English Medium कक्षा १० - CBSE Question Bank Solutions

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x³ – 3x² + 5x – 3, g(x) = x² – 2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : p(x) = x⁴ – 3x² + 4x + 5,   g(x) = x² + 1 – x

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x⁴ – 5x + 6, g(x) = 2 – x²

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial 

x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.

x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1

Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg p(x) = deg q(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg q(x) = deg r(x)

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm

deg r(x) = 0

If the polynomial x⁴ – 6x³ + 16x² – 25x + 10 is divided by another polynomial x² – 2x + k, the remainder comes out to be x + a, find k and a.

Solve the following pair of linear equation by the elimination method and the substitution method:

x + y = 5 and 2x – 3y = 4

Solve the following pair of linear equation by the elimination method and the substitution method: 

3x + 4y = 10 and 2x – 2y = 2

Solve the following pair of linear equation by the elimination method and the substitution method.

3x – 5y – 4 = 0 and 9x = 2y + 7

Solve the following pair of linear equation by the elimination method and the substitution method.

`x/2 + (2y)/3 = -1 and x - y /3 = 3`

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes `1/2` if we only add 1 to the denominator. What is the fraction?

Form the pair of linear equation in the following problem, and find its solutions (if they exist) by the elimination method:

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:

Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.