English Medium कक्षा १० - CBSE Question Bank Solutions

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 values of k for which the quadratic equation (k + 4) x² + (k + 1) x + 1 = 0 has equal roots. Also find these roots.

If the sum of the first n terms of an A.P. is `1/2`(3n² +7n), then find its n^th term. Hence write its 20^th term.

Find that value of p for which the quadratic equation (p + 1)x² – 6(p + 1)x + 3(p + 9) = 0, p ≠ –1 has equal roots. Hence, find the roots of the equation.

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

Solve the following quadratic equation for x :

9x² − 6b²x − (a⁴ − b⁴) = 0

Find the values of k for which the quadratic equation (3k + 1) x² + 2(k + 1) x + 1 = 0 has equal roots. Also, find the roots.

If S_n denotes the sum of first n terms of an A.P., prove that S₃₀ = 3[S₂₀ − S₁₀]

The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.

Find the value of p for which the quadratic equation (2p + 1)x² − (7p + 2)x + (7p − 3) = 0 has equal roots. Also find these roots.

Find the zeros of the quadratic polynomial 6x² - 13x + 6 and verify the relation between the zero and its coefficients.

Find the zeros of the quadratic polynomial 4x² - 9 and verify the relation between the zeros and its coffiecents.

Find the zeros of the quadratic polynomial 9x² - 5 and verify the relation between the zeros and its coefficients.

if α and β are the zeros of ax² + bx + c, a ≠ 0 then verify  the relation between zeros and its cofficients

Prove relation between the zeros and the coefficient of the quadratic polynomial ax² + bx + c

Verify that the numbers given along side of the cubic polynomials are their zeroes. Also, verify the relationship between the zeros and the coefficients.

`f(x) = 2x^3 + x^2 - 5x + 2 ; 1/2, 1, - 2`

Solve the following system of linear equations by applying the method of elimination by equating the coefficients

(i)4x – 3y = 4 

2x + 4y = 3

(ii)5x – 6y = 8

3x + 2y = 6

Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9

Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72

Solve the following system of equations by using the method of elimination by equating the co-efficients.

`\frac { x }{ y } + \frac { 2y }{ 5 } + 2 = 10; \frac { 2x }{ 7 } – \frac { 5 }{ 2 } + 1 = 9`