Q1.
The numerator of a fraction is increased by 20% and its denominator is decreased by 10% the value of fraction becomes 3/2. find the original
fraction .
(a) 4/7 (b) 9/8 (c) 2/3 (d) 1/3
Solution.
(b) 9/8
Let original fraction is x/y
120% of x/ 90% of y
=
3/ 2
12x/ 9y
=
3/ 2
x/ y
=
3 x 9/ 12 x 2
Solution
Q2.
In a party there are 6 persons. find the total number of shake hands, when each and every person shake hand to each other .
(a) 19 (b) 15 (c) 20 (d) 18
Solution.
c = nc
2 = 6c
2 =
6!/2! x 4!
=
6 x 5/2
= 15
Solution
Q3.
A mixture contains milk and water in the ratio 8:3, on adding 3 litre of water , the ratio of milk to water becomes 2:1 . find the quantity
of milk in the mixture .
(a) 24 litre (b) 15 litre (c) 20 litre (d) 25 litre
Solution.
M/W = 8/3,
M/(W + 3) = 2/1 ,
M = 2W + 6
M = 2(3M/8) + 6
8M = 6M + 48
2M = 48
M = 24
Solution
Q4.
The sum of n terms of two A.P are in the ratio (4n + 7) : (2n + 9), find the ratio of their 15th term :
(a) 123:67 (b) 111:60 (c) 67:40 (d) 141:91
Solution.
Sn/Sn'
=
4n + 7/2n + 9
2a1 + (n-1)d1/2a2 + (n-1)d2
=
4n + 7/2n + 9
2a1 + [(n-1)/2]d1/2a2 + [(n-1)/2]d2
=
4n + 7/2n + 9
n - 1/2
= 2
n = 29
=
4(29) + 7/2(29) + 9
=
116 + 7/58 + 9
=
123/67
Solution
Q5.
tan(x + y) . tan(x - y) = 1, so find the value of tan(4x/3).
(a) 2/√3 (b) √3 (c) 1 (d) 2
Solution.
(b) √3
tan(x + y) = 1/tan(x - y) = cot(x - y)
Solution
Q6.
A sum of Rs. 4800 is lent out in two parts in such a way that the interest on one part at 10% for 3 years is equal to that on another part
at 5% for 6 years . find the two sums ?
(a) 2,400 each (b) 2000,2800 (c) 3000, 1800 (d) 4000,800
Solution.
(a) 2,400 each
S1 : S2 = 1/r1t1 : 1/r2t2
S1 : S2 =
1/(10 x 3) : 1/(5 x 6)
= 1/30 : 1/30
= 30 : 30 = 1 : 1
Solution
Q7.
A person takes 26 hours to walk to office and ride back, he gained 6 hrs if he had covered both ways by riding . Find the time to walk both sides.
(a) 21 hrs (b) 32 hrs (c) 16 hrs (d) 40 hrs
Solution.
Walking + Riding = 26
2(Riding) = 20
Riding = 10
so, walking = 16hrs
total time to walk both side = 32 hrs
Solution
Q8.
In identity function Domain is equal to
(a) 0 (b) Range (c) 1 (d) ∞
Solution.
(b) Range
Solution
Q9.
Find x .
(x + 3) log 3 = 2log 9
(a) 2 (b) 1 (c) 3 (d) 4
Solution.
log 3(x + 3) = log 92
log 3(x + 3) = log 34
x + 3 = 4
x = 1
Solution
Q10.
Two cones have same height and radius are in ratio 9 : 8 , find the ratio of volume of both cones.
(a) 16:15 (b) 9:8
(c) 6:19 (d) 81:64
Solution.
v1/v2 = (1/3 π r12h)/(1/3 π r22h)
r12/ r22 = 81/64
v1:v2 = 81:64
Solution
