A has 5 elements and B has 2 elements. The number of subsets of A × B such that the number of elements in subset is more than or equal to 3 and less than 6, is?
Let $f:(0,1) \rightarrow R$ be a function defined by
$f(x)=\frac{1}{1-e^{-x}}$, and $g(x)=(f(-x)-f(x))$ Consider two statements
(I) $g$ is an increasing function in $(0,1)$
(II) $g$ is one-one in $(0,1)$Then,
Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.Let a be the area of the triangle ABC. Then the value of (64a)2 is
The line \(x=8\) is the directrix of the ellipse \(E : \frac{x^2}{ a ^2}+\frac{y^2}{b^2}=1\)with the corresponding focus \((2,0)\) If the tangent to \(E\)at the point \(P\) in the first quadrant passes through the point \((0,4 \sqrt{3})\)and intersects the\(x\)-axis at \(Q\), then \((3 PQ )^2\)is equal to ____
The coefficient of x7 in (1 – 2x + x3)10 is?
Let the sixth term in the binomial expansion of \(({\sqrt{2}^{log_{2}}(10-3^{x})+\sqrt[5]{2^{(x-2)log_{2}{3}}}})^{m}\), in the increasing powers of \(2^{(x-2)log_{2}3}\), be 21 If the binomial coefficients of the second, third and fourth terms in the expansion are respectively the first, third and fifth terms of an AP, then the sum of the squares of all possible values of x is
The sum of the common terms of the following three arithmetic progressions\(3,7,11,15, \ldots , 399\), \(2,5,8,11, \ldots , 359\)and \(2,7,12,17, \ldots , 197,\) is equal to _____
Number of integral solutions to the equation \(x+y+z=21\), where \(x \geq 1\), \(y \geq 3\), \(z \geq 4\), is equal to ___