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REAL NUMBERS

90428 Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion $\frac{7}{210}$ :

1 )Terminating decimal expansion

2 )Non -terminating decimal expansion

3 )Cannot be determined

4 )None

Explanation:

Exp: B
Non -terminating decimal expansion
Simplify it by dividing nominator and denominator both by 7 we get $\frac{1}{30}$
Factorize the denominator we get 30 = 2 × 3 × 5
Denominator has 3 also in denominator
So denominator is not in form of 2 $^{n}$ × 5 $^{n}$

REAL NUMBERS

90180 Euclid's division lemma sates that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:

1 )

1 < r < b

2 )

0 < r \leq b

3 )

0 \leq r < b

4 )

0 < r < b

Explanation:

Exp: C
$0 \leq r < b$
Euclid's division lemma states that,
For any positive integers a and b, there exist unique integers q and r such that
$a = bq + r,$ where $0 \leq r < b$
Never Active

REAL NUMBERS

90184 A die is thrown once. Find the probability of getting a number between 3 and 6.

1 )

\frac{2}{3}

2 )

\frac{1}{2}

3 )

\frac{1}{4}

4 )

\frac{1}{3}

Explanation:

Exp: D
$\frac{1}{3}$
Total number of outcomes ={1, 2, 3, 4, 5, 6} = 6
favourable outcomes in this case = {4, 5} = 2
$∴$ p (a number between 3 and 6)
$= \frac{favourable outcomes}{total outcomes} = \frac{2}{6} = \frac{1}{3}$

REAL NUMBERS

90185 If d is the HCF of 56 and 72, the values of x, y satisfying d = 56x + 72y:

1 )x = -3, y = 4

2 )x = 4, y = -3

3 )x = 3, y = -4

4 )x = -4, y = 3

Explanation:

Exp: B
x = 4, y = -3
Since, HCF of 56 and 72, by Euclid’s division lemma,
72 = 56 × 1 + 16 ...(i)
56 = 16 × 3 + 8 ...(ii)
16 = 8 × 2 + 0 ...(iii)
$∴$ HCF of 56 and 72 is 8.
$∴$ 8 = 56 - 16× 3 ( from eq. (ii))
8 = 56 - (72 - 56 × 1) × 3 [From eq. (i) : 16 = 72 - 56 × 1]
8 = 56 - 3 × 72 + 56 × 3
8 = 56 × 4 + (-3) × 72
$∴$ x = 4, y = -3

REAL NUMBERS

90428 Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion $\frac{7}{210}$ :

1 )Terminating decimal expansion

2 )Non -terminating decimal expansion

3 )Cannot be determined

4 )None

Explanation:

Exp: B
Non -terminating decimal expansion
Simplify it by dividing nominator and denominator both by 7 we get $\frac{1}{30}$
Factorize the denominator we get 30 = 2 × 3 × 5
Denominator has 3 also in denominator
So denominator is not in form of 2 $^{n}$ × 5 $^{n}$

REAL NUMBERS

90180 Euclid's division lemma sates that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:

1 )

1 < r < b

2 )

0 < r \leq b

3 )

0 \leq r < b

4 )

0 < r < b

Explanation:

Exp: C
$0 \leq r < b$
Euclid's division lemma states that,
For any positive integers a and b, there exist unique integers q and r such that
$a = bq + r,$ where $0 \leq r < b$
Never Active

REAL NUMBERS

90184 A die is thrown once. Find the probability of getting a number between 3 and 6.

1 )

\frac{2}{3}

2 )

\frac{1}{2}

3 )

\frac{1}{4}

4 )

\frac{1}{3}

Explanation:

Exp: D
$\frac{1}{3}$
Total number of outcomes ={1, 2, 3, 4, 5, 6} = 6
favourable outcomes in this case = {4, 5} = 2
$∴$ p (a number between 3 and 6)
$= \frac{favourable outcomes}{total outcomes} = \frac{2}{6} = \frac{1}{3}$

REAL NUMBERS

90185 If d is the HCF of 56 and 72, the values of x, y satisfying d = 56x + 72y:

1 )x = -3, y = 4

2 )x = 4, y = -3

3 )x = 3, y = -4

4 )x = -4, y = 3

Explanation:

Exp: B
x = 4, y = -3
Since, HCF of 56 and 72, by Euclid’s division lemma,
72 = 56 × 1 + 16 ...(i)
56 = 16 × 3 + 8 ...(ii)
16 = 8 × 2 + 0 ...(iii)
$∴$ HCF of 56 and 72 is 8.
$∴$ 8 = 56 - 16× 3 ( from eq. (ii))
8 = 56 - (72 - 56 × 1) × 3 [From eq. (i) : 16 = 72 - 56 × 1]
8 = 56 - 3 × 72 + 56 × 3
8 = 56 × 4 + (-3) × 72
$∴$ x = 4, y = -3

