Simplification - Study Mode

[#71] $$left( {999frac{{999}}{{1000}} imes 7}
ight)$$ xa0 is equal to = ?
Correct Answer

(C) $${ ext{6999}}frac{993}{{1000}}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression ,}} cr
& left( {1000 - frac{1}{{1000}}}
ight) imes 7 cr
& = left( {7000 - frac{7}{{1000}}}
ight) cr
& = 6999frac{{993}}{{1000}} cr} $$

[#72] The value of $${ ext{1 + }}frac{1}{{4 imes 3}} + frac{1}{{4 imes {3^2}}} + frac{1}{{4 imes {3^2}}} = ?$$
Correct Answer

(A) $$frac{{121}}{{108}}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& frac{{4 imes {3^3} + {3^2} + 3 + 1}}{{4 imes {3^3}}} cr
& = frac{{108 + 9 + 3 + 1}}{{108}} cr
& = frac{{121}}{{108}} cr} $$

[#73] $$frac{1}{{1.2.3}} + frac{1}{{2.3.4}} + frac{1}{{3.4.5}} + frac{1}{{4.5.6}}$$ xa0 xa0 xa0 is equal to = ?
Correct Answer

(A) $$frac{7}{{30}}$$

Explanation

Solution: $$eqalign{
& { ext{Given expression,}} cr
& frac{{4.5.6 + 5.6 + 2.6 + 2.3}}{{1.2.3.4.5.6}} cr
& = frac{{120 + 30 + 12 + 6}}{{720}} cr
& = frac{{168}}{{720}} cr
& = frac{7}{{30}} cr} $$

[#74] $$sqrt {frac{{0.009 imes 0.036 imes 0.016 imes 0.08}}{{0.002 imes 0.0008 imes 0.0002}}} $$ xa0 xa0 xa0 is equal to = ?
Correct Answer

(B) 36

Explanation

Solution: $$eqalign{
& { ext{According to question,}} cr
& sqrt {frac{{0.009 imes 0.036 imes 0.016 imes 0.08}}{{0.002 imes 0.0008 imes 0.0002}}} , cr
& Rightarrow sqrt {frac{{9 imes 36 imes 16 imes 8}}{{2 imes 8 imes 2}}} cr
& Rightarrow 3 imes 6 imes 2 cr
& Rightarrow 36 cr} $$

[#75] $$left[ {2sqrt {54} - 6sqrt {frac{2}{3}} - sqrt {96} }
ight]$$ xa0 xa0 is equal to = ?
Correct Answer

(A) 0

Explanation

Solution: $$eqalign{
& { ext{According to question,}} cr
& 2sqrt {54} - 6sqrt {frac{2}{3}} - sqrt {96} cr
& = ,6sqrt 6 - 2sqrt {frac{2}{3} imes 9} - 4sqrt 6 cr
& = 6sqrt 6 - 2sqrt 6 - 4sqrt 6 cr
& = 0 cr} $$