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Welcome to ICOME Quiz Corner

Q1. What is the remainder when 354 + 27 is divided by 28 ?

(a) 1 (b) 0 (c) 3 (d) 4

Solution.
(33)18 + 27

(27)18 + 27/28

1 + 27/28

Remainder = 0

Note :an/a+1 , gives remainder 1, when n is even.
Solution

Q2. In 60 litres mixture of milk and water the ratio of milk and water is 7:3. Find the quantity of water to be added in the mixture in order to make this ratio 3:7 .

(a) 20 litre (b) 80 litre (c) 40 litre (d) 10 litre

Solution.
= 42/18

42/(18 + x) = 3/7

294 = 54 + 3x

240 = 3x

x = 80
Solution

Q3. Find the unit digit in the product of 771 x 663 x 365 .

(a) 6 (b) 1 (c) 4 (d) 5

Solution.
(c) 4

771 = 74 x 17 + 3 = 1 x 343 = ----------3

663 = 64 x 15 + 3 = 6 x 216 = ---------6

365 = 34 x 16 + 3 = 1 x 3 = ---------3

= (---3)(--6)(---3)

= (-- 54)
Solution

Q4. 8 women and 10 men complete a work in 9 days . Each women take twice the time taken by a man. In how many days will 18 men finish the same work .

(a) 18 days (b) 11 days (c) 10 days (d) 7 days

Solution.
2 women = 1 man

8 women + 10 men = 14 men

14 x 9 = 18 x (x)

x = 7 days
Solution

Q5. At a certain rate of SI Rs.800 amounted to Rs.920 in 3 years . If the rate of interest is double ,what will be the interest after 3 years .

(a) Rs410 (b) Rs.328 (c) Rs.240 (d) Rs.300

Solution.
In first case SI = (120 x 100)/(800 x 3) = 5%

New interest = (800 x 10 x 3)/100 = 30 x 8

= Rs . 240
Solution

Q6. If sinθ + sin2θ = 1 , so find the value of cos12θ + 3cos10θ + cos8θ + 3cos6θ - 1 .

(a) 3 (b) 2 (c) 0 (d) 1

Solution.
sinθ = 1 - sin2θ

sinθ = cos2θ

= sin6θ + 3sin5θ + 3sin4θ + sin3θ - 1

= (sin2θ + sinθ)3 - 1

= 0
Solution

Q7. Find x̄ , if ui = (xi - 15)/10,∑ fiui = 12, N = 60

(a) 15 (b) 18 (c) 17 (d) 12

Solution.
x̄ = A + h{1/N ∑ fiui}

= 15 + 10 {1/60 x 12} = 17
Solution

Q8. Find the value of
(x-y)2/(y-z)(z-x)
+
(y-z)2/(x-y)(z-a)
+
(x-z)2/(x-y)(y-z)


(a) 7 (b) 3 (c) 2 (d) 6

Solution.
(x-y)3/(x-y)(y-z)(z-x)
+
(y-z)3/(y-z)(x-y)(z-x)
+
(x-z)3 /(x-z)(x-y)(y-z)


(x-y)3+ (y-z)3 + (x-z)3/ (x-y)(y-z)(z-x)
=
3(x-y)(y-z)(z-x)/ (x-y)(y-z)(z-x)


= 3

Note : a3 + b3 + c3 = 3abc
if a + b + c = 0
Solution

Q9. If log (x2 - 4x + 5) = 0, find x.

(a) 4 (b) 2 (c) 1 (d) 3

Solution.
log(x2 - 4x + 5) = log 1

x2 - 4x + 4 = 0

(x - 2)2 = 0

x = 2
Solution

Q10. Find the Range of the function
f(x) =
x - 4/ 3 - x


(a) R - {-1} (b) R (c) R{1} (d) None of these

Solution.
(a) R - {-1}

y =
x - 4/ 3 - x


x =
4 + 3y/ y + 1
Solution