Algebra - Study Mode
[#141] If x : y = 7 : 3 then the value of $$frac{{xy + {y^2}}}{{{x^2} - {y^2}}}{ ext{ is?}}$$
Correct Answer
(A) $$frac{3}{4}$$
Explanation
Solution: $$eqalign{
& x:y cr
& 7:3{ ext{ }} cr
& herefore { ext{ }}frac{{xy + {y^2}}}{{{x^2} - {y^2}}} cr
& = frac{{21 + 9}}{{49 - 9}} cr
& = frac{{30}}{{40}} cr
& = frac{3}{4} cr} $$
[#142] If [p] means the greatest positive integer less than or equal to p, then $$left[ { - frac{1}{4}}
ight] + left[ {4 - frac{1}{4}}
ight] + left[ 3
ight]$$ xa0 xa0 is equal to?
Correct Answer
(D) 7
Explanation
Solution: Given [p] means the greatest positive integer less than or [p] equal to p $$eqalign{
& Rightarrow left[ { ext{p}}
ight] = { ext{ p}} cr
& Rightarrow left[ -{ ext{p}}
ight] = { ext{ p}} cr
& Rightarrow left[ { - frac{1}{4}}
ight]{ ext{ + }}left[ {4 - frac{1}{4}}
ight] + left[ 3
ight] cr
& Rightarrow frac{1}{4} + 4 - frac{1}{4} + 3 cr
& Rightarrow 7 cr} $$
[#143] The value of $$frac{{{{left( {243}
ight)}^{frac{n}{5}}}{{.3}^{2n + 1}}}}{{{9^n}{{.3}^{n - 1}}}}{ ext{ is?}}$$
Correct Answer
(B) 9
Explanation
Solution: $$eqalign{
& frac{{{{left( {243}
ight)}^{frac{n}{5}}}{{.3}^{2n + 1}}}}{{{9^n}{{.3}^{n - 1}}}} cr
& = frac{{{{left( {{3^5}}
ight)}^{frac{n}{5}}}{{.3}^{2n + 1}}}}{{{3^{2n}}{{.3}^{n - 1}}}} cr
& = frac{{{3^{n + 2n + 1}}}}{{{3^{2n + n - 1}}}} cr
& = frac{{{3^{3n + 1}}}}{{{3^{3n - 1}}}} cr
& = {3^{3n + 1 - 3n + 1}} cr
& = {3^2} cr
& = 9 cr} $$
[#144] If x = 0.5 and y = 0.2, then the value of $$sqrt {0.6} imes {left( {3y}
ight)^x}$$ xa0 is equal to?
Correct Answer
(C) 0.6
Explanation
Solution: $$eqalign{
& x = 0.5 cr
& y = 0.2 cr
& sqrt {0.6} imes {left( {3y}
ight)^x}{ ext{ }} cr
& = sqrt {0.6} imes {left( {3 imes 0.2}
ight)^{0.5}}{ ext{ }} cr
& = sqrt {0.6} imes sqrt {0.6} cr
& = 0.6 cr} $$
[#145] If $${x^{xsqrt x }} = {left( {xsqrt x }
ight)^x}{ ext{,}}$$ xa0xa0 then x equals to?
Correct Answer
(C) $$frac{9}{4}$$
Explanation
Solution: $$eqalign{
& {x^{xsqrt x }} = {left( {xsqrt x }
ight)^x} cr
& {x^{xsqrt x }} = {left( {{x^{frac{3}{2}}}}
ight)^x} cr
& {x^{xsqrt x }} = {x^{frac{3}{2}x}} cr} $$ (If bases are same then their power is also same) $$eqalign{
& herefore xsqrt x = frac{3}{2}x cr
& Rightarrow sqrt x = frac{3}{2} cr
& Rightarrow x = {left( {frac{3}{2}}
ight)^2} cr
& Rightarrow x = frac{9}{4} cr} $$