Unit-2:
(a) Number system
(b) Elementary algebra
(c) H.C.F. and L.C.M.
(d) Fractions and decimal fractions
(e) Logarithms
Q1.
Find the unit digit in
641 x 218 x 48 x (2)6
(a) 4 (b) 6 (c) 2 (d) 1
Solution.
(b) 6
= 1 x 8 x 8 x 4
= 8 x 32
= 256
Solution
Q2.
If 13 + 23 + 33 + --------- + 103, so find the value of 4 + 32 + 108 + -------- + 4000.
(a) 12,800 (b) 11,000 (c) 12,050 (d) 12,100
Solution.
= 4(1 + 8 + 27 + ------- + 1000)
= 4(13 + 23 + 33 + -------- + 103)
= 4(3025)
= 12,100
Solution
Q3.
Write 0.121212------- in the form of p/q.
(a) 4/33 (b) 2/33 (c) 1/33 (d) 2/99
Solution.
= 0.121212------
= 12/99
= 4/33
Solution
Q4.
(256)1/4 ÷ 13/5 - 3 ÷ 5 = x, find x.
(a) 17 (b) 5 (c) 17/5 (d) 1/5
Solution.
{(4)4}1/4 x 1 - 3/5 = x
= 4 - 3/5
= 17/5
Solution
Q5.
The ratio of two numbers is 1:4 . The HCF and LCM of two numbers are 21 and 84 respectively.find the two numbers.
(a) (21,84)
(b) (21,80) (c) (84,60) (d) (60,40)
Solution.
Let two numbers are x and 4x,
product of two numbers = HCF x LCM
(x) x (4x) = 21 x 84
x2 = 441
x = 21
= (21,84)
Solution
Q6.
Find the HCF of UVW and XYZ.
(a) 1 (b) 0 (c) XYZ (d) UVW
Solution.
(a) 1
NOTE : There is no common factor.
Solution
Q7.
If loga 27 = 3 , find a.
(a) 27 (b) 1 (c) 3 (d) 2
Solution.
a3 = 27
a3 = (3)3
a = 3
Solution
Q8.
Find a, if log2 a = 4 + log24
(a) 30 (b) 64 (c) 60 (d) 45
Solution.
log2 a - log2 4 = 4 log2 2
log2 (a/4) = log2 (24)
a/4 = 16
a = 64
Solution
Q9.
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
Q10.
If log (x2 - 4x + 5) = 0, find x.
(a) 4 (b) 2 (c) 1 (d) 3
Solution.
log(x2 - 4x + 5) = log 1
x2 - 4x + 4 = 0
(x - 2)2 = 0
x = 2
Solution
