Number System - Study Mode
[#451] The fractions $$frac{1}{3}{ ext{,}}frac{4}{7}$$ and $$frac{2}{5}$$ written in ascending order given by -
Correct Answer
(C) $$frac{1}{3} < frac{2}{5} < frac{4}{7}$$
Explanation
Solution: $$eqalign{
& frac{1}{3}{ ext{,}}frac{4}{7},frac{2}{5} cr
& frac{1}{3} = 0.33,{ ext{ }} cr
& frac{4}{7} = 0.5, cr
& frac{2}{5} = 0.4 cr
& frac{1}{3} < frac{2}{5} < frac{4}{7} cr} $$
[#452] If 17 200 is divided by 18, the remainder is -
Correct Answer
(C) 1
Explanation
Solution: $$eqalign{
& = {17^{200}} div 18 cr
& = {left( {18 - 1}
ight)^{200}} div 18 cr} $$ Apply Binomial theorem $$ = {left( {18}
ight)^{200}}{left( { - 1}
ight)^0} + {left( {18}
ight)^{199}}{left( { - 1}
ight)^1} + $$ xa0 xa0 xa0 $$..... + , {left( {18}
ight)^1}{left( { - 1}
ight)^{199}}$$ xa0 $$ , + , {left( {18}
ight)^0}{left( { - 1}
ight)^{200}}$$ $$ Rightarrow $$ Remainder always comes from last term is (18) 0 (- 1) 200 $$eqalign{
& = frac{{{{left( {18}
ight)}^0}{{left( { - 1}
ight)}^{200}}}}{{18}} cr
& = 1 imes {1^{200}} cr
& = 1 cr
& { ext{So, remainder}} = 1 cr} $$
[#453] Given that, three numbers are such that the second number is twice the first and thrice the third. Also the average of the three numbers is 44. then the difference of the first and the third is :
Correct Answer
(C) 12
Explanation
Solution: Let numbers are 3x, 6x, 2x Average :
$$frac{11x}{3}$$ = 44 x = 12 = Difference
[#454] A number is doubled and 9 is added, If the resultant is tripled, it becomes 75. What is the number ?
Correct Answer
(C) 8
Explanation
Solution: $$eqalign{
& { ext{Let the number is }}x{ ext{}} cr
& { ext{According to question,}} cr
& { ext{3}}left( {2x + 9}
ight) = 75 cr
& 2x + 9 = 25 cr
& x = frac{{16}}{2} cr
& x = 8 cr} $$
[#455] A number of boys raised Rs. 400 for a famine relief fund, each boy giving as many 25 paise coins as there were boys. The number of boys was -
Correct Answer
(A) 40
Explanation
Solution: $$eqalign{
& { ext{Let number of boys}} = x cr
& { ext{Number of 25 paise coins}} = {x^2} cr
& { ext{According to question,}} cr
& frac{{{x^2}}}{4} = 400 cr
& {x^2} = 1600 cr
& x = 40,, cr} $$