Q1.If √12 + √27 = 8.66,so find the value of 3√3 + √147 .
Solution.
= √12 + √27
2√3 + 3√3
5√3 = 8.66
√3 =
8.66/5
√3 = 1.73
= 3√3 + 7√3
= 10√3
= 10×1.73
= 17.3
Solution
Q2.
Numerator of a fraction increased by 20% and denominator increased by 25%, then resultant fraction is 3/5 find the original fraction .
(a) 5/8 (b) 8/5 (c) 2/5 (d) 3/8
Solution.
Let original fraction is x/y
(120% of x)/(125% of y) = 3/5
x/y = (3 x 125)/(5 x 120)
= 375/600
= 5/8
Solution
Q3.
If 9 men can do a piece of work in 60 days of 8 hours each, how many men will it take to do 5 times the amount work if they work for 30 days of 8 hours.
(a) 40 (b) 90 (c) 60 (d) 30
Solution.
W2 x M1 x D1 x H1 = W1 x M2 x D2 x H2
5 x 9 x 60 x 8 = 1 x M2 x 30 x 8
M2 = 90 men
Solution
Q4.
A can row a certain distance downstream in 6 hrs and return the same distance in 9 hrs . If the stream flows at the rate of 3 km/hr. find
the speed of A in still water.
(a) 20 km/hr (b) 15 km/hr (c) 10 km/hr (d) 5 km/hr
Solution.
m be the speed of boat in still water,z is the speed of stream.
s1 t1 = s2 t2
6(m + z) = 9(m -z)
6(m + 3) = 9(m - 3)
6m + 18 = 9m - 27
45 = 3m
m = 15
Solution
Q5.
The length of the minute hand of a clock is 44 cm . find the area swept by the minute hand in 5 minute.
(a) 199 cm2 (b) 322.6 π cm2 (c) 308 π cm2 (d) 176 cm2
Solution.
A = θ/360 x πr2
θ = 30o
A = 30o/360o x π x 44 x 44
= 1/6 x π x 44 x 44
A = [(22 x 44)/3] π
= 322.6 π cm2
Solution
Q6.
A sum of Rs.3600 is lent out in two parts in such a way that the interest on one part at 10% for 2 years is equal to that on another
part at 5% for 4 years . find the two sums .
(a) 1800,1800 (b) 2000,1600 (c) 3000,600 (d) 2500, 1100
Solution.
(a) 1800,1800
S
1 : S
2 =
1 / r1 t1
:
1 / r2 t2
=
1 / 20
:
1 / 20
S
1 : S
2 = 1 : 1
Solution
Q7.
Find the value of
5C2 + 5C3 =
(a)6C3
(b) 6C4 (c) 6C1
(d) 5C3
Solution.
(a)6C3
NOTE : ncr + ncr+1 = n+1cr+1
Solution
Q8.
α and β are the roots of the equation 2x2 + 3x + 7 = 0 , find the value of α/β + β/α is .
(a) 6/7 (b) -19/14 (c) 9/4 (d) -2/3
Solution.
(b) -19/14
Solution
Q9.
A person swims downstream 40 km and upstream 32 km, taking 8 hrs each time. Find the velocity of current ?
(a) 0.9 km/hr
(b) 0.5 km/hr (c) 1 km/hr (d) 2 km/hr
Solution.
Person's rate downstream = 5 km/hr
Person's rate upstream = 4 km/hr
x = Person's rate in still water
y = rate of the current
x + y = 5
x - y = 4
2x = 9
x = 4.5 km/hr
y = 0.5 km/hr
Solution
Q10.
If (5)1/2 = 2.236
(3)1/2 = 1.732
find the value of 1/(5)1/2 + (3)1/2
Solution.
(5)1/2 - (3)1/2/2 = 2.236 - 1.732/2
0.504/2 = 0.252
Solution
