English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

For what value of n, the n^th terms of the arithmetic progressions 63, 65, 67, ... and 3, 10, 17, ... equal?

The 19^th term of an A.P. is equal to three times its sixth term. If its 9^th term is 19, find the A.P.

The 9^th term of an A.P. is equal to 6 times its second term. If its 5^th term is 22, find the A.P.

If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\], find its (63)^rd term. 

The sum of 5^th and 9^th terms of an A.P. is 30. If its 25^th term is three times its 8^th term, find the A.P.

Find the sum of the first 15 terms of each of the following sequences having nth term as  x_n = 6 − n .

If the sum of a certain number of terms starting from first term of an A.P. is 25, 22, 19, ..., is 116. Find the last term.

Find the sum of all 2-digit natural numbers divisible by 4.

Find the sum  (−5) + (−8)+ (−11) + ... + (−230) .

Find the sum:  1 + 3 + 5 + 7 + ... + 199 .

Find the sum \[7 + 10\frac{1}{2} + 14 + . . . + 84\]

Find the sum:  

\[18 + 15\frac{1}{2} + 13 + ... + \left( - 49\frac{1}{2} \right)\]

If the equation \[\left(1 + m^2 \right) x^2 + 2mcx + \left(c^2 - a^2 \right) = 0\] has equal roots, prove that c² = a²(1 + m²).

Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + ....\]

In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.

In an A.P., the first term is 22, nth term is −11 and the sum to first n terms is 66. Find n and d, the common difference

​The first and the last terms of an A.P. are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.