English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30^th installment? What amount of loan has he paid after 30^th installment?

If x = 3 is one of the roots of the quadratic equation x² – 2kx – 6 = 0, then the value of k is ______.

Read the following passage:

1. In which year, the production is 29,200 sets?
2. Find the production in the 8^th year.
   OR
   Find the production in first 3 years.
3. Find the difference of the production in 7^th year and 4^th year.

A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.

If p(x) = x² + 5x + 6, then p(– 2) is ______.

Assertion (A): If one root of the quadratic equation 4x² – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.

Reason (R): Roots of the quadratic equation x² – x + 1 = 0 are real.

Find the discriminant of the quadratic equation `3x^2 - 2x + 1/3` = 0 and hence find the nature of its roots.

Find the zeroes of the quadratic polynomial x² + 6x + 8 and verify the relationship between the zeroes and the coefficients.

Find the sum of first 25 terms of the A.P. whose nth term is given by a_n = 5 + 6n. Also, find the ratio of 20^th term to 45^th term.

A quadratic polynomial whose sum and product of zeroes are 2 and – 1 respectively is ______.

If α, β are zeroes of the quadratic polynomial x² – 5x + 6, form another quadratic polynomial whose zeroes are `1/α, 1/β`.

Find a quadratic polynomial whose zeroes are 6 and – 3.

Find the zeroes of the polynomial x² + 4x – 12.

Find the value of k for which the roots of the quadratic equation 5x² – 10x + k = 0 are real and equal.

If one root of the quadratic equation 3x² – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.

The zeroes of the polynomial p(x) = 25x² – 49 are ______.

The zeroes of the polynomial p(x) = 2x² – x – 3 are ______.

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.