# Exercise : 8

^{5}⁄

_{7}

(b)

^{3}⁄

_{4}

(c)

^{2}⁄

_{3}

(d)

^{6}⁄

_{7}

(e)

^{7}⁄

_{8}

**Ans.e**

**Note** : If the difference between the numerator and the denominator is constant, then the fraction which has larger value in the numerator is the larger fraction.

Using the above, among the options (a), (c), (d) and (e), (e) has the larger value. Now, compared to option(a), (e) has the larger value.

^{4}⁄

_{9}of

^{3}⁄

_{10}of

^{5}⁄

_{8}of a number is 45, what is the number?

(b) 550

(c) 560

(d) 650

(e) None of these

**Ans.e**

Number = \(\frac{45 \times 9 \times 10 \times 8}{4 \times 3 \times 5} \Rightarrow 540\)

25^{7.5} × 5^{2.5} ÷ 125^{1.5} = 5^{?}

(b) 17.5

(c) 8.5

(d) 13

(e) None of these

**Ans.d**

25^{7.5} × 5^{2.5} ÷ 125^{1.5} = 5^{?}

or, 5^{2 × 7.5} × 5^{2.5} ÷ 5^{3 × 1.5} = 5^{?}

or 5^{15} × 5^{2.5} × ^{1}⁄_{54.5} = 5^{?}

or, 5^{13} = 5^{?} or, ? = 13

(b) 593.27 – 167.20 + 439.60

(c) 490.92 + 439.65 – 64.9

(d) (7189.3 – 2860.93) + 5

(e) 2(269.40 + 163.435)

**Ans.d**

Others are equal to 865.67.

^{2}– x

^{2}y + 2x

^{2}y

^{2}

(b) xy

^{2}(1 – 2x) + x

^{2}y(2y – 1)

(c) xy

^{2}(1 + x) – x

^{2}y(1 – y)

(d) xy[y(1 + x) – x(1 – y)]

(e) xy(y – x + 2xy)

**Ans.b**

The other parts are equal to xy^{2} – x^{2}y + 2x^{2}y^{2}.

^{2}+ 4ab

(b) a(a + b) + b(a + b)

(c) (a

^{2}– b

^{2}) + 2b(b + a)

(d) (a – b)b + (a + b)2b

(e) (a + b)

^{2}– 2a(a – b) + a(2a – 2b)

**Ans.d**

The other parts are equal to (a + b)^{2}.

^{2}+ 5ab + 6b

^{2}

(b) (a + 3b)(a + 2b)

(c) a(a + 3b) + 2b(a + 3b)

(d) (3a + b)(a + 2b)

(e) a(a + 2b) + 3b(a + 2b)

**Ans.d**

The other parts are equal to a^{2} + 5ab + 6b^{2}.

^{2}– ab + 3b

^{2}

(b) (a – b)(2a – 3b) + 4ab

(c) (a – b)

^{2}+ (a

^{2}+ ab + 2b

^{2})

(d) (a + b)

^{2}+ (a

^{2}+ 2b

^{2}– 3ab)

(e) (a + b)(a – b) + (2a

^{2}– ab + 4b

^{2})

**Ans.e**

The other parts are equal to 34.

16\(\sqrt{524}\) + 1492 - 250.0521?

(b) 1800

(c) 1900

(d) 2400

(e) 1400

**Ans.a**

? ≈ 16 × 23 + 1490 – 250 ≈ 1600

^{2}– 12

^{2}+ 112 ÷ 14

(b) 17 × 12 + 59 × 4

(c) 15 × 28 + 20

(d) 27 × 16 + 56 ÷ 8

(e) 185 × 6 ÷ 2 – 23 × 5

**Ans.d**

Other parts are equal to 440.