Simplification - Study Mode

[#211] The value of $$frac{4}{5} div 3frac{1}{4}{ ext{ of }}frac{8}{{13}} - frac{{frac{1}{5} - frac{1}{8}}}{{frac{1}{5} + frac{1}{8}}} imes 5frac{1}{5} + frac{5}{6},{ ext{is:}}$$
Correct Answer

(D) $$frac{1}{{30}}$$

Explanation

Solution: $$eqalign{
& frac{4}{5} div 3frac{1}{4}{ ext{ of }}frac{8}{{13}} - frac{{frac{1}{5} - frac{1}{8}}}{{frac{1}{5} + frac{1}{8}}} imes 5frac{1}{5} + frac{5}{6} cr
& = frac{4}{5} div frac{{13}}{4} imes frac{8}{{13}} - frac{{frac{1}{5} - frac{1}{8}}}{{frac{1}{5} + frac{1}{8}}} imes 5frac{1}{5} + frac{5}{6} cr
& = frac{2}{5} - frac{3}{{13}} imes frac{{26}}{5} + frac{5}{6} cr
& = frac{2}{5} - frac{6}{5} + frac{5}{6} cr
& = frac{{12 - 36 + 25}}{{30}} cr
& = frac{1}{{30}} cr} $$

[#212] Which of the following statement is correct? I. The value of 100 2 - 99 2 + 98 2 - 97 2 + 96 2 - 95 2 + 94 2 - 93 2 + . . . . + 2 2 - 1 2 is 5050. II. If 8x + $$frac{8}{{ ext{x}}}$$ = -16 and x < 0, then the value of x 197 + x -197 is 2.
Correct Answer

(A) Only I

Explanation

Solution: I . 100 2 − 99 2 ⎵ + 98 2 − 97 2 + . . . . + 2 2 − 1 2 $$eqalign{
& = left( {100 + 99}
ight)left( {100 - 99}
ight) + left( {98 + 97}
ight)left( {98 - 97}
ight) + left( {96 + 95}
ight)left( {96 - 95}
ight) + ,.,.,.,., + left( {2 + 1}
ight)left( {2 - 1}
ight) cr
& Rightarrow frac{{nleft( {n + 1}
ight)}}{2} = { ext{ sum of }}n{ ext{ terms}} cr
& = frac{{100 imes 101}}{2} cr
& = 5050 cr
& { ext{Statement I is true}} cr
& { ext{II}}{ ext{. }}8x + frac{8}{x} = - 16 cr
& { ext{Put }}x = - 1 cr
& { ext{Then }}{x^{197}} + {x^{ - 197}} cr
& = {left( { - 1}
ight)^{197}} + {left( { - 1}
ight)^{ - 197}} cr
& = - 1 - 1 cr
& = - 2 cr
& { ext{Statement II is incorrect}} cr} $$

[#213] The value of $$frac{3}{4} imes 2frac{2}{3} div frac{5}{9}{ ext{ of }}1frac{1}{5} + frac{2}{{23}} imes 3frac{5}{6} div frac{2}{7}{ ext{ of }}2frac{1}{3}$$ xa0 xa0 xa0 xa0is:
Correct Answer

(C) $$3frac{1}{2}$$

Explanation

Solution: $$eqalign{
& frac{3}{4} imes 2frac{2}{3} div frac{5}{9}{ ext{ of }}1frac{1}{5} + frac{2}{{23}} imes 3frac{5}{6} div frac{2}{7}{ ext{ of }}2frac{1}{3} cr
& = frac{3}{4} imes frac{8}{3} div frac{5}{9}{ ext{ of }}frac{6}{5} + frac{2}{{23}} imes frac{{23}}{6} div frac{2}{7}{ ext{ of }}frac{7}{3} cr
& = frac{3}{4} imes frac{8}{3} div frac{2}{3} + frac{2}{{23}} imes frac{{23}}{6} div frac{2}{3} cr
& = frac{3}{4} imes frac{8}{3} imes frac{3}{2} + frac{2}{{23}} imes frac{{23}}{6} div frac{2}{3} cr
& = 3 + frac{1}{2} cr
& = 3frac{1}{2} cr} $$

[#214] The value of $$3frac{1}{3} div 2frac{1}{2}{ ext{ of }}1frac{3}{5} + left( {frac{3}{8} + frac{1}{7} imes 1frac{3}{4}}
ight)$$ xa0 xa0 xa0is:
Correct Answer

(B) $$frac{{35}}{{24}}$$

Explanation

Solution: $$eqalign{
& 3frac{1}{3} div 2frac{1}{2}{ ext{ of }}1frac{3}{5} + left( {frac{3}{8} + frac{1}{7} imes 1frac{3}{4}}
ight) cr
& = frac{{10}}{3} div frac{5}{2} imes frac{8}{5} + left( {frac{3}{8} + frac{1}{7} imes frac{7}{4}}
ight) cr
& = frac{{10}}{3} imes frac{1}{4} + frac{5}{8} cr
& = frac{5}{6} + frac{5}{8} cr
& = frac{{35}}{{24}} cr} $$

[#215] Evaluate: {7 + 7 × (7 + 7 ÷ 7)} + 7 ÷ 7.
Correct Answer

(D) 64

Explanation

Solution: [7 + 7 × (7 + 7 ÷ 7)] + 7 ÷ 7 = [7 + 7 × (7 + 1)] + 1 = [7 + 56] + 1 = 64