Q1.
xm= yn= zp and y4 = x2z3 find n.
(a) 4mp/(2p + 3m) (b) 8mp/(6p + m) (c) mp/(p + 13m) (d) 3mp/(8p + 3m)
Solution.
xm= yn= zp = k (say)
x = k1/m, y = k1/n, z = k1/p
Now, y4 = x2z3
k4/n = k2/m.k3/p
4/n = 2/m + 3/p
4/n = (2p +3m)/mp
n = 4mp/(2p + 3m)
Solution
Q2.
a/b + b/a = 1 a ≠ 0 , b ≠ 0, find a3 + b3
(a) 3 (b) 2 (c) 0
(d) 1
Solution.
a2 + b2 = ab
a2 + b2 - ab = 0
a3 + b3 =
(a + b)(a2 + b2 - ab) = 0
Solution
Q3.
The age of a man is 4 times that of his son. 5 yrs ago the man was nine times as old as his son was at that time . what is present age of son?
(a) 8 (b) 10 (c) 12 (d) 14
Solution.
y = 4x ------------------ 1
y = father's age
x = son's age
(y - 5) = 9(x - 5)
4x - 5 = 9x - 45
x = 8
Solution
Q4.
If 4 men and 12 women can do a piece of work in 5 days , and 3 men and 7 women can do the same job in 4 days . In how many days 10 men and
10 women will finish the same job.
(a) 3 (b) 14/5 (c) 2 (d) 4
Solution.
4 men + 12 women = 5 days
3 men + 7 women = 4 days
20 men + 60 women = 12 days + 28 women
M = 9 W
28 x 5 = 50 x D
28 = 10 D
D = 14/5
Solution
Q5.
Find the equation of line which has equal intercept and passes through the point (2,3).
(a) x+y = 2 (b) x = y
(c) x + y = 5 (d) x + y = 7
Solution.
x/a + 4/b = 1
∴ a = b
x/a + y/a = 1
(x + y)/a = 1
x + y = a
2 + 3 = a
a = 5
x + y = 5
Solution
Q6.
What annual payment will discharge a dept of Rs.900 due in 6 year, the rate of interest being 5% per annum .
(a) 67.6 (b) 133.4 (c) 140 (d) 149.5
Solution.
=
100 A/100t +
rt (t - 1)/2
=
100 x 900/100 x 6 +
(5/6)(5)/2
=
90000/600 + 75
=
90000/675
= 133.4
Solution
Q7.
If the sum of n terms of an A.P is n(2n + 3), find d(commom difference)
(a) 1 (b) 2 (c) 4 (d) 3
Solution.
Sn = 2n2 + 3n
Tn = Sn - Sn - 1 = Sn + 1 - Sn = 4n + 1
d = Tn - Tn-1 = Tn+1 - Tn
d = {4(n + 1) + 1} - {4n + 1}
= 4n + 5 = 4n - 1
= 4
Solution
Q8.
Two runners cover the same distance at the rate of 15 km and 18 km per hour respectively. Find the distance travelled when one takes a minutes longer
than the other
(a) 30 km/hr (b) 13.5 km/hr (c) 14 km/hr (d) 20 km/hr
Solution.
Distance =
multiplication of speeds/ difference of speeds
x difference in time to cover distance
=
15 x 18/ 18 - 15
x
9/ 60
= 13.5 km/hr
Solution
Q9.
If every 12th unit is selected from universal set then this type of sampling is known as.
(a) Stratified sampling
(b) Quota sampling (c) Systematic sampling (d) None of these
Solution.
(c) Systematic sampling
Solution
Q10.
The four lines ax ± by ± c = 0 , enclose a rhombus whose area is .
(a) 2a2/abc
(b) abc (c) 2/ab (d) 2c2/ab
Solution.
(d) 2c2/ab
Solution
