Simplification - Study Mode

[#136] $$frac{{20 + 8 imes 0.5}}{{20 - ?}}{ ext{ = 12}}$$ xa0 xa0 Find the value in place of (?)
Correct Answer

(C) 18

Explanation

Solution: Let the missing number is x $$eqalign{
& { ext{Given,}} cr
& frac{{20 + 8 imes 0.5}}{{20 - x}}{ ext{ = 12}} cr
& Rightarrow frac{{20 + 4}}{{20 - x}} = 12 cr
& Rightarrow frac{{24}}{{20 - x}} = 12 cr
& Rightarrow 20 - x = frac{{24}}{{12}} = 2 cr
& Rightarrow x = 20 - 2 cr
& ,,,,,,,,,,,, = 18 cr
& { ext{Hence, the number is 18}} cr} $$

[#137] Let 0 < x < 1, then the correct inequality is = ?
Correct Answer

(C) $${x^2} < x < sqrt x $$

Explanation

Solution: $$eqalign{
& 0 < x < 1, cr
& { ext{Let }}x = frac{4}{{10}} cr
& { ext{So}},sqrt x = frac{2}{{sqrt {10} }},& , cr
& ,,{x^2} = frac{{16}}{{100}} = 0.16 cr
& { ext{Now}}, cr
& x08ecause 0.16 < frac{4}{{10}} < frac{2}{{sqrt {10} }} cr
& herefore {x^2} < x < sqrt x cr} $$

[#138] If $$frac{a}{b}{ ext{ + }}frac{b}{a}{ ext{ = 2,}}$$ xa0xa0 then the value of (a - b) is = ?
Correct Answer

(D) 0

Explanation

Solution: $$eqalign{
& { ext{Given,}}frac{a}{b}{ ext{ + }}frac{b}{a}{ ext{ = 2}} cr
& Rightarrow frac{{{a^2} + {b^2}}}{{ab}} = 2 cr
& Rightarrow {a^2} + {b^2} = 2ab cr
& Rightarrow {a^2} + {b^2} - 2ab = 0 cr
& Rightarrow {left( {a - b}
ight)^2} = 0 cr
& Rightarrow left( {a - b}
ight){ ext{ = 0 }} cr} $$

[#139] 24.96 2 ÷ (34.11 ÷ 20.05) + 67.96 - 89.11 = ?
Correct Answer

(B) 346

Explanation

Solution: Given, 24.96 2 ÷ (34.11 ÷ 20.05) + 67.96 - 89.11 ≈ (25) 2 ÷ (34 ÷ 20) + 68 - 89 ≈ (25) 2 ÷ $$frac{{34}}{{20}}$$ + 68 - 89 ≈ 625 ÷ 1.7 + 68 - 89 ≈ 367.6 + 68 - 89 ≈ 367 + 68 - 89 ≈ 346

[#140] The value of $$frac{{{x^2} - {{left( {y - z}
ight)}^2}}}{{{{left( {x + z}
ight)}^2} - {y^2}}}{ ext{ + }}$$ xa0 $$frac{{{y^2} - {{left( {x - z}
ight)}^2}}}{{{{left( {x + y}
ight)}^2} - {z^2}}} + $$ xa0 $$frac{{{z^2} - {{left( {x - y}
ight)}^2}}}{{{{left( {y + z}
ight)}^2} - {x^2}}}$$ xa0 is = ?
Correct Answer

(C) 1

Explanation

Solution: $$eqalign{
& { ext{Given xepression ,}} cr
& frac{{left( {x + y - z}
ight)left( {x - y + z}
ight)}}{{left( {x + y + z}
ight)left( {x + z - y}
ight)}} + frac{{left( {y + x - z}
ight)left( {y - x + z}
ight)}}{{left( {x + y + z}
ight)left( {x + y - z}
ight)}} + frac{{left( {z + x - y}
ight)left( {z - x + y}
ight)}}{{left( {y + z + x}
ight)left( {y + z - x}
ight)}} cr
& = frac{{left( {x + y - z}
ight)}}{{left( {x + y + z}
ight)}} + frac{{left( {y - x + z}
ight)}}{{left( {x + y + z}
ight)}} + frac{{left( {x - y + z}
ight)}}{{left( {x + y + z}
ight)}} cr
& = frac{{left( {x + y - z}
ight) + left( {y - x + z}
ight) + left( {x - y + z}
ight)}}{{left( {x + y + z}
ight)}} cr
& = frac{{x + y + z}}{{x + y + z}} cr
& = 1 cr} $$