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Let A = {1, 2, 3, 4, 5, 6}. Define a relation on set A by R = {(X, Y): y = x +1}

(i) Depict this relation using an arrow diagram.

(ii) Write down the domain, codomain and range of R.

Find the general solutions of $2co{s}^{2}x+\sqrt{3}cosx=0$

Find the centre of the sphere

$x^2+y^2+z^2+2z-x=0$

The greatest integer less than or equal to $(\sqrt{2}+1{)}^6$ is

The solution set of the inequality $|[|x|-5]|-7<0$ is

$\left(\right[.]$ denotes the greatest integer function$)$

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is:

In the expansion of $(x+a{)}^n$, if the sum of odd terms be P and sum of even terms be Q. Consider the following statements:

(i) $P^2-Q^2=(x^2-a^2{)}^n$

(ii) $P^2+Q^2=(x^2+a^2{)}^n$

(iii) 4PQ = $(x+a{)}^{2n}-(x-a{)}^{2n}$

(iv) P - Q = $(x-a{)}^n$

Then the correct statement are:

Let $A,B$ & $C$ be $3$ arbitary events defined on a sample space $S$ and if, $P\left(A\right)+P\left(B\right)+P\left(C\right)=p_1,P(A\cap B)+P(B\cap C)+P(C\cap A)=p_2$ & $P(A\cap B\cap C)=p_3$, then the probability that exactly one of the three events occurs is given by:

Solve $\frac{|x-2|-1}{|x-2|-2}\le 0,xϵR$.

If $z$ is a complex number such that $|z-3+2i|=4$ and $m,M$ are the minimum and maximum values of $|z|$ respectively, then the value of $m^2+M^2$ is equal to

$co{s}^2{48}^0-si{n}^2{12}^0$ =

${lim}_{\pi \to \infty }\frac{1^{99}+2^{99}+3^{99}+\cdots \cdots n^{99}}{n^{100}}=$ [EAMCET 1994]

Which of the following statements is not a tautology?

How many 3-digit numbers can be formed by using the digits 1 to 9, if no digit is repeated?

Find the perpendicular distance of (1,1) from $x-y+\sqrt{2}$

If $|5x+6|+4<1$, then $x\in$

Find the number of solutions of $sinx=\left(\frac{x}{10}\right)$.

If $c$ is a point at which Rolle's theorem holds for the function, $f\left(x\right)={\log }_e\left(\frac{x^2+\alpha }{7x}\right)$ in the interval $[3,4]$, where $a\in R$, then $f"\left(c\right)$ is equal to:

Find the ${20}^{th}$ term in the binomial expansion of $(1+x{)}^{20}$ when $x=-5$

The number of numbers from 1 to ${10}^{100}$ having the sum of their digits equal to 3 is

If $(1+x{)}^n=\sum _{r=0}^n{a}_r{x}^r$, then $(1+\frac{a_1}{a_0})(1+\frac{a_2}{a_1})\dots (1+\frac{a_n}{a_{n-1}})$ is equal to

$P\left(n\right):5^{2n+1}+3^{n+2}{.2}^{n-1}$ is divisible by

Find the sum of the series ${}^n{C}_0{}^n{C}_2+{}^n{C}_1{}^n{C}_3+{}^n{C}_2{}^n{C}_4.....{}^n{C}_{n-2}{}^n{C}_n$

The equation of the curve which passes through the point (2a,a) and for which the sum of the Cartesian sub tangent and the abscissa is equal to the constant a is

Let $A$ be a matrix such that $A\cdot \left[\begin{array}{cc}1& 2\\ 0& 3\end{array}\right]$ is a scalar matrix and $|3A|=108$. Then $A^2$ equals :

The equation of the line passing through $(-4,3,1)$, parallel to the plane $x+2y-z-5=0$ and intersecting the line $\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z-2}{-1}$ is:

If $\tan \theta =\frac{5}{12}$ and $\theta$ is not in the fourth quardrant then $\frac{\tan ({90}^{\circ }+\theta )-\sin ({180}^{\circ }-\theta )}{\sin ({270}^{\circ }-\theta )+cosec({360}^{\circ }-\theta )}=$

Represent the given set in Roster form

A = {x: x is an integer, $\frac{-3}{2}$ < x < $\frac{11}{2}$}

If $y=\frac{\ln x}{x}$, then $\frac{dy}{dx}$ will be

The value of ${-}^{15}{C}_1+2\times {}^{15}{C}_2-3\times {}^{15}{C}_3+...-15\times {}^{15}{C}_{15}+{}^{14}{C}_1{+}^{14}{C}_3+{}^{14}{C}_5+...+{}^{14}{C}_{11}$ is :

If $n$ is an integer and

${(1+i\sqrt{3})}^n+{(1-i\sqrt{3})}^n=2^{n+1}\cos \theta ,$ then $\theta$ is equal to

Area bounded by the curve $y=x{e}^{x^2}$ x - axis and the ordinates x = 0, x = a

IF $S_n={\sum }_{r=0}^n\frac{1}{{}^n{C}_r}$ and $t_n={\sum }_{r=0}^n\frac{r}{{}^n{C}_r},$ then $\frac{t_n}{S_n}$ is equal to

Let one root of $a{x}^2+bx+c=0$ where $a,b,c$ are integers be $3+\sqrt{5}$, then the other root is

If $\frac{1}{b-a}+\frac{1}{b-c}=\frac{1}{a}+\frac{1}{c},$ then a,b,c, are in

A steel wire $2\text{m}$ long is suspended from the ceiling. When a mass is hung at its lower end, the increase in length recorded is $1\text{cm}$. Determine the strain in the wire.

The value of ${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$ is

Number of divisors of n=38808 (except 1 and n) is

[RPET 2000]

The power set of the set $D=\varnothing$ is

A solution of the equation ${\log }_2(\sin x+\cos x)-{\log }_2\left(\cos x\right)+1=0$ in $(-\frac{\pi }{4},\frac{\pi }{4})$ is

Please go through the following formulas for derivatives. You can move to next question by pressing NO.

List of formulas

Let $f\left(x\right)=\{\begin{array}{cc}\frac{3x(x-1)}{x^2-3x+2}& \text{for}x\ne 1,2\\ -3& \text{for}x=1\\ 4& \text{for}x=2\end{array}$ .Then f(x) is continuous

An equilateral triangle is inscribed in the parabola $y^2=4ax$ such that one vertex of this triangle coincides with the vertex of the parabola. The length of side of this triangle is

The angle between the pair of straight lines $x^2-y^2-2y-1=0$, is

If $A\subseteq B$ then for any set C, prove that $(C-B)\subseteq (C-A)$

A student is constructing a family tree. If he wants to track back through $10$ generations to calculate the total number of ancestors he has, then the total number of ancestors after the ${10}^{th}$ generation is