PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions

Find the middle term in the expansion of: 

(iii) \[\left( x^2 - \frac{2}{x} \right)^{10}\]

Find the middle term in the expansion of: 

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

Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.

Find the middle terms in the expansion of: 

(i)  \[\left( 3x - \frac{x^3}{6} \right)^9\]

The income of a person is Rs 300,000 in the first year and he receives an increase of Rs 10000 to his income per year for the next 19 years. Find the total amount, he received in 20 years.

Find the middle terms in the expansion of:

(ii) \[\left( 2 x^2 - \frac{1}{x} \right)^7\]

A man starts repaying a loan as first instalment of Rs 100 = 00. If he increases the instalments by Rs 5 every month, what amount he will pay in the 30th instalment?

Find the middle terms in the expansion of: 

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

Find the middle terms in the expansion of:

(iv)  \[\left( x^4 - \frac{1}{x^3} \right)^{11}\]

A carpenter was hired to build 192 window frames. The first day he made five frames and each day thereafter he made two more frames than he made the day before. How many days did it take him to finish the job? 

A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

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

(i) \[\left( x - \frac{1}{x} \right)^{10}\]

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

(ii)  \[\left( 1 - 2x + x^2 \right)^n\]

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

(iii)  \[\left( 1 + 3x + 3 x^2 + x^3 \right)^{2n}\]

We know that the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, ... sides form an arithmetic progression. Find the sum of the interior angles for a 21 sided polygon.

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

(iv)  \[\left( 2x - \frac{x^2}{4} \right)^9\]

In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?

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

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

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

(vi)  \[\left( \frac{x}{3} + 9y \right)^{10}\]