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Solve $|x+1|-|1-x|=2$

If $p$ is true, $q$ is false and $r$ is false, then which of the following is true?

If $(3x{)}^{log3}=(4y{)}^{log4}$ and $(4{)}^{logx}=(3{)}^{logy}$, then x equals

Find the mean deviation about the median for the data given below.

45, 36, 50, 60, 53, 46, 51, 48, 72, 42

Prove that cos 4x = 1 - 8 sin${}^{2}x{\text{cos}}^{2}x$.

Find the set of real values of x for which ${\log }_2$ ($x^2$ - x - 6) + ${\log }_{0.5}$ (x - 3) < 2${\log }_{2}3$.

If $(x_1,y_1)$ is a point inside the circle $x^2+y^2+2gx+2fy+c=0$ Given two expressions $S_1$ and $T_1$ such that,

$S_1=x_1^2+{y_1}^2+2g{x}_1+2f{y}_1+c$

$T_1=x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c$

Then the equation of chord centered at $(x_1,y_1)$ is

Which of the following is /are correct?

We wish to select 6 persons from 8, but if the person A is chose, then B must be chosen. In how many ways can the selection be made ?

The term independent of x in $(x^2-\frac{1}{x}{)}^9$ is

How many dissimilar terms are there in the expansion of $(x+y{)}^{25}$

The number of terms which are free from radical

signs in the expansion of $(y^{\frac{1}{5}}+x^{\frac{1}{10}}{)}^{55}$ is

If $P(\frac{1+t}{\sqrt{2}},\frac{2+t}{\sqrt{2}})$ be any point on a line, then the range of values of t for which the point P lies between the parallel lines x + 2y = 1 and 2x + 4y = 15, is

Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25} and R be a relation defined from A to B as

R = {(x,y): x $ϵ$ A, y $ϵ$ B and y =$x^2$}

(i) Depict this relation using arrow diagram.

(ii) Find domain of R.

(iii) Find range of R.

(iv) Write codomain of R.

(v) Does the truthfulness and honesty may have any relation?

The digits of a three-digit positive integer are in A.P. and their sum is $15$. The number obtained by reversing the digits is $594$ less than the original number. Then the number is

Which of the following options has (have) the correct combination of the function and its graph?

Let $f\left(x\right)=\frac{3}{x-2}-\frac{1}{x+3}$ and $g\left(x\right)=\frac{x^2-4x+19}{x^2+x-6}$. If $f\left(x\right)=g\left(x\right)$, then $x=$

Superman is going on a vacation to his home planet krypton from earth via. Sun. (Let's assume for a moment that Krypton is not destroyed). His energy v/s distance travelled graph is as shown below:

At which point is superman's (dE/ds) positive?

The general solution of the inequality $-9\le 1-2(x+3)<1$ and $-5\le \frac{x-9}{2}\le 8$ is

If (a+ib)(c+id)(e+if)(g+ih)=A+iB, then ($a^2$+$b^2$)($c^2$+$d^2$)($e^2$+$f^2$)($g^2$+$h^2$)=

The coefficient of three consecutive terms in the expansion of $(1+x{)}^n$ are in the ratio 1 : 7 : 42. Find r and n. Also, determine the square root of n + 1-r.

Or

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

Given that ($\overline{x}$) is the mean and ${\sigma }^2$ is the variance of n observations $x_1,x_2,....x_n$. Prove that the mean and variance of the observations $a{x}_1,a{x}_2,a{x}_3...a{x}_n$are a$\overline{x}$ and $a^2{\sigma }^2$ respectively $(a\ne 0)$

Calculate mean deviation about mean and median for given observations {1, 1, 4, 2, 6, 100, 150, 200, 400}

If Z = $\frac{13-5i}{4-9i}$ can be written in a+ib. Find the value of a+b.

Find the numerically greatest term in the expansion of $(4+6x{)}^{24}$ when $x=\frac{1}{6}$.

The Side of $△$ ABC are $AB=\sqrt{13}cm,BC=4\sqrt{3}cm,CA=7cm$, Then $sin\theta$,
Where $\theta$ is the smallest angle of the triangle, is equal to

Find the general solutions of cos 4x = cos 2x

Which of the following is/are compound events?

If $|z-\frac{4}{z}|$ = 2, then the maximum value of $\left|z\right|$ is equal to

The coefficient of $x^{10}$ in $(1+x+x^2+x^3{)}^5$ is

The negation of the compound statement $p\vee (\sim p\vee q)$ is ___.

If sin $\theta =\frac{-4}{5}$ and $\pi <0<\frac{3\pi }{2}$, find the values of all the other five trigonometric functions.

Solution set of the inequality $lo{g}_{0.8}\left(lo{g}_6\frac{x^2+x}{x+4}\right)<0$

If 7 points out of 12 are in the straight line, then the numbers of triangles formed by joining them is

Given both vector A & B have the same magnitude of 1 unit. Find $\overrightarrow{c}$ such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$?

Given the following data:

Find X if the ratio between Laspeyre's and Paasche's index number is 28:27.

Find the derivative of $y\left(x\right)=\frac{x^3}{(x+1{)}^2}$ with respect to $x$.

If z = x+ iy is a complex number such that |z| = Re(iz)+1, then the locus of z is

An urn contains 9 red, 7 white and 4 black balls. If two balls are drawn at random find the probability that

(i) both the balls are red.

(ii) one is white and other is red.

(iii) the balls are of same Colour.

Or

A box contains 10 bulbs, of which just three are defective. If at random a sample of five bulbs is drawn, find the probabilities that the sample contains

(i) exactly one defective bulb.

(ii) exactly two defective bulbs.

(iii) no defective bulbs.

Find the slope of the line, which makes an angle of ${30}^{\circ }$ with the positive direction of y - axis measured anticlockwise.

Write down the truth value of statement 'Delhi is in India and 3 + 3 = 6.'

If $cos\theta +2cos\varphi +3cos\Psi =sin\theta +2sin\varphi +3\Psi =0,$ then $sin3\theta +8sin3\varphi +27sin3\psi =$

If sin(${log}_e$ $i^i)$ = A+iB where i = $\sqrt{-1}$.Find the value of cos(${log}_e$ $i^i)$.

The coefficient of $x^4$ of the expression ( 1 + 5x +$9x^2+......\infty \left)\right(1+x^2{)}^{11}$ is

If one root of the quadratic equation $a{x}^2$ + bx + c = 0 is equal to the n^th power of the other root, then the value of $(a{c}^n{)}^{\frac{1}{n+1}}$ + $(a^{n}c{)}^{\frac{1}{n+1}}$

The first term of a harmonic is $\frac{1}{7}$ and the second term is $\frac{1}{9}$. The ${12}^{th}$ term is