Algebra - Study Mode

[#161] If $$sqrt {0.03 imes 0.3a} $$ xa0 = $${ ext{0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} imes sqrt b { ext{,}}$$ xa0xa0 value of $$frac{a}{b},{ ext{is?}}$$
Correct Answer

(C) 0.9

Explanation

Solution: $$eqalign{
& sqrt {0.03 imes 0.3a} = { ext{0}}{ ext{.3}} imes { ext{0}}{ ext{.3}} imes sqrt b cr
& { ext{Squaring both sides}} cr
& Rightarrow { ext{0}}{ ext{.03}} imes { ext{0}}{ ext{.3a}} = {left( {0.3}
ight)^2} imes {left( {0.3}
ight)^2} imes b cr
& Rightarrow frac{3}{{100}} imes frac{3}{{10}}a = frac{9}{{100}} imes frac{9}{{100}} imes b cr
& Rightarrow 9a = frac{{81}}{{10}}b cr
& Rightarrow 90a = 81b cr
& Rightarrow 10a = 9b cr
& Rightarrow frac{a}{b} = frac{9}{{10}} cr
& Rightarrow frac{a}{b} = 0.9 cr} $$

[#162] If x * y = (x + 3) 2 (y - 1), then the value of 5 * 4 is?
Correct Answer

(A) 192

Explanation

Solution: $$eqalign{
& x*y = {left( {x + 3}
ight)^2}left( {y - 1}
ight) cr
& Leftrightarrow 5*4 = {left( {5 + 3}
ight)^2}left( {4 - 1}
ight) cr
& Leftrightarrow 5*4 = 64 imes 3 cr
& Leftrightarrow 5*4 = 192 cr} $$

[#163] $${ ext{If }}sqrt {1 + frac{x}{{961}}} = frac{{32}}{{31}}{ ext{,}}$$ xa0 xa0 then the value of x is?
Correct Answer

(A) 63

Explanation

Solution: $$eqalign{
& sqrt {1 + frac{x}{{961}}} = frac{{32}}{{31}} cr
& left( {{ ext{Squaring both sides}}}
ight) cr
& Rightarrow 1 + frac{x}{{961}} = frac{{1024}}{{961}} cr
& Rightarrow frac{{961 + x}}{{961}} = frac{{1024}}{{961}} cr
& Rightarrow x = 1024 - 961 cr
& Rightarrow x = 63 cr} $$

[#164] If $$sqrt {0.04 imes 0.4 imes a} $$ xa0xa0 = 0.004 × 0.4 × $$sqrt b ,$$xa0 then the value of $$frac{a}{b},{ ext{is?}}$$
Correct Answer

(C) $${ ext{16}} imes { ext{1}}{{ ext{0}}^{ - 5}}$$

Explanation

Solution: $$eqalign{
& { ext{ }}sqrt {0.04 imes 0.4 imes a} = 0.004 imes 0.4 imes sqrt b cr
& Rightarrow sqrt {frac{4}{{100}} imes frac{4}{{10}} imes a} = frac{4}{{1000}} imes frac{4}{{10}} imes sqrt b cr
& Rightarrow frac{4}{{10}}sqrt {frac{a}{{10}}} = frac{4}{{10}} imes frac{4}{{1000}} imes sqrt b cr
& Rightarrow frac{a}{{10}} = frac{{16}}{{1000000}} imes b cr
& Rightarrow frac{a}{b} = frac{{16 imes 10}}{{1000000}} cr
& Rightarrow frac{a}{b} = frac{{16}}{{100000}} cr
& Rightarrow frac{a}{b} = 16 imes {10^{ - 5}} cr} $$

[#165] If $$frac{a}{b} = frac{c}{d} = frac{e}{f} = 3,$$ xa0xa0 then $$frac{{2{a^2} + 3{c^2} + 4{e^2}}}{{2{b^2} + 3{d^2} + 4{f^2}}}$$ xa0xa0 = ?
Correct Answer

(D) 9

Explanation

Solution: $$eqalign{
& frac{a}{b} = frac{c}{d} = frac{e}{f} = frac{3}{1} cr
& Rightarrow frac{{2 imes 9 + 3 imes 9 + 4 imes 9}}{{2 imes 1 + 3 imes 1 + 4 imes 1}} cr
& Rightarrow frac{{18 + 27 + 36}}{{2 + 3 + 4}} cr
& Rightarrow frac{{81}}{9} cr
& Rightarrow 9 cr} $$