PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

The 10th and 18th terms of an A.P. are 41 and 73 respectively. Find 26th term.

In a certain A.P. the 24th term is twice the 10th term. Prove that the 72nd term is twice the 34th term.

If (m + 1)th term of an A.P. is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.

Find the 12th term from the following arithmetic progression:

 3, 5, 7, 9, ... 201

Find the 12th term from the following arithmetic progression:

3, 8, 13, ..., 253

Find the 12th term from the following arithmetic progression:

1, 4, 7, 10, ..., 88

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

An A.P. consists of 60 terms. If the first and the last terms be 7 and 125 respectively, find 32nd term.

The sum of 4th and 8th terms of an A.P. is 24 and the sum of the 6th and 10th terms is 34. Find the first term and the common difference of the A.P.

How many numbers are there between 1 and 1000 which when divided by 7 leave remainder 4?

The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.

If < a_n > is an A.P. such that \[\frac{a_4}{a_7} = \frac{2}{3}, \text { find }\frac{a_6}{a_8}\].

\[\text { If } \theta_1 , \theta_2 , \theta_3 , . . . , \theta_n \text { are in AP, whose common difference is d, then show that }\]

\[\sec \theta_1 \sec \theta_2 + \sec \theta_2 \sec \theta_3 + . . . + \sec \theta_{n - 1} \sec \theta_n = \frac{\tan \theta_n - \tan \theta_1}{\sin d} \left[ NCERT \hspace{0.167em} EXEMPLAR \right]\]

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.

Find the four numbers in A.P., whose sum is 50 and in which the greatest number is 4 times the least.