English Medium इयत्ता १० - CBSE Question Bank Solutions

If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?

If two positive integers a and b are written as a = x³ y² and b = xy³; x, y are prime numbers, then HCF (a, b) is ______.

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is ______.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Find k so that x² + 2x + k is a factor of 2x⁴ + x³ – 14 x² + 5x + 6. Also find all the zeroes of the two polynomials.

Given that `x - sqrt(5)` is a factor of the cubic polynomial `x^3 - 3sqrt(5)x^2 + 13x - 3sqrt(5)`, find all the zeroes of the polynomial.

For which values of a and b, are the zeroes of q(x) = x³ + 2x² + a also the zeroes of the polynomial p(x) = x⁵ – x⁴ – 4x³ + 3x² + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?

The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. Find x and y.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

The angles of a cyclic quadrilateral ABCD are ∠A = (6x + 10)°, ∠B = (5x)°, ∠C = (x + y)°, ∠D = (3y – 10)°. Find x and y, and hence the values of the four angles. 

Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF (a, b) = p^mqⁿ and LCM (a, b) = p^rq^s, then (m + n)(r + s) = ______.

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

A 2-digit number is such that the product of its digits is 24. If 18 is subtracted from the number, the digits interchange their places. Find the number.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.

Find the HCF and LCM of 26, 65 and 117, using prime factorisation.