English Medium Class 10 - CBSE Question Bank Solutions

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Three numbers in A.P. have the sum of 30. What is its middle term?

Find the value of ‘c’ for which the quadratic equation 

(c + 1) x² - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1

has real and equal roots.

If α and β are the zeroes of the polynomial x² + x − 2, then find the value of `alpha/beta+beta/alpha`

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`

Solve the following system of linear equations by using the method of elimination by equating the coefficients √3x – √2y = √3 = ; √5x – √3y = √2

Solve for x and y : `\frac { ax }{ b } – \frac { by }{ a } = a + b ; ax – by = 2ab`

Solve the following system of linear equations :

2(ax – by) + (a + 4b) = 0

2(bx + ay) + (b – 4a) = 0

Solve (a – b) x + (a + b) y = `a^2 – 2ab – b^2 (a + b) (x + y) = a^2 + b^2`

Prove the following trigonometric identities:

(i) (1 – sin²θ) sec²θ = 1

(ii) cos²θ (1 + tan²θ) = 1

Prove the following trigonometric identities:

`(\text{i})\text{ }\frac{\sin \theta }{1-\cos \theta }=\text{cosec}\theta+\cot \theta `