Simplification - Study Mode

[#226] Evaluated : $${{9left| {3 - 5}
ight| - 5left| 4
ight| div 10} over { - 3left( 5
ight) - 2 imes 4 div 2}}$$
Correct Answer

(C) $$ - frac{16}{{19}}$$

Explanation

Solution: $$eqalign{
& { ext{According to question}} cr
& frac{{9|3 - 5| - 5|4| div 10}}{{ - 3left( 5
ight) - 2 imes 4 div 2}} cr
& Rightarrow frac{{9 imes 2 - 20 div 10}}{{ - 15 - 2 imes 2}} cr
& Rightarrow frac{{18 - 2}}{{ - 15 - 4}} cr
& Rightarrow - frac{{16}}{{19}} cr} $$

[#227] 5 - [4 - {3 - (3 - 3 - 6)}] is equal to:
Correct Answer

(A) 10

Explanation

Solution: Given, 5 - [4 - {3 - (3 - 3 - 6)}] = 5 - [4 - {3 - (-6)}] = 5 - [4 - {3 +6}] = 5 - [4 - {9}] = 5 - [4 - 9] = 5 - [-5] = 5 + 5 = 10

[#228] Evaluate : $${{ - {{left( {4 - 6}
ight)}^2} - 3left( { - 2}
ight) + left| { - 6}
ight|} over {18 - 9 div 3 imes 5}}$$
Correct Answer

(C) $$frac{8}{3}$$

Explanation

Solution: $$eqalign{
& frac{{ - {{left( {4 - 6}
ight)}^2} - 3left( { - 2}
ight) + left| { - 6}
ight|}}{{18 - 9 div 3 imes 5}} cr
& = frac{{ - {{left( { - 2}
ight)}^2} - left( { - 6}
ight) + 6}}{{18 - 3 imes 5}} cr
& = frac{{ - 4 + 6 + 6}}{{18 - 15}} cr
& = frac{8}{3} cr} $$

[#229] The value of $$frac{2}{3} imes frac{3}{{frac{5}{6} div frac{2}{3}{ ext{ of 1}}frac{1}{4}}} = ?$$
Correct Answer

(A) 2

Explanation

Solution: $$eqalign{
& { ext{According to question,}} cr
& ,,,,,,frac{2}{3} imes frac{3}{{frac{5}{6} div frac{2}{3}{ ext{of 1}}frac{1}{4}}} cr
& Rightarrow frac{2}{3} imes frac{3}{{frac{5}{6} div left( {frac{2}{3} imes frac{5}{4}}
ight)}} cr
& Rightarrow frac{2}{3} imes frac{3}{{frac{5}{6} div frac{5}{6}}} cr
& Rightarrow frac{2}{3} imes frac{3}{1} cr
& Rightarrow 2 cr} $$

[#230] The value of (0.98) 3 + (0.02) 3 + 3 × 0.98 × 0.02 - 1 = ?
Correct Answer

(D) 0

Explanation

Solution: According to question, (0.98) 3 + (0.02) 3 + 3 × 0.98 × 0.02 - 1 = (0.98) 3 + (0.02) 3 + 3 × 0.98 × 0.02(0.98 + 0.02) - 1 = (0.98 + 0.02) 3 - 1 xa0 [∴ (a + b) 3 = a 3 + b 3 + 3ab(a + b)] = (1) 3 - 1 = 0 Alternate a = 0.98, b = 0.02, c = -1 a + b + (-c) = 0 So, a 3 + b 3 + (-c) 3 - 3abc = 0