Mathematics Tes...

If \(a_{0}, a_{1}, a_{2}, \ldots,\) be the coefficients in the expansion of \(\left(1+x+x^{2}\right)^{n}\) in ascending powers

of \(x,\) then \(a_{0} a_{1}-a_{1} a_{2}+a_{2} a_{3}-\ldots\)

find the 7 th term in the expansion of \(\left(4 x-\frac{1}{2 \sqrt{x}}\right)^{13}\) ?

The coefficient of \(x^{m}\) in \(:(1+x)^{m}+(1+x)^{m+1}+\ldots .+(1+x)^{n}, \quad m \leq n\) is ?

Value of \(20_{1}^{C}-2 \times 20_{2}^{C}+3 \times 20_{3}^{C} \ldots 20 \times 20_{2}^{C} 0\) is :

In the expansion of (1 + x)ⁿ(1 + y)ⁿ(1+ z)ⁿ, then the sum of coefficients of the terms of degree mm is :

\(\sum_{r=0}^{n-1} \frac{{ }^{n} C_{r}}{{ }^{n} C_{r}+{ }^{n} C_{r+1}}\) ?

If matrix A is an circulant matrix whose elements of first row are a, b, c all >0 such that abc =1

and A^TA = I then a³+ b³+ c³ equals :