English Medium कक्षा १० - CBSE Question Bank Solutions

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

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α² + β².

If α, β are zeroes of quadratic polynomial 5x² + 5x + 1, find the value of α^–1 + β^–1.

Find the zeroes of the quadratic polynomial 4s² – 4s + 1 and verify the relationship between the zeroes and the coefficients.

Consider the number 12ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 12ⁿ ends with the digital zero.

Consider the number 6ⁿ where n is a natural number. Check whether there is any value of n ∈ N for which 6ⁿ is divisible by 7.

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`

Express the number as a product of its prime factor:

140

Find the LCM and HCF of the following integers by applying the prime factorisation method.

12, 15 and 21

Given that HCF (306, 657) = 9, find LCM (306, 657).

Check whether 6ⁿ can end with the digit 0 for any natural number n.

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?