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Diameter of the circle given by $|(z-\alpha )/(z-\beta )|=k,k\ne 1$ , where $\alpha ,\beta$ are fixed points and $z$ is varying point in argand plane is

Let A = {1, 2, 3} and $R=\left\{\right(a,b):|a^2-b^2|\le 5,a,bϵA\}$. Then write R as set of ordered pairs.

What will be the next number in the following sequence?

10, 100, 1000, 10000, _______

If the length of latusrectum of an Ellipse is equal to semi minor axis then Its eccentricity is

The image of the point $(3,-1,11)$ w.r.t the line $\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is:

If $(\sqrt{3}+i{)}^{100}=2^{99}(p+iq),$ then $p$ and $q$ are roots of the equation

The first and last term of an ap are 1 and 11 if the sum of its terms is 36 then a = ______,d=_____,n=_____&a_n=_________

If $y=\sin \left(\log \sin x\right),$ then $\frac{dy}{dx}=$

For every positive integral value of n, $3^n$ > $n^3$ when

If $\int \frac{se{c}^{2}x-2010}{si{n}^{2010}x}dx=\frac{P\left(x\right)}{(sinx{)}^{2010}}+C$

Why constants like gravitational constant are not dimensionless but constants like 2,3 are dimensionless

The value of $I={\int }_0^3\left(\right[x]+[x+\frac{1}{3}]+[x+\frac{2}{3}])dx$, where $[\cdot ]$ denotes the greatest integer function, is equal to

The number of different ways in which a committee of $4$ members formed out of $6$ Asians, $3$ Europeans and $4$ Americans if the committee is to have at least one member from each of the regional groups, is

Let $F\left(x\right)=f\left(x\right)+f\left(\frac{1}{x}\right),$ where $f\left(x\right)=\underset{1}{\overset{x}{\int }}\frac{\log t}{1+t}dt$.

Then the value of $F\left(e\right)$ is:

${lim}_{h\to 0}2\left\{\frac{\sqrt{3}sin(\frac{\pi }{6}+h)-cos(\frac{\pi }{6}+h)}{\sqrt{3h(\sqrt{3}cosh-sinh)}}\right\}$ is equal to

150 workers were engaged to finish a piece of work in a certain number of days. Four workers stopped working on the second day, four more workers stopped their work on the third day and so on. It took 8 more days to finish the work. Then the number of days in which the work was completed is

A and B are two mutually exclusive and exhaustive events. If $P\left(A\right)=\frac{1}{7}$ find the value of $49\times P\left(B\right)$.

If A is a symmetric matrix and B is a skew symmetric matrix of the same order then $A^2+B^2$ is a

The value of $\underset{x\to 0}{lim}\frac{1+\sin x-\cos x+{\log }_e(1-x)}{x^3}$ is

Question 2

The product of two consecutive positive integers is divisible by 2: Is this statement true or false? Give reasons.

The shape of $Xe{F}_2,Xe{F}_4$ and $Xe{O}_2{F}_2$ are respectively.

The range of $f\left(x\right)=\frac{1}{2x^2-6x+7}$ is

The solution y(x) of the differential equation $\frac{d^{2}y}{d{x}^2}=sin3x+e^x+x^2$ when $y_1\left(0\right)=1$ and y(0) = 0 is

Match the functions with their corresponding derivatives.

The sum to $50$ terms of the series $\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+\dots$ is

Which of the following statements are correct ? Write a correct form of each of the incorrect statements.

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

(ii) {a} $ϵ$ {a, b, c}

(iii) a $ϵ$ {(a), b}

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

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

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

(vii) $\varphi ϵ$ {a, b}

(viii) $\varphi \subset$ {a, b, c}

(ix) {x : x +3 = 3} = $\varphi$

The zeroes of the polynomial $f\left(x\right)=x^2-3$ are $x=$