English Medium कक्षा १० - CBSE Question Bank Solutions

Find the sum of the following arithmetic progressions 

`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`

Find the sum of the following arithmetic progressions:

`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`,  .....to n terms

Find the sum of the following arithmetic progressions:

−26, −24, −22, …. to 36 terms

Find the sum to n term of the A.P. 5, 2, −1, −4, −7, ...,

Find the sum of n terms of an A.P. whose nth terms is given by a_n = 5 − 6n.

Find the sum of the first 25 terms of an A.P. whose nth term is given by a_n = 7 − 3n

How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?

How many terms of the A.P. 63, 60, 57, ... must be taken so that their sum is 693?

Determine the nature of the roots of the following quadratic equation:

`3/5x^2-2/3x+1=0`

If the 12th term of an A.P. is −13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

Determine the nature of the roots of the following quadratic equation:

`3x^2-2sqrt6x+2=0`

Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.

Determine the nature of the roots of the following quadratic equation:

(x - 2a)(x - 2b) = 4ab

Find the sum of all natural numbers between 1 and 100, which are divisible by 3.

Find the sum of first n odd natural numbers

Determine the nature of the roots of the following quadratic equation:

9a²b²x² - 24abcdx + 16c²d² = 0

Find the sum of all odd numbers between 100 and 200.

Determine the nature of the roots of the following quadratic equation:

2(a² + b²)x² + 2(a + b)x + 1 = 0

Show that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.

Determine the nature of the roots of the following quadratic equation:

(b + c)x² - (a + b + c)x + a = 0