Decimal Fraction - Study Mode

[#141] $$2frac{1.5}{5}$$ + 2$$frac{1}{6}$$ - $$1frac{3.5}{15}$$ = $$left( {frac{{{{(?)}^{frac{1}{3}}}}}{4}}
ight)$$xa0 + $$1frac{7}{30}$$
Correct Answer

(C) 512

Explanation

Solution: $$eqalign{
& 2frac{{1.5}}{5} + 2frac{1}{6} - 1frac{{3.5}}{{15}} = frac{{{x^{frac{1}{3}}}}}{4} + 1frac{7}{{30}} cr
& Rightarrow frac{{11.5}}{5} + frac{{13}}{6} - frac{{18.5}}{{15}} = frac{{{x^{frac{1}{3}}}}}{4} + frac{{37}}{{30}} cr} $$ ⇒ L.C.M. of 5, 6 and 15 is 30 $$eqalign{
& Rightarrow frac{{69 + 65 - 37}}{{30}} = frac{{{x^{frac{1}{3}}}}}{4} + frac{{37}}{{30}} cr
& Rightarrow frac{{97}}{{30}} = frac{{{x^{frac{1}{3}}}}}{4} + frac{{37}}{{30}} cr
& Rightarrow frac{{{x^{frac{1}{3}}}}}{4} = frac{{97}}{{30}} - frac{{37}}{{30}} cr
& Rightarrow {x^{frac{1}{3}}} = frac{{60}}{{30}} imes 4 cr
& Rightarrow {x^{frac{1}{3}}} = 8 cr
& Rightarrow x = {left( 8
ight)^3} cr
& Rightarrow x = 512 cr} $$ Hence, the number is 512

[#142] $$frac{4.41 × 0.16}{2.1 × 1.6 × 0.21}$$ xa0 is simplified to :
Correct Answer

(A) 1

Explanation

Solution: Given expression : = $$frac{441 × 16}{21 × 16 × 21}$$ = $$frac{{7056}}{{7056}}$$ = 1

[#143] The value of (0.98) 3 + (0.02) 3 + 3 × 0.98 × 0.02 - 1 is :
Correct Answer

(A) 0

Explanation

Solution: Given expression : [(0.98) 3 + (0.02) 3 + 3 × 0.98 × 0.02 (0.98 + 0.02)] - 1 = (0.98 + 0.02) 3 - 1 = (1) 3 - 1 = 0

[#144] Solve (41.99 2 - 18.04 2 ) ÷ ? = 13.11 2 - 138.99
Correct Answer

(A) 48

Explanation

Solution: {(41.99) 2 - (18.04) 2 } ÷ ? = (13.11) 2 - 138.99 ⇒ {(42) 2 - (18) 2 } ÷ ? = (13) 2 - 139 {∵ a 2 - b 2 = (a + b) (a - b)} ⇒ {(42 + 18) (42 - 18)} ÷ ? = 169 - 139 ⇒ 60 × 24 ÷ ? = 30 ⇒ ? = $$frac{60 × 24}{30}$$ ⇒ ? = 48

[#145] $$frac{{.009}}{?} = .01$$
Correct Answer

(C) .9

Explanation

Solution: $$eqalign{
& { ext{Let}},frac{{.009}}{x} = .01
cr
& { ext{Then}},x = frac{{.009}}{{.01}} cr
& ,,,,,,,,,,,,,,,,,,,, = frac{{.9}}{1} cr
& ,,,,,,,,,,,,,,,,,,,, = .9 cr} $$