English Medium Class 10 - CBSE Important Questions

Solve for x :

`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.

A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.

For what value of k, the roots of the equation x² + 4x + k = 0 are real?

Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.

Write the number of zeroes in the end of a number whose prime factorization is 2² × 5³ × 3² × 17.

Which of the following equations has 2 as a root?

Solve the quadratic equation: x² – 2ax + (a² – b²) = 0 for x.

Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)² = 0 has real and equal roots.

‘The sum of the ages of a boy and his sister (in years) is 25 and product of their ages is 150. Find their present ages.

Find the value of 'k' so that the quadratic equation 3x² – 5x – 2k = 0 has real and equal roots.

If x = 3 is one root of the quadratic equation 2x² + px + 30 = 0, find the value of p and the other root of the quadratic equation.

The roots of the equation x² + 3x – 10 = 0 are ______.

Determine the A.P. whose 3^rd term is 16 and the 7^th term exceeds the 5^th term by 12.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

If the ratio of sum of the first m and n terms of an AP is m² : n², show that the ratio of its  m^th and n^th terms is (2m − 1) : (2n − 1) ?

The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.

The Sum of first five multiples of 3 is ______.

If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.