English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

If tan θ = `x/y`, then cos θ is equal to ______.

sec θ when expressed in term of cot θ, is equal to ______.

Which of the following is true for all values of θ (0° ≤ θ ≤ 90°)?

(sec² θ – 1) (cosec² θ – 1) is equal to ______.

(1 – cos² A) is equal to ______.

Prove that `(1 + tan^2 A)/(1 + cot^2 A)` = sec² A – 1

Prove that `(cot A - cos A)/(cot A + cos A) = (cos^2 A)/(1 + sin A)^2`

Prove that (sec θ + tan θ) (1 – sin θ) = cos θ

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.

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.

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?

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?

State fundamental theorem of arithmetic.