(a) VBODMAS (b) Divisibility (c) Cube and cube roots (d) Square and square roots
(e)Surds, indices and rationalisation
Q1.
What is the remainder when 354 + 27 is divided by 28 ?
Solution.
(33)18 + 27
(27)18 + 27/28
1 + 27/28
Remainder = 0
Note :an/a+1 , gives remainder 1, when n is even.
Solution
Q2.
Find remainder when 91785 is divided by 8.
Solution.
(8+1)1785/8
Remainder = 1
Note :(a+1)n/a always gives remainder 1.
Solution
Q3.
Some players decided to collect as many rupees from each member of group as is the number of players.If the total collection to Rs.1225
,find the number of players.
Solution.
Let number of players = x
So,x.x = 1225
x2 = 1225
x = 35
Solution
Q4.
If = 0.2319, then find the value of {(a2+2a + 1)1/2 - 1}.
Solution.
= {(a + 1)2}1/2 - 1
= a + 1 - 1
a = 0.2319
Solution
Q5.
32.31.5.3x = (9)3, find x.
Solution.
32+1.5+x =(32)3
33.5+x = 36
3.5 + x = 6
x = 6 - 3.5 = 2.5
Solution
Q6.
If 13 + 23 + 33 + 43 + 53 = 225, so find (23 + 43 + 63 +
83 + 103 ).
Solution.
23 + 23.23 + 23.33 + 23.43 + 23.53
23 (13 + 23 + 33 + 43 + 53)
8(225)
= 1800
Solution
Q7.
Find remainder when 4y6 - 5y3 - 3 is divided by y3 - 2
Solution.
y3 = x, then x - 2
f(x)= 4x2 - 5x - 3
put, x = 2
f(2)= 4(2)2 - 5(2) - 3
= 3
Solution
Q8.
Find the value of x, (4x - 7)1/3 = 5
Solution.
(4x - 7) = 53
4x - 7 = 125
4x = 132
x = 33.
Solution
Q9.
Find the value of x, 35x รท 3x = (320)1/5.
Solution.
35x/3x = 34
34x = 34
x = 1
Solution
Q10.
If x + 1/x = (3)1/2, Find the value of x3 + 1/x3
Solution.
( x + 1/x)3 = {(3)1/2}3
x3 + 1/x3 + 3(3)1/2 = (3)3/2
x3 + 1/x3 = 0
Solution
