Simplification - Study Mode
[#56] $$frac{{{{left( {0.73}
ight)}^3} + {{left( {0.27}
ight)}^3}}}{{{{left( {0.73}
ight)}^2} + {{left( {0.27}
ight)}^2} - 0.73 imes 0.27}}$$ xa0 xa0 xa0= ?
Correct Answer
(D) 1
Explanation
Solution: $$eqalign{
& { ext{Given,}} cr
& frac{{{{left( {0.73}
ight)}^3} + {{left( {0.27}
ight)}^3}}}{{{{left( {0.73}
ight)}^2} + {{left( {0.27}
ight)}^2} - 0.73 imes 0.27}} cr
& { ext{let }}a = 0.73{ ext{ and }}b = 0.27 cr} $$ $$ = frac{{left( {0.73 + 0.27}
ight)left[ {{{left( {0.73}
ight)}^2} + {{left( {0.27}
ight)}^2} - 0.73 imes 0.27}
ight]}}{{{{left( {0.73}
ight)}^2} + {{left( {0.27}
ight)}^2} - 0.73 imes 0.27}}$$ $$eqalign{
& left[ {x08ecause {a^3} + {b^3} = left( {a + b}
ight)left( {{a^2} + {b^2} - ab}
ight)}
ight] cr
& = 0.73 + 0.27 cr
& = 1 cr} $$
[#57] $$frac{{{{left( {a - b}
ight)}^2} - {{left( {a + b}
ight)}^2}}}{{ - 4a}}{ ext{ = }}frac{x}{y}$$ xa0 xa0 On simplifying the given equations, which of the following equations will be obtained ?
Correct Answer
(D) yb = x
Explanation
Solution: $$eqalign{
& frac{{{{left( {a - b}
ight)}^2} - {{left( {a + b}
ight)}^2}}}{{ - 4a}}{ ext{ = }}frac{x}{y} cr
& Rightarrow frac{{left( {{a^2} + {b^2} - 2ab}
ight) - left( {{a^2} + {b^2} + 2ab}
ight)}}{{ - 4a}} = frac{x}{y} cr
& Rightarrow frac{{ - 4ab}}{{ - 4a}} = frac{x}{y} cr
& Rightarrow b = frac{x}{y} cr
& Rightarrow x = yb cr} $$
[#58] Let $$x = frac{{5frac{3}{4} - frac{3}{7} imes 15frac{3}{4} + 2frac{2}{{35}} div 1frac{{11}}{{25}}}}{{frac{3}{4} div 5frac{1}{4} + 5frac{3}{5} div 3frac{4}{{15}}}}.$$ xa0 xa0 xa0When y is added to x, the result is $$frac{7}{{13}}.$$xa0What is the value of y?
Correct Answer
(B) $$frac{4}{{13}}$$
Explanation
Solution: $$eqalign{
& x = frac{{5frac{3}{4} - frac{3}{7} imes 15frac{3}{4} + 2frac{2}{{35}} div 1frac{{11}}{{25}}}}{{frac{3}{4} div 5frac{1}{4} + 5frac{3}{5} div 3frac{4}{{15}}}} cr
& x = frac{{frac{{23}}{4} - frac{3}{7} imes frac{{63}}{4} + frac{{72}}{{35}} div frac{{36}}{{25}}}}{{frac{3}{4} div frac{{21}}{4} + frac{{28}}{5} div frac{{49}}{{15}}}} cr
& x = frac{{frac{{23}}{4} - frac{{27}}{4} + frac{{10}}{7}}}{{frac{1}{7} + frac{{12}}{7}}} cr
& x = frac{{ - frac{4}{4} + frac{{10}}{7}}}{{frac{{13}}{7}}} cr
& x = frac{{frac{{ - 7 + 10}}{7}}}{{frac{{13}}{7}}} cr
& x = frac{3}{{13}} cr
& x + y = frac{7}{{13}} cr
& y = frac{7}{{13}} - frac{3}{{13}} cr
& y = frac{4}{{13}} cr} $$
[#59] Which of the following is the smallest fraction?
Correct Answer
(C) $$frac{4}{7}$$
Explanation
Solution: A. $$frac{{12}}{{15}}$$ = 0.8 B. $$frac{{11}}{{16}}$$ = 0.6875 C. $$frac{4}{7}$$ = 0.5714 D. $$frac{7}{{12}}$$ = 0.5833 Smallest fraction = $$frac{4}{7}$$ Answer
[#60] 2.8 + (5.2 ÷ 1.3 × 2) - 6 × 3 ÷ 8 + 2 the value of:
Correct Answer
(D) 10.55
Explanation
Solution: 2.8 + (5.2 ÷ 1.3 × 2) - 6 × 3 ÷ 8 + 2 = 2.8 + (4 × 2) - $$frac{{6 imes 3}}{8}$$xa0+ 2 = 2.8 + 8 - 2.25 + 2 = 10.55