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Rajesh reads $\frac{2}{9}$ of a book on Friday, $\frac{1}{3}$ of it on Saturday and the remaining $160$ on Sunday. How many pages does the book have in all?

If the new coordinates of the point (1,2,3) when the origin shifts from (0,0,0) to (3,4,6) is (l,m,n) then find the value of -(l+m+n)

If ${}^n{C}_r=C_r$ then $C_0+(C_0+C_1)+(C_0+C_1+C_2)+....+(C_0+C_1+.....+C_n)$ =

The value of $\sum _{r=0}^{50}(-1{)}^r\frac{{}^{50}{C}_r}{r+2}$ is equal to

If $\cos x+\sin x=\frac{1}{2}$, where $x\in (0,\pi )$, then the maximum possible value of $\tan x$ is

The resultant force of 5 N and 10 N can not be

Find the value of $\frac{cos\left(\frac{5\pi }{4}\right)cos\left(\frac{-\pi }{4}\right)}{sin\left(\frac{3\pi }{4}\right)cos\left(\frac{3\pi }{4}\right)}$

Find the 20th term of the series 3 + $\frac{1}{2}$(3 + 5) + $\frac{1}{3}$(3 + 5 + 7) + $\frac{1}{4}$(3 + 5 + 7 + 9) + .........

Equation of the locus of the pole with respect to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ of any tangent line to the auxiliary circle is the curve

$\frac{x^2}{a^4}+\frac{y^2}{b^4}={\lambda }^2$ where

In how many ways can the letters of the word ASSASSINATION be arranged so that all the 'S' s are together?

If R denotes circum radius, then, in $△ABC,\frac{b^2-c^2}{2aR}$ is equal to

If $z_{1}and{z}_2$ are two complex number and a,b are two real numbers, then

$|a{z}_1-b{z}_2{|}^2+|b{z}_1+a{z}_2{|}^2$ equals

The number of real roots of the equation $5+|2^x-1|=2^x(2^x-2)$ is

The unit vector which is orthogonal to the vector $3\hat{i}+2\hat{j}+6\hat{k}$ and is coplanar with the vectors $2\hat{i}+\hat{j}+\hat{k}and\hat{i}-\hat{j}+\hat{k}$

If $i{z}^3+z^2-z+i=0$, then $|z|$ equals

Find the value of $\theta$, if the equation $\cos \theta x^2-2\sin \theta x-\cos \theta =0$ has real roots

Slope of tangent to $x^2=4y$ from (-1, -1) can be

Let $A$ and $B$ be two non-null events such that $A\subset B.$ Then, which of the following statements is always correct?

The points (a, b), (c, d) and $(\frac{kc+la}{k+l},\frac{kd+lb}{k+l})$ are

If two different numbers are taken from the set {0, 1, 2, 3,.... 10}, then the probability that their sum as well as absolute difference are both multiple of 4, is ?

If (i, j)th element of matrix A is 2+3i , what is the corresponding element in A* or conjugate of A.

The solution set of the equation $x^{lo{g}_x(1-x{)}^2}=9$ is

1. 2048

If A=(2,4) and B=[3, 5), find $A\cap B$.

The sum of all two digit positive numbers which when divided by $7$ yield $2$ or $5$ as remainder is :

$x^2-11x+a$ and $x^2-14x+2a$ will have a common factor, if a =

Area bounded by $y=x^3,y=8$ and $x=0$ is ……..

If A = ф, n(B) = 4 then n(A x B) is

A confused student multiplies a number x by 6, instead of dividing it by 6. What is the percentage change in the result due to his mistake?

Consider the following population and year graph, find the slope of the line AB and using it, find what will be the population in the year 2010?

If for all real triplets $(a,b,c)$, $f\left(x\right)=a+bx+c{x}^2$; then $\underset{0}{\overset{1}{\int }}f\left(x\right)dx$ is equal to :

If A and B are two sets containing 3 and 6 elements respectively, what can be the maximum number of elements in $A\cup B$?
Find also the minimum number of elements in $A\cup B$

A box has 50 pens of which 20 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement, at most one is defective?

Calculate the price index no by: (a) Laspeyre's method (b) Paasche's method:

Find the sum of the powers of X and Y of ${17}^{th}$ term in the expansion of $(X+Y{)}^{21}$

Find the set of values of $\lambda$ for which the

line $3x-4y+\lambda =0$ intersects the ellipse

$\frac{x^2}{16}+\frac{y^2}{a}=1$ at 2 distinct point.

In a plane there are $37$ straight lines of which $13$ pass through point $A$ and $11$ pass through the point $B$. Besides, no three lines pass through one point, no line passes through both $A$ and $B$, and no two lines are parallel.

Then the total number of intersection points of the lines are

A bag contains $30$ tokens numbered serially from $0$ to $29.$ The number of ways of selecting $3$ tokens from the bag, such that sum of numbers on them is $30$, is

Three six faced fair dice are rolled together. The probability that the sum of the numbers appearing on the dice is 8, is

The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $6x^2-11x+\alpha =0$ are rational numbers is :

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $x^2+9y^2=9$, meets its auxiliary circle at the point M. Then the area of the triangle with vertices at A, M and the origin ‘O’ is

Observe the following statements

$\left(i\right)In\Delta ABC,bco{s}^2\frac{C}{2}+cco{s}^2\frac{B}{2}=s$

$\left(ii\right)In\Delta ABC,cot\frac{A}{2}=\frac{b+c}{a}\Rightarrow B={90}^0$

Which of the following is correct?

$\underset{x\to 2}{lim}\frac{sin(e^{x-2}-1)}{log(x-1)}$

1) $cos2x=co{s}^{2}x-si{n}^{2}x$

2) $1+sin2x=(cosx+sinx{)}^2$

3) $1-sin2x=(cosx-sinx{)}^2$

How many of the above statements are correct?

If $z$ and $\omega$ be two non-zero compex numbers such that $|z|=|\omega |$ and $arg\left(z\right)+arg\left(\omega \right)=\pi$, then $z$ equals