English Medium Class 10 - CBSE Question Bank Solutions

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

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs 27 for a book kept for seven days, while Susy paid Rs 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

What is the HCF of the smallest prime number and the smallest composite number?

Find HCF and LCM of 404 and 96 and verify that HCF × LCM = Product of the two given numbers.

A merchant has 120 liters of oil of one kind, 180 liters of another kind and 240 liters of third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin?

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:

f(x) = x³ – 6x² + 11x – 6, g(x) = x² + x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:

f(x) = 10x⁴ + 17x³ – 62x² + 30x – 3, g(x) = 2x² + 7x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:

f(x) = 4x³ + 8x + 8x² + 7, g(x) = 2x² – x + 1

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:

f(x) = 15x³ – 20x² + 13x – 12, g(x) = 2 – 2x + x²

Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:

g(x) = 2x² – x + 3, f(x) = 6x⁵ – x⁴ + 4x³ – 5x² – x – 15

Obtain all zeros of f(x) = x³ + 13x² + 32x + 20, if one of its zeros is –2.

Obtain all zeros of the polynomial f(x) = x⁴ − 3x³ − x² + 9x − 6, if two of its zeros are `-sqrt3` and `sqrt3`

Find all zeros of the polynomial f(x) = 2x⁴ – 2x³ – 7x² + 3x + 6, if its two zeros are `-sqrt(3/2)` and `sqrt(3/2)`.

What must be added to the polynomial f(x) = x⁴ + 2x³ − 2x² + x − 1 so that the resulting polynomial is exactly divisible by x² + 2x − 3 ?

What must be subtracted from the polynomial f(x) = x⁴ + 2x³ − 13x² − 12x + 21 so that the resulting polynomial is exactly divisible by x² − 4x + 3 ?

Find all the zeros of the polynomial x⁴ + x³ – 34x² – 4x + 120, if two of its zeros are 2 and –2.

Find all zeros of the polynomial 2x⁴ + 7x³ – 19x² – 14x + 30, if two of its zeros are `sqrt(2)` and `-sqrt(2)`.

Find all the zeros of the polynomial 2x³ + x² – 6x – 3, if two of its zeros are `-sqrt(3)` and `sqrt(3)`.

Find all the zeros of the polynomial x³ + 3x² – 2x – 6, if two of its zeros are `-sqrt(2)` and `sqrt(2)`.

State fundamental theorem of arithmetic.

Verify division algorithm for the polynomial f(x)= (8 + 20x + x² – 6x³) by g(x) = (2 + 5x – 3x²).