English Medium कक्षा १० - CBSE Important Questions for Mathematics

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?

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

If `x=2/3` and x =−3 are roots of the quadratic equation ax² + 7x + b = 0, find the values of a and b.

If `x = (-1)/2`, is a solution of the quadratic equation 3x² + 2kx – 3 = 0, find the value of k. 

Solve the quadratic equation 2x² + ax − a² = 0 for x.

Find the value of k for which the equation x² + k(2x + k – 1) + 2 = 0 has real and equal roots.

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

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

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 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.

In an A.P., if S5 + S7 = 167 and S₁₀₌235, then find the A.P., where Sn denotes the sum of its first n terms.

Find the 9^th term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185

Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

What value is generated in the above situation?

Find the sum of first 15 multiples of 8.

Find how many integers between 200 and 500 are divisible by 8.