Q1.
A train travels from A and B at the rate of 30 km/hr and from B to A at the rate of 40 km/hr. what is the average rate for the whole journey ?
(a) 40 km/hr (b) 240/7 km/hr (c) 90 km/hr (d) 38 km/hr
Solution.
A =
2xy/x + y
A =
2 x 30 x 40/30 + 40
=
2400/7
=
240/7
km/hr
Solution
Q2.
Find the value of x.
(
2/ 3
)3
. (2/ 3
)-6
= (2/ 3
)2x-1
(a) 2 (b) -1 (c) -2 (d) 8
Solution.
(
2/ 3
)
-3
= (
2/ 3
)
2x-1
-3 = 2x - 1
-2 = 2x
x = -1
Solution
Q3.
Product LCM and HCF of two numbers is 24 difference of two numbers is 2. find the numbers .
(a) (8,6) (b) (6,5)
(c) (2,4) (d) (6,4)
Solution.
xy = 24
x -y = 2 --------1
(x - y)2 = x2 + y2 - 2xy
4 = x2 + y2 - 48
x2 + y2 = 52
(x + y)2 = x2 + y2
+ 2xy
(x + y)2 = 52 + 48 = 100
x + y = 10 -------2
x - y = 2 --------1
2x = 12
x = 6
y = 4
Solution
Q4.
1 man or 2 women or 3 boys can do a job in 22 days then in how many days will 1 man , 1 woman and 1 boy do the work .
(a) 10 days (b) 8 days (c) 20 days (d) 12 days
Solution.
= [1/(1/22 x 1)+(1/22 x 2)+(1/22 x 3)]
= [1/(1/22)(1/44)+(1/66)]
= 12 days
Solution
Q5.
If 4cotA = 5, so find the value of
5sinA - 3cosA/sinA + 2cosA
(a) 5/14 (b) 1/14 (c) 4/14 (d) 6/11
Solution.
(a) 5/14
Solution
Q6.
These are 5 books on maths, 4 books on statistics and 3 books on english. In how many ways can there books be placed on a shelf if
the books on the same subject are to be together ?
(a) 12! (b) 20! (c) 5! x 4! x 3! x 3! (d) 5! x 4! x 3!
Solution.
(c) 5! x 4! x 3! x 3!
Solution
Q7.
If IAI = 0 , then the value A-1 is
(a) 0 (b) not exist (c) 2 (d) A
Solution.
(b) not exist
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.
In a quadratic equation x2 + px + q = 0 , (2 - √3) is a root of this equation find the value of p and q.
(a) (3,2) (b) (4,1) (c) (2,3) (d) (-4,1)
Solution.
(d) (-4,1)
Solution
Q10.
A sum is deposited at CI ,payable annually . The interest in two successive years was Rs 124 and Rs 172 . find the rate .
(a) 26% (b) 38.7% (c) 41.2% (d) 18%
Solution.
=
C2 - C1 /C1
x 100
=
(172 - 124) /124
x 100
=
4800 /124
= 38.7%
Solution
