CBSE X Real Numbers practice questions

Question 1

Express 3825 as a product of prime factors.

Accepted Answer

3²×5²×17

Answer

3×5²×17

Answer

3²×5×17

Answer

3²×5²×19

Question 2

Why is √7 irrational?

Accepted Answer

Assuming √7=p/q in lowest terms forces both p and q to be divisible by 7

Answer

Every non-integer is irrational

Answer

7 cannot divide a square

Answer

Its decimal expansion has a fixed finite length

Question 3

If a = x³y² and b = xy³, where x and y are distinct prime numbers, what is HCF(a, b)?

Accepted Answer

xy²

Answer

xy

Answer

x³y³

Answer

x²y²

Question 4

For distinct primes x,y, let a=x³y² and b=xy³. Find HCF(a,b).

Accepted Answer

xy²

Answer

xy

Answer

x³y³

Answer

x²y²

Question 5

Find HCF and LCM of 426, 576.

Accepted Answer

HCF=6; LCM=40896

Answer

HCF=12; LCM=40896

Answer

HCF=6; LCM=81792

Answer

HCF=6; LCM=20448

Question 6

Find the least positive integer divisible by every integer from 1 to 10 inclusive.

Accepted Answer

2520

Answer

1260

Answer

5040

Answer

720

Question 7

Suppose √3=a/b, where a and b are coprime positive integers. Which contradiction establishes irrationality?

Accepted Answer

Both a and b are divisible by 3

Answer

Neither a nor b is divisible by 3

Answer

a and b are both odd

Answer

b is necessarily 1

Question 8

Find HCF(2160,3520).

Accepted Answer

80

Answer

40

Answer

160

Answer

120