\right)$, for all $x,y\in [0,1]$, and $f\left(0\right)\ne 0$. If $y=y\left(x\right)$ satisfies the differential equation, $\frac{dy}{dx}=f\left(x\right)$ with $y\left(0\right)=1,\text{then}y\left(\frac{1}{4}\right)+y\left(\frac{3}{4}\right)$ is equal to :

Check whether the following sentences are statements.

(i) Answer this question.

(ii) Everyone in this room is rich.

(iii) There is no rain without clouds.

(iv) Mathematics is fun.

(v) She is a commerce graduate.

(vi) $\sqrt{2}$ is a rational number.

(vii) Fire is always hot.

(viii) The sides of a quadrilateral have equal length.

Let W denote the words in the English dictionary. Define the relation R by $R=\left\{\right(x,y)ϵW\times W|$ the words x and y have at least one letter in common.} Then R is

If $a$ and $b$ are rational numbers and $b$ is not a perfect square, then the quadratic equation with rational coefficients whose one root is $\frac{1}{a+\sqrt{b}}$, is

Given three sets $A,B\&C$such that $A\subset B$ and $B\&C$ are disjoint sets, then the correct representation of the three sets is:

The area (in sq. units) bounded by the curves $C_1:y=2x-x^2,x\in R$ and $C_2:y=\tan \left(\frac{\pi }{4}x\right),x\in [0,2)$ is equal to

In a $\Delta ABC,if\angle C={30}^{\circ },a=47cmandb=94cm$, then the triangle is

Solution set of $\frac{3x-4}{2}\ge \frac{x+1}{4}-1$ is