Number System - Study Mode

[#151] For what value of X, 211X will be a perfect square?
Correct Answer

(C) 6

Explanation

Solution: 211X Go through option C (46) 2 = 2116

[#152] If $$
oot 3 of { ext{N}} $$ lies between 6 and 7, where N is an integer then how many values N can take?
Correct Answer

(B) 126

Explanation

Solution: 6 < $$
oot 3 of { ext{N}} $$ < 7 On cubing, 216 < N < 343 Number of terms = (342 - 217) + 1 = 125 + 1 = 126

[#153] If the sum of all the prime numbers is 'x' and that of all the odd prime numbers is 'y', then what is the value of x - y?
Correct Answer

(A) 2

Explanation

Solution: Sum of all prime numbers (x) = 2 + 3 + 5 + 7 + . . . . . . . . Sum of all odd prime numbers (y) = 3 + 5 + 7 + . . . . . . . . x - y = 2 Answer

[#154] What is the value of $$frac{{sqrt {29.16} }}{{sqrt {1.1664} }} + frac{{sqrt {0.2916} }}{{sqrt {116.64} }} + frac{{sqrt {0.0036} }}{{sqrt {0.36} }},?$$
Correct Answer

(B) $$frac{{103}}{{20}}$$

Explanation

Solution: $$eqalign{
& frac{{sqrt {29.16} }}{{sqrt {1.1664} }} + frac{{sqrt {0.2916} }}{{sqrt {116.64} }} + frac{{sqrt {0.0036} }}{{sqrt {0.36} }}, cr
& = frac{{5.4}}{{1.08}} + frac{{0.54}}{{10.8}} + frac{{0.06}}{{0.6}} cr} $$ [left[ x08egin{gathered}
x08ecause sqrt {294} = 54 hfill \
sqrt {11664} = 108 hfill \
sqrt {36} = 6 hfill \
end{gathered}
ight.] $$eqalign{
& = frac{{540}}{{108}} + frac{{54}}{{1080}} + frac{6}{{60}} cr
& = 5 + frac{1}{{20}} + frac{1}{{10}} cr
& = frac{{103}}{{20}} cr} $$

[#155] How many numbers are there from 2000 to 7000 which are both perfect squares and perfect cubes?
Correct Answer

(B) 1

Explanation

Solution: $$eqalign{
& 2000{ ext{ - - - - - - }}7000 cr
& { ext{Perfect square}} = sqrt {4096} = 64 cr
& { ext{Perfect cube}} = sqrt {4096} = 16 cr} $$