The absolute difference of the coefficients of \(x^{10}\) and \(x^7\) in the expansion of \(\left(2x^2 + \frac{1}{2x}\right)^{11}\) is equal to:
Let \( A = \{1, 2, 3, 4, 5, 6, 7\} \). Then the relation \( R = \{(x, y) \in A \times A : x + y = 7\} \) is:
If the number of words, with or without meaning, which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k , is equal to
The number of solutions of tanx+secx=2cosx, n(0,2π) are?
Area of the Region bounded by the curve y=√49-x2 and x-axis is .
If the line ax+by+c=0 is a normal to the curve xy=1, then
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If the value of real number a> 0 for which \(x^2\)-5ax+1-0 and \(x^2-a x-5-0\) have a common real root is \(\frac{3}{\sqrt{2 \beta}}\) then \( \beta\) is equal to_______
Let $A =\left[ a _{i j}\right], a _{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$ The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is _____
Let $A$ be the event that the absolute difference between two randomly choosen real numbers in the sample space $[0,60]$ is less than or equal to a If $P(A)=\frac{11}{36}$, then a is equal to _____
Let the area of the region $\left\{(x, y):|2 x-1| \leq y \leq\left|x^2-x\right|, 0 \leq x \leq 1\right\}$ be $A$ Then $(6 A +11)^2$ is equal to ____
Let A be a $n \times n$ matrix such that $| A |=2$ If the determinant of the matrix$\operatorname{Adj}\left(2 \cdot \operatorname{Adj}\left(2 A ^{-1}\right)\right) \cdot$ is $2^{84}$, then $n$ is equal to ____