English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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

Find the sum of all integers between 84 and 719, which are multiples of 5.

Find the sum of all integers between 50 and 500, which are divisible by 7.

Find the values of k for which the roots are real and equal in each of the following equation:

kx² + 4x + 1 = 0

Find the values of k for which the roots are real and equal in each of the following equation:

`kx^2-2sqrt5x+4=0`

Find the value of k for which the roots are real and equal in the following equation:

3x2 − 5x + 2k = 0

Find the sum of all even integers between 101 and 999.

Find the sum of all integers between 100 and 550, which are divisible by 9.

In an A.P., if the first term is 22, the common difference is −4 and the sum to n terms is 64,  find n.