Number System - Study Mode

[#621] 8 + 88 + 888 + 8888 + 88888 + 888888 = ?
Correct Answer

(D) 987648

Explanation

Solution: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 + xa0 xa0 xa0 xa0 xa0 xa0 8 9 8 7 6 4 8

[#622] If a + b + c = 0, (a + b) (b + c) (c + a) equals
Correct Answer

(C) - abc

Explanation

Solution: a + b + c = 0 ⇒ (a + b) = - c (b + c) = - a and (c + a) = - b ⇒ (a + b) (b + c) (c + a) = (- c) × (- a) × (- b) = - (abc)

[#623] If x is a rational number and y is an irrational number, then-
Correct Answer

(D) x + y is necessarily irrational, but xy can be either rational or irrational

Explanation

Solution: (a) Let x = 0 and y = $$sqrt 2 $$ Then, x is rational and y is irrational. ∴ x + y = 0 + $$sqrt 2 $$ xa0= $$sqrt 2 $$ , which is irrational Thus, x + y is not rational (b) Let x = 0 and y = $$sqrt 2 $$ Then, x is rational and y is irrational ∴ xy = 0 × $$sqrt 2 $$ xa0= 0, which is rational Hence, xy is not irrational (c) As shown in (B), xy is not necessarily irrational (d) x + y is necessary irrational. But xy can be either rational or irrational. Hence, (D) is true.

[#624] The digit in the unit's place of [(251) 98 + (21) 29 - (106) 100 + (705) 35 - 16 4 + 259] is :
Correct Answer

(B) 4

Explanation

Solution: Unit digit in [(251) 98 + (21) 29 - (106) 100 + (705) 35 - 16 4 + 259] = unit digit in (1 + 1 - 6 + 5 - 6 + 9) = 4

[#625] 252 m of pant cloth and 141 m of shirt cloth are available in a cloth store. To stitch one pant and one shirt, $$2frac{1}{2}$$ m and $$1frac{3}{4}$$ m of cloth are needed respectively. Then the approximate number of pants and shirts that can be made out of it are :
Correct Answer

(B) (100, 80)

Explanation

Solution: Number of pants can be made = $$frac{{252}}{{frac{5}{2}}}$$ = 100 Number of shirts can be made = $$frac{{141}}{{frac{7}{4}}}$$ = 80 Number of pants and shirts = 100, 80