English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

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.

Find the sum of the integers between 100 and 200 that are not divisible by 9.

The ratio of the 11^th term to the 18^th term of an AP is 2 : 3. Find the ratio of the 5^th term to the 21^st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`

Solve the equation

– 4 + (–1) + 2 + ... + x = 437

Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30^th instalment? What amount of loan does he still have to pay after the 30^th instalment?

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Find the value of a₂₅ – a₁₅ for the AP: 6, 9, 12, 15, ………..

If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12^th term.