Number System - Study Mode

[#261] If sum of two numbers be a and their product be b, then the sum of their reciprocals is :
Correct Answer

(C) $$frac{{a}}{{b}}$$

Explanation

Solution: Let the two number are P and Q P + Q = a PQ = b ⇒ $$frac{{1}}{{P}}$$ + $$frac{{1}}{{Q}}$$ ⇒ $$frac{{Q + P}}{{PQ}}$$ ⇒ $$frac{{a}}{{b}}$$

[#262] If the numbers $$
oot 3 of {9} ,
oot 4 of 20 ,
oot 6 of {25} $$ xa0 are arranged in ascending order, then the right arrangement is -
Correct Answer

(C) $$ oot 6 of {25} , < oot 3 of 9 , < oot 4 of {20} $$

Explanation

Solution: $$
oot 3 of 9 ,,,
oot 4 of {20} ,,,
oot 6 of {25} $$ Taking L.C.M of 3, 4 and 6 $$eqalign{
& =
oot {12} of {{9^4}} ,,,
oot {12} of {{{20}^3}} ,,,
oot {12} of {{{25}^2}} cr
& =
oot {12} of {6561} ,,,
oot {12} of {8000} ,,,
oot {12} of {625} cr} $$ So, ascending order $$ =
oot 6 of {25} , <
oot 3 of 9 , <
oot 4 of {20} $$

[#263] Which of the following fraction is the smallest ? $$frac{8}{{15}},$$ $$frac{{14}}{{33}},$$ $$frac{7}{{13}},$$ $$frac{{11}}{{13}}$$
Correct Answer

(B) $$frac{{14}}{{33}}$$

Explanation

Solution: $$frac{8}{{15}},frac{{14}}{{33}},frac{7}{{13}},frac{{11}}{{13}}$$ (264) , (210) ↑ ↑ $$frac{8}{{15}}$$ ⤩ $$frac{14}{{33}}$$ = $$frac{8}{{15}}$$ > $$frac{14}{{33}}$$ (182) , (231) ↑ ↑ $$frac{14}{{33}}$$ ⤩ $$frac{7}{{13}}$$ = $$frac{14}{{33}}$$ < $$frac{7}{{13}}$$ < $$frac{11}{{13}}$$ $${ ext{So}}frac{{14}}{{33}},{ ext{is}},{ ext{smallest}}$$

[#264] When 'n' is divisible by 5 the remainder is 2. What is the remainder when n 2 is divided by 5 ?
Correct Answer

(D) 4

Explanation

Solution: $$eqalign{
& frac{{ ext{n}}}{5} Rightarrow { ext{remainder}},,2 cr
& { ext{if we put n = 7}} cr} $$ Then it satisfies above situation $$eqalign{
& { ext{so n = 7}} cr
& frac{{{{ ext{n}}^2}}}{5} = frac{{{7^2}}}{5} = frac{{49}}{5} cr
& Rightarrow { ext{remainder = 4}} cr} $$

[#265] The number π is :
Correct Answer

(D) An irrational number

Explanation

Solution: Clearly, π is an irrational number