Number System - Study Mode

[#11] A rational number between $${ ext{ }}frac{3}{4}$$ and $${ ext{ }}frac{3}{8}$$ is :
Correct Answer

(C) $${ ext{ }}frac{5}{9}$$

Explanation

Solution: given $${ ext{ }}frac{3}{4}$$ = 0.75 xa0 xa0 $${ ext{ }}frac{3}{8}$$ = 0.375 (a) $${ ext{ }}frac{7}{9}$$ → 0.77 (b) $${ ext{ }}frac{7}{3}$$ → 2.3 (c) $${ ext{ }}frac{5}{9}$$ → 0.55 (d) $${1 ext{ }}frac{9}{16}$$ = $${ ext{ }}frac{25}{16}$$ → 1.5 $${ ext{ }}frac{5}{9}$$ = 0.55

[#12] If the operation '*' is defined by a * b = a + b - ab, then 5 * 7 equals :
Correct Answer

(C) - 23

Explanation

Solution: 5 * 7 = 5 + 7 - 5 × 7 = 12 - 35 = - 23

[#13] The smallest five digit number which is divisible by 12, 18 and 21 is :
Correct Answer

(A) 10080

Explanation

Solution: We know, Smallest five digit number is = 10000 L.C.M. of 12, 18, 21 = 252 10000 is divided by 252 then the remainder is 172 Difference = 252 - 172 = 80 Then number is = 10000 + 80 = 10080

[#14] $$1 + frac{1}{2} + frac{1}{4} + frac{1}{7} + frac{1}{{14}} + frac{1}{{28}}$$ xa0 xa0 xa0is equal to :
Correct Answer

(A) 2

Explanation

Solution: $$eqalign{
& = 1 + frac{1}{2} + frac{1}{4} + frac{1}{7} + frac{1}{{14}} + frac{1}{{28}} cr
& = frac{{28 + 14 + 7 + 4 + 2 + 1}}{{28}} cr
& = frac{{56}}{{28}} cr
& = 2 cr} $$

[#15] In a two digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is :
Correct Answer

(D) 47

Explanation

Solution: Let the ten's digits be x Unit digit be 2x - 1 Original number : = 10x + 2x - 1 = 12x - 1 New number : = 10(2x - 1) + x = 20x - 10 + x = 21x - 10 According to the question, (21x - 10) - (12x - 1) = (12x - 1) - 20 9x - 9 = 12x - 21 3x = 12 x = 4 Original number : = 12x - 1 = 12 × 4 - 1 = 47