Real Numbers - CBSE STD 10 Maths Questions - Vidyadip

Question types

Real Numbers question types

84 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

84

Questions

5

Question groups

5

Question types

M.C.Q (1 Marks)

1 Marks Question

2 Marks Questions

3 Marks Question

5 Marks Questions

Sample Questions

Real Numbers questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark

If $a=\left(2^2 \times 3^3 \times 5^4\right)$ and $b=\left(2^3 \times 3^2 \times 5\right)$, then $HCF (a, b)$ is equal to:

A
$900$
✓
$180$
C
$360$
D
$540$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark

If $p$ and $q$ are two co-prime numbers, then HCF $(p, q)$ is:

A
$p$
B
$q$
C
$p q$
✓
1

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark

Decimal expansion of $\frac{23}{\left(2^3 5^2\right)}$ will be:

✓
Terminating
B
Non-terminating
C
Non terminating and repeating.
D
Non-terminating and non-repeating

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark

L.C.M. of $2^3 \times 3^2$ and $2^3 \times 3^3$ is:

A
$2^3$
B
$3^3$
✓
$2^3 \times 3^3$
D
$2^2 \times 3^2$

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark

The decimal expansion of $\frac{6}{1250}$ will terminate after how many places of decimal?

A
$1$
B
$2$
C
$3$
✓
$4$

Answer: D.

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Q 61 Marks Question1 Mark

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

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Q 71 Marks Question1 Mark

The $\text{HCF}$ of two numbers is $27$ and their $\text{LCM}$ is $162$ , if one of the number is $54$ , find the other number.

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Q 81 Marks Question1 Mark

Write the number of zeroes in the end of a number whose prime factorization is $2^2 \times 5^3 \times 3^2 \times 17$.

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Q 91 Marks Question1 Mark

Find a rational number between $\sqrt{2}$ and $\sqrt{7}$

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Q 102 Marks Questions2 Marks

Given that $\sqrt{2}$ is irrational, prove that $(5+3 \sqrt{2})$ is an irrational number.

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Q 112 Marks Questions2 Marks

Find how many integers between $200$ and $500$ are divisible by $8.$

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Q 122 Marks Questions2 Marks

Write down the decimal expansion of $\frac{76}{6250}$, without actual division.

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Q 132 Marks Questions2 Marks

Express 5050 as product of its prime factors. Is it unique?

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Q 142 Marks Questions2 Marks

Show that $(\sqrt{3}+\sqrt{5})^2$ is an irrational number.

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Q 153 Marks Question3 Marks

Using division algorithm find quotient and remainder dividing $x^3+13 x^2+x-2$ by $2 x+1$

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Q 163 Marks Question3 Marks

Find the greatest number of six digit number exactly divisible by $18,24$ and $36 .$

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Q 173 Marks Question3 Marks

Explain whether the number $3 \times 5 \times 13 \times 46+23$ is a prime number or a composite number.

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Q 183 Marks Question3 Marks

Pens are sold in pack of $8$ and notepads are sold in pack of $12$ . Find the least number of pack of each type that one should buy so that there are equal number of pens and notepads.

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Q 193 Marks Question3 Marks

Find $\text{HCF}$ and $\text{LCM}$ of $180,252$ and $324.$

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Q 205 Marks Questions5 Marks

Define irrational number and prove that $3+\sqrt[2]{5}$ is an irrational number.

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Q 215 Marks Questions5 Marks

Use Euclid's Division Lemma to show that the square of any positive integer is either of the form $3 m$ or $3 m+1$ for some integer m.

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Q 225 Marks Questions5 Marks

Prove that $\sqrt{5}$ is an irrational number.

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