English Medium Class 10 - CBSE Question Bank Solutions

Find whether the following equation have real roots. If real roots exist, find them.

`x^2 + 5sqrt(5)x - 70 = 0`

If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.

The sum of first five multiples of 3 is ______.

Find the sum:

1 + (–2) + (–5) + (–8) + ... + (–236)

Find the sum:

`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms

Find the sum:

`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms

Which term of the AP: –2, –7, –12,... will be –77? Find the sum of this AP upto the term –77.

In an AP, if S_n = n(4n + 1), find the AP.

In an A.P., if S_n = 3n² + 5n and a_k = 164, find the value of k.

If S_n denotes the sum of first n terms of an AP, prove that S₁₂ = 3(S₈ – S₄)

Find the sum of first 17 terms of an AP whose 4^th and 9^th terms are –15 and –30 respectively.

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Find the sum of all the 11 terms of an A.P. whose middle most term is 30.

Find the sum of last ten terms of the AP: 8, 10, 12,.., 126.

Find the sum of first seven numbers which are multiples of 2 as well as of 9.

How many terms of the AP: –15, –13, –11,... are needed to make the sum –55? Explain the reason for double answer.

Kanika was given her pocket money on Jan 1^st, 2008. She puts Rs 1 on Day 1, Rs 2 on Day 2, Rs 3 on Day 3, and continued doing so till the end of the month, from this money into her piggy bank. She also spent Rs 204 of her pocket money, and found that at the end of the month she still had Rs 100 with her. How much was her pocket money for the month?

Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?

Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.