Q1.
If a = (2)1/2+ 1, find the value of (a - 1/a)2.
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(d) 4
Solution
Q2.
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
Q3.
The ratio of the father's age to the son's is 3:1 . The product of their ages 27, find the age of son ?
(a) 6 (b) 3 (c) 2 (d) 1
Solution.
Let the ratio of proportionality be y,then
3y . y = 27
3y2 = 27
y2 = 9
y = 3
Solution
Q4.
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
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.
One side of rectangle lies along the line 4x - 7y + 3 = 0, Two of its vertices are (1,1) and (-2,1),find the equationof side which is
parallel to given line.
(a) 4x + 7y + 15 = 0 (b) 4x - 7y + 15 = 0 (c) 4x - 9y + 3 = 0 (d) 4x - 7y - 15 = 0
Solution.
(b) 4x - 7y + 15 = 0
Point (1,1) lies on the given line. so point (-2,1) lies on the another line which is parallel to given line .
4x - 7y + k = 0
4(-2) - 7(1) + k = 0
-8 - 7 + k = 0
-15 + k = 0
k = 15
Solution
Q9.
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
Q10.
Average speed of a train is 60 km/hr , without stoppage and with stoppage it travels the same distance at an average speed of 40 km/hr .
How many minutes per hour does the train stops ?
(a) 18 minutes (b) 20 minutes (c) 10 minutes (d) 25 minutes
Solution.
(b) 20 minutes
Solution
