English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

If LCM(x, 18) = 36 and HCF(x, 18) = 2, then x is ______.

For some integer m, every even integer is of the form ______.

For some integer q, every odd integer is of the form ______.

n² – 1 is divisible by 8, if n is ______.

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is ______.

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is ______.

Explain why 3 × 5 × 7 + 7 is a composite number.

If cos A = `4/5`, then the value of tan A is ______.

If sin A = `1/2`, then the value of cot A is ______.

Given that sinα = `1/2` and cosβ = `1/2`, then the value of (α + β) is ______.

The value of the expression `[(sin^2 22^circ + sin^2 68^circ)/(cos^2 22^circ + cos^2 68^circ) + sin^2 63^circ + cos 63^circ sin 27^circ]` is ______.

Prove the following:

If tan A = `3/4`, then sinA cosA = `12/25`

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?

If 4 tanθ = 3, then `((4 sintheta - costheta)/(4sintheta + costheta))` is equal to ______.

The value of the expression (sin 80° – cos 80°) is negative.