Number System - Study Mode
[#626] In a farm there are cows and hens. If heads are counted there are 180, if legs are counted there are 420. The number of cows in the farm is :
Correct Answer
(D) 30
Explanation
Solution: Let the number of cows be x. Then, number of hens would be (180 - x) According to the question (180 - x) × 2 + 4x = 420 ⇒ 360 - 2x + 4x = 420 ⇒ 2x = 420 - 360 = 60 ⇒ 2x = 60 ∴ x = $$frac{{60}}{2}$$ = 30
[#627] $$frac{1}{{20}}$$ $$ + $$ $$frac{1}{{30}}$$ $$ + $$ $$frac{1}{{42}}$$ $$ + $$ $$frac{1}{{56}}$$ $$ + $$ $$frac{1}{{72}}$$ $$ + $$ $$frac{1}{{90}}$$ $$ + $$ $$frac{1}{{110}}$$xa0 $$ + $$ $$frac{1}{{132}}$$xa0 is equal to :
Correct Answer
(C) $$frac{1}{6}$$
Explanation
Solution: $$frac{1}{{20}} + frac{1}{{30}} + frac{1}{{42}} + frac{1}{{56}} + frac{1}{{72}} + frac{1}{{90}}$$ xa0 xa0 xa0$$ + frac{1}{{110}}$$ xa0 $$ + frac{1}{{132}}$$ $$ = left( {frac{1}{{4 imes 5}}}
ight) + left( {frac{1}{{5 imes 6}}}
ight) + left( {frac{1}{{6 imes 7}}}
ight)$$ xa0 xa0 xa0 $$ + ..... + $$ xa0 $$left( {frac{1}{{11 imes 12}}}
ight)$$ $$ = left( {frac{1}{4} - frac{1}{5}}
ight) + left( {frac{1}{5} - frac{1}{6}}
ight) + left( {frac{1}{6} - frac{1}{7}}
ight)$$ xa0 xa0 xa0 $$ + ..... + $$ xa0 $$left( {frac{1}{{11}} - frac{1}{{12}}}
ight)$$ $$ = frac{1}{4} - frac{1}{5} + frac{1}{5} - frac{1}{6} + frac{1}{6} - frac{1}{7} , + .....$$ xa0 xa0 xa0$$ + frac{1}{{11}}$$ xa0$$ - frac{1}{{12}}$$ $$eqalign{
& = frac{1}{4} - frac{1}{{12}} cr
& = frac{{3 - 1}}{{12}} cr
& = frac{2}{{12}} cr
& = frac{1}{6} cr} $$
[#628] The greatest number among the following : $$0.7 + sqrt {0.16} ,$$ xa0 $$1.02 - frac{{0.6}}{{24}},$$ xa0 $$1.2 imes 0.83,$$ xa0 and $$sqrt {1.44} $$
Correct Answer
(B) $$sqrt {1.44} $$
Explanation
Solution: $$eqalign{
& { ext{0}}{ ext{.7 + }}sqrt {0.16} = 0.7 + 0.4 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = 1.1 cr
& 1.02 - frac{{0.6}}{{24}} = 1.02 - 0.025 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,, = 0.995 cr
& 1.2 imes 0.83 = 0.996 cr
& sqrt {1.44} = sqrt {frac{{144}}{{100}}} cr
& ,,,,,,,,,,,,,, = frac{{12}}{{10}} cr
& ,,,,,,,,,,,,,,, = 1.2 cr
& { ext{ So }}sqrt {1.44} { ext{ is the greatest}}{ ext{.}} cr} $$
[#629] The least number that must be subtracted from 63520 to make the result a perfect square is -
Correct Answer
(D) 16
Explanation
Solution: According to the question, As we know that the square of 252 is which that is near to the value of 63520. Therefore, 63520 - x = 63504 ∴ x = 16
[#630] If n is a whole number greater then 1, then n 2 (n 2 - 1) is always divisible by -
Correct Answer
(B) 12
Explanation
Solution: n 2 (n 2 - 1) put n = 2 = 2 2 (2 2 - 1) = 4(4 - 1) = 4 × 3 = 12 Check the option it is divisible by 12. $$eqalign{
& { ext{Take n = 3}} cr
& Rightarrow {{ ext{3}}^3}left( {{3^3} - 1}
ight) cr
& Rightarrow 9left( {9 - 1}
ight) cr
& Rightarrow 9 imes 8 = 72 cr
& { ext{It is divisible by 12}} cr
& { ext{So 12 is answer}} cr} $$