REAL NUMBERS

90428 Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion $\frac{7}{210}$ :

1 )Terminating decimal expansion

2 )Non -terminating decimal expansion

3 )Cannot be determined

4 )None

Explanation:

Exp: B
Non -terminating decimal expansion
Simplify it by dividing nominator and denominator both by 7 we get $\frac{1}{30}$
Factorize the denominator we get 30 = 2 × 3 × 5
Denominator has 3 also in denominator
So denominator is not in form of 2 $^{n}$ × 5 $^{n}$

REAL NUMBERS

90180 Euclid's division lemma sates that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:

1 )

1 < r < b

2 )

0 < r \leq b

3 )

0 \leq r < b

4 )

0 < r < b

Explanation:

Exp: C
$0 \leq r < b$
Euclid's division lemma states that,
For any positive integers a and b, there exist unique integers q and r such that
$a = bq + r,$ where $0 \leq r < b$
Never Active

REAL NUMBERS

90184 A die is thrown once. Find the probability of getting a number between 3 and 6.

1 )

\frac{2}{3}

2 )

\frac{1}{2}

3 )

\frac{1}{4}

4 )

\frac{1}{3}

Explanation:

Exp: D
$\frac{1}{3}$
Total number of outcomes ={1, 2, 3, 4, 5, 6} = 6
favourable outcomes in this case = {4, 5} = 2
$∴$ p (a number between 3 and 6)
$= \frac{favourable outcomes}{total outcomes} = \frac{2}{6} = \frac{1}{3}$

REAL NUMBERS

90185 If d is the HCF of 56 and 72, the values of x, y satisfying d = 56x + 72y:

1 )x = -3, y = 4

2 )x = 4, y = -3

3 )x = 3, y = -4

4 )x = -4, y = 3

Explanation:

Exp: B
x = 4, y = -3
Since, HCF of 56 and 72, by Euclid’s division lemma,
72 = 56 × 1 + 16 ...(i)
56 = 16 × 3 + 8 ...(ii)
16 = 8 × 2 + 0 ...(iii)
$∴$ HCF of 56 and 72 is 8.
$∴$ 8 = 56 - 16× 3 ( from eq. (ii))
8 = 56 - (72 - 56 × 1) × 3 [From eq. (i) : 16 = 72 - 56 × 1]
8 = 56 - 3 × 72 + 56 × 3
8 = 56 × 4 + (-3) × 72
$∴$ x = 4, y = -3

REAL NUMBERS

90428 Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion $\frac{7}{210}$ :

1 )Terminating decimal expansion

2 )Non -terminating decimal expansion

3 )Cannot be determined

4 )None

Explanation:

Exp: B
Non -terminating decimal expansion
Simplify it by dividing nominator and denominator both by 7 we get $\frac{1}{30}$
Factorize the denominator we get 30 = 2 × 3 × 5
Denominator has 3 also in denominator
So denominator is not in form of 2 $^{n}$ × 5 $^{n}$

REAL NUMBERS

90180 Euclid's division lemma sates that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy:

1 )

1 < r < b

2 )

0 < r \leq b

3 )

0 \leq r < b

4 )

0 < r < b

Explanation:

Exp: C
$0 \leq r < b$
Euclid's division lemma states that,
For any positive integers a and b, there exist unique integers q and r such that
$a = bq + r,$ where $0 \leq r < b$
Never Active

REAL NUMBERS

90184 A die is thrown once. Find the probability of getting a number between 3 and 6.

1 )

\frac{2}{3}

2 )

\frac{1}{2}

3 )

\frac{1}{4}

4 )

\frac{1}{3}

Explanation:

Exp: D
$\frac{1}{3}$
Total number of outcomes ={1, 2, 3, 4, 5, 6} = 6
favourable outcomes in this case = {4, 5} = 2
$∴$ p (a number between 3 and 6)
$= \frac{favourable outcomes}{total outcomes} = \frac{2}{6} = \frac{1}{3}$

REAL NUMBERS

90185 If d is the HCF of 56 and 72, the values of x, y satisfying d = 56x + 72y:

1 )x = -3, y = 4

2 )x = 4, y = -3

3 )x = 3, y = -4

4 )x = -4, y = 3

Explanation:

Exp: B
x = 4, y = -3
Since, HCF of 56 and 72, by Euclid’s division lemma,
72 = 56 × 1 + 16 ...(i)
56 = 16 × 3 + 8 ...(ii)
16 = 8 × 2 + 0 ...(iii)
$∴$ HCF of 56 and 72 is 8.
$∴$ 8 = 56 - 16× 3 ( from eq. (ii))
8 = 56 - (72 - 56 × 1) × 3 [From eq. (i) : 16 = 72 - 56 × 1]
8 = 56 - 3 × 72 + 56 × 3
8 = 56 × 4 + (-3) × 72
$∴$ x = 4, y = -3