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REAL NUMBERS

90186 $2. \overset{―}{35}$ is:

1 )An integer.

2 )A rational number.

3 )An irrational number.

4 )None of these.

Explanation:

Exp: B
A rational number.
$2. \overset{―}{35} = 2.35353535 \dots$
Which is repeating decimal number, and hence is a rational number.
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REAL NUMBERS

90191 Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is:

1 )200 litres

2 )180 litres

3 )170 litres

4 )190 litres

Explanation:

Exp: C
170 litres
Here, the maximum capacity of measuring container = HCF(680, 850)
$∴$ Applying Euclid’s division algorithm to 850 and 680
850 = 680 × 1 + 170
$\Rightarrow$ 680 = 170 × 4 + 0 [Zero remainder]
$∴$ HCF = (680, 850) = 170
Applying

REAL NUMBERS

90193 The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is:

1 )

\sqrt{27}

2 )

3 \sqrt{3}

3 )

\sqrt{3}

4 )

3

Explanation:

Exp: C
$\sqrt{3}$
$\sqrt{27} = \sqrt{3 \times 3 \times 3}$
$= 3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).
Applying

REAL NUMBERS

90194 If p and q are co-prime numbers, then p $^{2}$ and q $^{2}$ are:

1 )Co-prime.

2 )Not co-prime.

3 )Even.

4 )Odd.

Explanation:

Exp: A
Co-prime.
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, p $^{2}$ and q $^{2}$ have the same factors with twice of the exponents of p and q respectively, which again will not have any common factor.
Thus we can conclude that p $^{2}$ and q $^{2}$ are co-prime numbers.
Hence, the correct choice is (a).

REAL NUMBERS

90196 Which of the following is a pair of co-primes?

1 )(14, 35)

2 )(18, 25)

3 )(31, 93)

4 )(32, 62)

REAL NUMBERS

90186 $2. \overset{―}{35}$ is:

1 )An integer.

2 )A rational number.

3 )An irrational number.

4 )None of these.

Explanation:

Exp: B
A rational number.
$2. \overset{―}{35} = 2.35353535 \dots$
Which is repeating decimal number, and hence is a rational number.
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REAL NUMBERS

90191 Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is:

1 )200 litres

2 )180 litres

3 )170 litres

4 )190 litres

Explanation:

Exp: C
170 litres
Here, the maximum capacity of measuring container = HCF(680, 850)
$∴$ Applying Euclid’s division algorithm to 850 and 680
850 = 680 × 1 + 170
$\Rightarrow$ 680 = 170 × 4 + 0 [Zero remainder]
$∴$ HCF = (680, 850) = 170
Applying

REAL NUMBERS

90193 The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is:

1 )

\sqrt{27}

2 )

3 \sqrt{3}

3 )

\sqrt{3}

4 )

3

Explanation:

Exp: C
$\sqrt{3}$
$\sqrt{27} = \sqrt{3 \times 3 \times 3}$
$= 3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).
Applying

REAL NUMBERS

90194 If p and q are co-prime numbers, then p $^{2}$ and q $^{2}$ are:

1 )Co-prime.

2 )Not co-prime.

3 )Even.

4 )Odd.

Explanation:

Exp: A
Co-prime.
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, p $^{2}$ and q $^{2}$ have the same factors with twice of the exponents of p and q respectively, which again will not have any common factor.
Thus we can conclude that p $^{2}$ and q $^{2}$ are co-prime numbers.
Hence, the correct choice is (a).

REAL NUMBERS

90196 Which of the following is a pair of co-primes?

1 )(14, 35)

2 )(18, 25)

3 )(31, 93)

4 )(32, 62)

REAL NUMBERS

90186 $2. \overset{―}{35}$ is:

1 )An integer.

2 )A rational number.

3 )An irrational number.

4 )None of these.

Explanation:

Exp: B
A rational number.
$2. \overset{―}{35} = 2.35353535 \dots$
Which is repeating decimal number, and hence is a rational number.
Never Active

REAL NUMBERS

90191 Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is:

1 )200 litres

2 )180 litres

3 )170 litres

4 )190 litres

Explanation:

Exp: C
170 litres
Here, the maximum capacity of measuring container = HCF(680, 850)
$∴$ Applying Euclid’s division algorithm to 850 and 680
850 = 680 × 1 + 170
$\Rightarrow$ 680 = 170 × 4 + 0 [Zero remainder]
$∴$ HCF = (680, 850) = 170
Applying

REAL NUMBERS

90193 The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is:

1 )

\sqrt{27}

2 )

3 \sqrt{3}

3 )

\sqrt{3}

4 )

3

Explanation:

Exp: C
$\sqrt{3}$
$\sqrt{27} = \sqrt{3 \times 3 \times 3}$
$= 3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).
Applying

REAL NUMBERS

90194 If p and q are co-prime numbers, then p $^{2}$ and q $^{2}$ are:

1 )Co-prime.

