PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?

Find the middle terms(s) in the expansion of: 

(vii) \[\left( 3 - \frac{x^3}{6} \right)^7\]

A man saved ₹66000 in 20 years. In each succeeding year after the first year he saved ₹200 more than what he saved in the previous year. How much did he save in the first year?

Find the middle terms(s) in the expansion of:

(viii)  \[\left( 2ax - \frac{b}{x^2} \right)^{12}\]

In a cricket team tournament 16 teams participated. A sum of ₹8000 is to be awarded among themselves as prize money. If the last place team is awarded ₹275 in prize money and the award increases by the same amount for successive finishing places, then how much amount will the first place team receive?

Find the middle terms(s) in the expansion of:

(ix)  \[\left( \frac{p}{x} + \frac{x}{p} \right)^9\]

Find the middle terms(s) in the expansion of:

(x)  \[\left( \frac{x}{a} - \frac{a}{x} \right)^{10}\]

Write the common difference of an A.P. whose nth term is xn + y.

Write the common difference of an A.P. the sum of whose first n terms is

Find the term independent of x in the expansion of the expression: 

(i) \[\left( \frac{3}{2} x^2 - \frac{1}{3x} \right)^9\]

Find the term independent of x in the expansion of the expression:

(ii)  \[\left( 2x + \frac{1}{3 x^2} \right)^9\]

If the sum of n terms of an AP is 2n² + 3n, then write its nth term.

Find the term independent of x in the expansion of the expression: 

(iii)  \[\left( 2 x^2 - \frac{3}{x^3} \right)^{25}\]

Find the term independent of x in the expansion of the expression: 

(iv) \[\left( 3x - \frac{2}{x^2} \right)^{15}\]

Find the term independent of x in the expansion of the expression: 

(v)  \[\left( \frac{\sqrt{x}}{3} + \frac{3}{2 x^2} \right)^{10}\]

Find the term independent of x in the expansion of the expression: 

(vi)  \[\left( x - \frac{1}{x^2} \right)^{3n}\]

Find the term independent of x in the expansion of the expression: 

(vii)  \[\left( \frac{1}{2} x^{1/3} + x^{- 1/5} \right)^8\]

If log 2, log (2^x − 1) and log (2^x + 3) are in A.P., write the value of x.

If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.

Find the term independent of x in the expansion of the expression: 

(ix) \[\left( \sqrt[3]{x} + \frac{1}{2 \sqrt[3]{x}} \right)^{18} , x > 0\]