Q1.
Two numbers are in the ratio 2:3, if 4 is added in numerator and 6 is substracted in denominator, they are in the ratio of 6:7 .
Find the numerator .
(a) 10,12 (b) 16,24 (c) 32,48 (d) 30,40
Solution.
Let the numbers are 2x and 3x
(2x + 4)/(3x - 6) = 6/7
4x = 64
x = 16
32,48
Solution
Q2.
How many numbers between 200 and 500 are divisible by 3,4 and 5 together .
(a) 6 (b) 4 (c) 3 (d) 5
Solution.
LCM of 3, 4 and 5 = 60
Total numbers which are divisible by 60
upto 200 = 3.
Total numbers which are divisible by 60
upto 500 is = 8
So, the required number is 5
Solution
Q3.
Which number is irrational number
(a) 4/5 (b) 0.454545----- (c) 10.34444---- (d) 1.242442444-----
Solution.
(d) 1.242442444-----
Note : Non-terminating and non-repeating numbers are irrational numbers.
Solution
Q4.
If x + y + z = 0, then find the value of
1/(y2 + z2 + x2) + 1/(z2 + x2 + y2) +
1/(x2 + y2 + z2)
(a) 3 (b) 2 (c) 1 (d) 0
Solution.
x + y + z = 0
x + y = -z
squaring both sides
x2 + y2 + 2xy = z2
x2 + y2 - z2 = -2xy
Similarly
y2 + z2 - x2
= -2yz
x2 + z2 - y2 = - 2xz
=
1/(-2yz) + 1/(-2xz) + 1/(-2xy)
x/(-2xyz) + y/(-2xyz) + z/(-2xyz)
= (x + y + z)/(-2xyz)
= 0
Solution
Q5.
When x - 1/x = 5 , find the value of x2 + 1/x2
(a) 14 (b) 26 (c) 27 (d) 25
Solution.
(x - 1/x)2 = 25
x2 + 1/x2 - 2 = 25
x2 + 1/x2 = 27
Solution
Q6.
Six bells rang simultaneously . After this they rang in the interval of 2,4,6,8,10 and 12 second . In 30 minutes how many times all bells
will ring simultaneously.
(a) 16 (b) 15 (c) 17 (d) 14
Solution.
(a) 16
In this case , find LCM of 2,4,6,8,10,12 = 120 second
Solution
Q7.
Put the Decimal Fraction in 0.1226262626...... in the p/q form.
(a) 607/4950 (b) 2/3 (c) 706/140 (d) 24/25
Solution.
0.12262626..... = (1226 - 12)/9900
= 1214/9900
= 607/4950
Solution
Q8.
In a class boys students are 2/5 of the total students, if 4/9 population of boys and 3/8 population of girls are absent respectively .
find the total present population of students.
(a) 16/19 (b) 43/72 (c) 49/64 (d) 23/90
Solution.
= total boy x present boys + total girls x present girls
= 2/5 x 5/9 + 3/5 x 5/8
= 2/9 + 3/8
= (16 + 27)/72
= 43/72
Solution
Q9.
log3 [log4(log3x)] = 0, find x.
(a) 3 (b) 9 (c) 27 (d) 81
Solution.
log3 [log4(log3x)] = log31
log4(log3x) = log44
log3x = 4log33
log3x = log334
x = 81
Solution
Q10.
log8x + log4x + log2x = 11, find x.
(a) 128 (b) 16 (c) 64 (d) 256
Solution.
(a) 128
Solution