2 )Not co-prime.

3 )Even.

4 )Odd.

Explanation:

Exp: A
Co-prime.
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, p $^{2}$ and q $^{2}$ have the same factors with twice of the exponents of p and q respectively, which again will not have any common factor.
Thus we can conclude that p $^{2}$ and q $^{2}$ are co-prime numbers.
Hence, the correct choice is (a).

REAL NUMBERS

90196 Which of the following is a pair of co-primes?

1 )(14, 35)

2 )(18, 25)

3 )(31, 93)

4 )(32, 62)

REAL NUMBERS

90186 $2. \overset{―}{35}$ is:

1 )An integer.

2 )A rational number.

3 )An irrational number.

4 )None of these.

Explanation:

Exp: B
A rational number.
$2. \overset{―}{35} = 2.35353535 \dots$
Which is repeating decimal number, and hence is a rational number.
Never Active

REAL NUMBERS

90191 Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is:

1 )200 litres

2 )180 litres

3 )170 litres

4 )190 litres

Explanation:

Exp: C
170 litres
Here, the maximum capacity of measuring container = HCF(680, 850)
$∴$ Applying Euclid’s division algorithm to 850 and 680
850 = 680 × 1 + 170
$\Rightarrow$ 680 = 170 × 4 + 0 [Zero remainder]
$∴$ HCF = (680, 850) = 170
Applying

REAL NUMBERS

90193 The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is:

1 )

\sqrt{27}

2 )

3 \sqrt{3}

3 )

\sqrt{3}

4 )

3

Explanation:

Exp: C
$\sqrt{3}$
$\sqrt{27} = \sqrt{3 \times 3 \times 3}$
$= 3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).
Applying

REAL NUMBERS

90194 If p and q are co-prime numbers, then p $^{2}$ and q $^{2}$ are:

1 )Co-prime.

2 )Not co-prime.

3 )Even.

4 )Odd.

Explanation:

Exp: A
Co-prime.
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, p $^{2}$ and q $^{2}$ have the same factors with twice of the exponents of p and q respectively, which again will not have any common factor.
Thus we can conclude that p $^{2}$ and q $^{2}$ are co-prime numbers.
Hence, the correct choice is (a).

REAL NUMBERS

90196 Which of the following is a pair of co-primes?

1 )(14, 35)

2 )(18, 25)

3 )(31, 93)

4 )(32, 62)

REAL NUMBERS

90186 $2. \overset{―}{35}$ is:

1 )An integer.

2 )A rational number.

3 )An irrational number.

4 )None of these.

Explanation:

Exp: B
A rational number.
$2. \overset{―}{35} = 2.35353535 \dots$
Which is repeating decimal number, and hence is a rational number.
Never Active

REAL NUMBERS

90191 Two tankers contain 850 litres and 680 litres of petrol. The maximum capacity of a container which can measure the petrol of each tanker in exact number of times is:

1 )200 litres

2 )180 litres

3 )170 litres

4 )190 litres

Explanation:

Exp: C
170 litres
Here, the maximum capacity of measuring container = HCF(680, 850)
$∴$ Applying Euclid’s division algorithm to 850 and 680
850 = 680 × 1 + 170
$\Rightarrow$ 680 = 170 × 4 + 0 [Zero remainder]
$∴$ HCF = (680, 850) = 170
Applying

REAL NUMBERS

90193 The smallest number by which $\sqrt{27}$ should be multiplied so as to get a rational number is:

1 )

\sqrt{27}

2 )

3 \sqrt{3}

3 )

\sqrt{3}

4 )

3

Explanation:

Exp: C
$\sqrt{3}$
$\sqrt{27} = \sqrt{3 \times 3 \times 3}$
$= 3 \sqrt{3}$
Out of the given choices $\sqrt{3}$ is the only smallest number by which if we multiply $\sqrt{27}$ we get a rational number.
Hence, the correct choice is (c).
Applying

REAL NUMBERS

90194 If p and q are co-prime numbers, then p $^{2}$ and q $^{2}$ are:

1 )Co-prime.

2 )Not co-prime.

3 )Even.

4 )Odd.

Explanation:

Exp: A
Co-prime.
We know that the co-prime numbers have no factor in common, or, their HCF is 1.
Thus, p $^{2}$ and q $^{2}$ have the same factors with twice of the exponents of p and q respectively, which again will not have any common factor.
Thus we can conclude that p $^{2}$ and q $^{2}$ are co-prime numbers.
Hence, the correct choice is (a).

REAL NUMBERS

90196 Which of the following is a pair of co-primes?

1 )(14, 35)

2 )(18, 25)

3 )(31, 93)

4 )(32, 62)

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