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If $1\le r\le n$ then $n^{n-1}{C}_{r-1}$ is equal to .........

find the domain and range of the real function f defined by $f\left(x\right)=\sqrt{x-1}$

Or

Let f= {(1,1), (2,3),(0,-1),(-1,-3)} be a function from Z to Z defined by f(x) = ax+b from some integers a and b. Determine a and b.

The quadratic equation whose roots are $si{n}^2{18}^{\circ }$ and $co{s}^2{36}^{\circ }$ is

Which one of the following compounds has the ratio of radius of cation and anion smallest

If ${}^n{C}_x{=}^n{C}_y$ then

In the system $A_{\left(g\right)}$ $\leftrightharpoons$ 2$B_{\left(g\right)}$ + 3$C_{\left(g\right)}$if the concentration of 'C' at equilibrium is increased by a factor of 2, it will cause the equilibrium concentration of B to change to:

O is the origin and A is the point (3,4). If a point P moves so that the line segment OP is always

parallel to the line segment OA, then the equation to the locus of P is

If $-\frac{\pi }{2}<x<\frac{\pi }{2}$ and the sum to infinite number of terms of the series$cosx+\frac{2}{3}cosxsi{n}^{2}x+\frac{4}{9}cosxsi{n}^{4}x+.....$ is finite, then $x$ lies in the set

The mean deviation from the mean for the set of observations – 1, 0, 4 is

Find the integral of the given function w.r.t - x

$y=e^{(5x+10)}$

In 2011-2012, total production of foodgrains was 1,928 lakh tonnes of which production of rice, wheat and other crops were 860, 708 and 360 lakh tonnes, respectively. The percentage share of rice, wheat and other crops in the total production of foodgrains were 44.60, 36.72 and 18.68 respectively. Present their information in the form of a table indicating its various parts.

The value of $1+\frac{4}{7}+\frac{9}{7^2}+\frac{16}{7^3}+\frac{25}{7^4}+\cdots \text{upto}\infty$ is

The domain of the function $f\left(x\right)=e^{\left(\sqrt{5x-3-2x^2}\right)}$ is

The value(s) of $x$ satisfying the equation $x^9+\frac{9}{8}{x}^6+\frac{27}{64}{x}^3-x+\frac{219}{512}=0$ is/are

Dhoni and Raina are standing in the field at point $a=(3,4)$ and $b=(6,8)$ respectively. The shortest distance (in units) between them is

Given $f\left(x\right)=log\left(\frac{1+x}{1-x}\right)andg\left(x\right)=\frac{3x+x^3}{1+3x^2}$ then fog (x) equals

If

$f\left(x\right)=\{\begin{array}{cc}xsin\frac{1}{x}& x\ne 0\\ 0& x=0\end{array},$

then $\underset{x\to 0}{lim}f\left(x\right)=$

Solve the integral $I={\int }_0^{\pi }{\sin }^{2}xdx$

Evaluate: $\int \left(\cos \right(x)+x^2)dx$

Solution set of $(x^2-1)(x^3-1)(x^4-1)>0$ is

If A and G are respectively the arithmetic and geometric means between two distinct positive numbers a and b then prove that A>G.

(i) Find the remainder, when $5^{99}$ is divided by 13.

(ii) If the middle term of ${(\frac{1}{x}+xsinx)}^{10}$ is equal to $7\frac{7}{8}$, then find the value of x.

The smallest positive values of x and y that satisfy 2(sinx + sin y) - 2 cos (x - y) = 3 is

For the equation $x^2$ - 2ax + $a^2$ - 1 = 0, the values of 'a' for which 3 lies in between the roots of given equation is

The number of all the possible triplets $(a_1,a_2,a_3)$ such that $a_1+a_{2}cos\left(2x\right)+a_{3}si{n}^2\left(x\right)=0$ for all x is

Sum of the series S = 1 + $\frac{1}{2}$(1 + 2) + $\frac{1}{3}$(1 + 2 + 3) + $\frac{1}{4}$ (1 + 2 + 3 + 4) + .........upto 20 terms is

Write the first five terms of the sequences whose $n^{th}$ term is :

$a_n=2^n$

The values of $\theta$ satisfying $\sin 7\theta =\sin 4\theta -\sin \theta$ in 0 < $\theta$ < $\frac{\pi }{2}$ are

Find the mean, variance and standard deviation using short-cut method

$\begin{array}{cccccccccc}\text{Height in cm}& 70-75& 75-80& 80-85& 85-90& 90-95& 95-100& 100-105& 105-110& 110-115\\ \text{No. of children}& 3& 4& 7& 7& 15& 9& 6& 6& 3\end{array}$

Solve for $x$:

$3\left(9^x\right)<8\left(3^x\right)+3$

Write the component statement of the following compound statement and check whether the compound statement is true or false. All living things have two hands and two eyes."

The trigonometric equation $\frac{1-\sin \theta }{1+\sin \theta }$ is equal to
[Given, ${\sin }^2\theta +{\cos }^2\theta =1$]

If a,b,c are in A.P, a ≠ b ≠ c and $x^{c-b}$ $z^{b-a}$ = $y^{c-a}$,then x,y,z are in

The mean and variance of eight observations are 9 and 9.25 respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations

Coefficient of $y^3.x^6$ in the binomial expansion $(x+2y{)}^9$

The general solution of $cosx=cos\alpha ,\alpha ϵ[0,\pi ]$ is

The value of $\frac{{}^{11}{C}_0}{1}+\frac{{}^{11}{C}_1}{2}+\frac{{}^{11}{C}_2}{3}+\cdots +\frac{{}^{11}{C}_{11}}{12}$ will be

If 15 $si{n}^4\alpha$ + 10 $co{s}^4\alpha$ = 6 then the value of 8 $cose{c}^6\alpha$ - 27 $se{c}^6\alpha$ is __.

Reduce the expression $y=\frac{x^2-x+1}{x^2+x+1}$ to the form $a{x}^2+bx+c$ and give condition for x to be real.

The combined equation of the asymptotes for the hyperbola $x^2-2y^2=2$

Write the following as intervals:

(i) {x : x $\in R,-4<x\le 6$}

(ii) {x : x$\in R,-12<x<-10$}

(iii) {x : x $\in R,0\le x<7$}

(iv) {x : x $\in R,3\le x\le 4$}

If $x+\frac{1}{x}=2cos\theta ,then{x}^3+\frac{1}{x^3}=$

In an examination, a question paper consists of 12 questions divided into two parts i.e., part I and part II containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

1. 2