PUC Science Class 11 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find the 5th term from the end in the expansion of \[\left( 3x - \frac{1}{x^2} \right)^{10}\]

Find the 8th term in the expansion of  \[\left( x^{3/2} y^{1/2} - x^{1/2} y^{3/2} \right)^{10}\]

Find the 7th term in the expansion of \[\left( \frac{4x}{5} + \frac{5}{2x} \right)^8\]

Find the 4th term from the beginning and 4th term from the end in the expansion of \[\left( x + \frac{2}{x} \right)^9\] .

Find the 4th term from the end in the expansion of \[\left( \frac{4x}{5} - \frac{5}{2x} \right)^8\] .

Find the 7th term from the end in the expansion of \[\left( 2 x^2 - \frac{3}{2x} \right)^8\] .

Find the sixth term in the expansion  \[\left( y^\frac{1}{2} + x^\frac{1}{3} \right)^n\] , if the binomial coefficient of the third term from the end is 45.

Find n in the binomial \[\left( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}} \right)^n\] , if the ratio of 7^th term from the beginning to the 7^th term from the end is  \[\frac{1}{6}\]

if the seventh term from the beginning and end in the binomial expansion of  \[\left( \sqrt[3]{2} + \frac{1}{\sqrt[3]{3}} \right)^n\] are equal, find n.

Write the number of terms in the expansion of \[\left( 2 + \sqrt{3}x \right)^{10} + \left( 2 - \sqrt{3}x \right)^{10}\] . 

Write the number of terms in the expansion of \[\left( 2 + \sqrt{3}x \right)^{10} + \left( 2 - \sqrt{3}x \right)^{10}\] . 

Write the number of terms in the expansion of \[\left( 1 - 3x + 3 x^2 - x^3 \right)^8\]

Which term is independent of x, in the expansion of \[\left( x - \frac{1}{3 x^2} \right)^9 ?\]

Write the number of terms in the expansion of  \[\left[ \left( 2x + y^3 \right)^4 \right]^7\] .

Find the number of terms in the expansion of\[\left( a + b + c \right)^n\]

If rth term in the expansion of \[\left( 2 x^2 - \frac{1}{x} \right)^{12}\]  is without x, then r is equal to

If the fifth term of the expansion  \[\left( a^{2/3} + a^{- 1} \right)^n\]  does not contain 'a'. Then n is equal to

The coefficient of \[x^{- 3}\]  in the expansion of \[\left( x - \frac{m}{x} \right)^{11}\]  is

The coefficient of the term independent of x in the expansion of \[\left( ax + \frac{b}{x} \right)^{14}\] is 

If the coefficients of the (n + 1)^th term and the (n + 3)^th term in the expansion of (1 + x)²⁰are equal, then the value of n is