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 : a
3 + b
3 + c
3 = 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