If the mean of the frequency distribution

Class:	\(0-10\)	\(10-20\)	\(20-30\)	\(30-40\)	\(40-50\)
Frequency	\(2\)	\(3\)	\(x\)	\(5\)	\(4\)

is \(28\) , then its variance is \(........\).

The natural number \(m\), for which the coefficient of \(x\) in the binomial expansion of \(\left( x ^{ m }+\frac{1}{ x ^{2}}\right)^{22}\) is \(1540,\) is

Let \(A\) be a non-singular matrix of order \(3\). If \(\det(3 \, \operatorname{adj}(2 \, \operatorname{adj}((\det A)A))) = 3^{-13} \cdot 2^{-10}\) and \(\det(3 \, \operatorname{adj}(2A)) = 2^{m} \cdot 3^{n}\), then \(|3m + 2n|\) is equal to ______.

Let \(N\) denotes the sum of the numbers obtained when two dice are rolled. If the probability that \(2^{ N } < N !\) is \(\frac{m}{n}\), where \(m\) and \(n\) are coprime, then \(4 m -3 n\) is equal to \(......\).

If the area (in \(sq. units\)) of the region \(\left\{ {\left( {x,y} \right):{y^2} \le 4x,x + y \le 1,x \ge 0,y \ge 0} \right\}\) is \(a\sqrt 2  + b\), then \(a -b\) is equal to

Let \(A\,=\,\{\,x\,\in \,R\,:\,x\) is not a positive int eger \(\}\) Define a function \(f\,:\,A\,\to \,R\) as \(f\,(x)\, = \frac{{2x}}{{x - 1}}\) then \(f\) is

In a survey of \(220\) students of a higher secondary school, it was found that at least \(125\) and at most \(130\) students studied Mathematics; at least \(85\) and at most \(95\) studied Physics; at least \(75\) and at most \(90\) studied Chemistry; \(30\) studied both Physics and Chemistry; \(50\) studied both Chemistry and Mathematics; \(40\) studied both Mathematics and Physics and \(10\) studied none of these subjects. Let \(\mathrm{m}\) and \(\mathrm{n}\) respectively be the least and the most number of students who studied all the three subjects. Then \(\mathrm{m}+\mathrm{n}\) is equal to ...........

If \(\mathop {\lim }\limits_{x \to 1} \frac{{{x^2}\,\, - \,ax\, + \,b}}{{x\, - \,1}}\,\, = \,3,\) then \(a + b\) is equal to

Let the centre of a circle, passing through the point \((0,0),(1,0)\) and touching the circle \(x^2+y^2=9\), be \((h, k)\). Then for all possible values of the coordinates of the centre \((h, k), 4\left(h^2+k^2\right)\) is equal to .............

The sum of all natural numbers \(‘n’\) such that \(100 < n < 200\) and \(H.C. F\, (91, n) > 1\) is

Let \({A_n} = \left( {\frac{3}{4}} \right) - {\left( {\frac{3}{4}} \right)^2} + {\left( {\frac{3}{4}} \right)^3} - ..... + {\left( { - 1} \right)^{n - 1}}{\left( {\frac{3}{4}} \right)^n}\) and \(B_n \,= 1 - A_n\) . Then, the least odd natural number \(p\) , so that \({B_n} > {A_n}\), for all \(n \geq p\) is

Let \(\mathrm{x}^{\mathrm{k}}+\mathrm{y}^{\mathrm{k}}=\mathrm{a}^{\mathrm{k}},(\mathrm{a}, \mathrm{K}>0)\) and \(\frac{\mathrm{dy}}{\mathrm{dx}}+\left(\frac{\mathrm{y}}{\mathrm{x}}\right)^{\frac{1}{3}}=0\) then \(\mathrm{k}\) is

If \(y = m _{1} x + c _{1}\) and \(y = m _{2} x + c _{2}, m _{1} \neq m _{2}\) are two common tangents of circle \(x^{2}+y^{2}=2\) and parabola \(y^{2}=x\), then the value of \(8\left|m_{1} m_{2}\right|\) is equal to