Mathematics

Real Numbers Quiz

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Question 1

Unique prime factorisation

Difficulty: easySource: NCERT Exercise 1.1 alignedTopic: fundamental-theorem-of-arithmetic

Which is the prime factorisation of $3825$ ?

1 $3\times5^2\times17$ 2 $3^2\times5^2\times17$ 3 $3^2\times5\times17$ 4 $5^3\times17$

Question 2

HCF and LCM

Difficulty: easySource: NCERT Exercise 1.1 alignedTopic: fundamental-theorem-of-arithmetic

The HCF of $26$ and $91$ is $13$ . Their LCM is:

1 $91$ 2 $117$ 3 $182$ 4 $2366$

Question 3

Ending in zero

Difficulty: mediumSource: NCERT Exercise 1.1 alignedTopic: fundamental-theorem-of-arithmetic

Why can no power $6^n$ , $n$ a natural number, end in $0$ ?

1Its prime factorisation has no factor $2$ .2Its prime factorisation has no factor $3$ .3Its prime factorisation has no factor $5$ .4Every power of $6$ is prime.

Question 4

Theorem used in irrationality

Difficulty: easySource: NCERT Theorem 1.2 alignedTopic: irrational-numbers

If prime $p$ divides $a^2$ , the textbook theorem allows us to conclude:

1 $a$ divides $p$ 2 $p$ divides $a$ 3 $p=a^2$ 4 $a$ is prime

Question 5

Contradiction in the square-root proof

Difficulty: mediumSource: NCERT Exercise 1.2 alignedTopic: irrational-numbers

What contradiction completes the proof that $\sqrt5$ is irrational?

1Both numerator and denominator are divisible by $5$ although the fraction was in lowest form.2The denominator becomes zero.3The numerator is negative.4The square root becomes an integer.

Question 6

Rational plus irrational

Difficulty: mediumSource: NCERT Exercise 1.2 alignedTopic: irrational-numbers

Why is $6+\sqrt2$ irrational?

1Every sum is irrational.2If it were rational, subtracting $6$ would make $\sqrt2$ rational.3Six is irrational.4Its square is negative.

Question 7

Three-number HCF

Difficulty: easySource: NCERT Exercise 1.1 alignedTopic: ncert-exercises-and-revision

The HCF of $8$ , $9$ and $25$ is:

1 $1$ 2 $2$ 3 $5$ 4 $25$

Question 8

Circular path

Difficulty: mediumSource: NCERT Exercise 1.1 alignedTopic: ncert-exercises-and-revision

Two runners take $18$ minutes and $12$ minutes per lap. After how long will both again be at the start together?

1 $6$ minutes2 $24$ minutes3 $30$ minutes4 $36$ minutes

Real Numbers Quiz

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Real Numbers Quiz

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Unique prime factorisation

HCF and LCM

Ending in zero

Theorem used in irrationality

Contradiction in the square-root proof

Rational plus irrational

Three-number HCF

Circular path

Preparing your questions...

I’m stuck

Select your answers

Unique prime factorisation

HCF and LCM

Ending in zero

Theorem used in irrationality

Contradiction in the square-root proof

Rational plus irrational

Three-number HCF

Circular path