Unit-1:
(a) VBODMAS (b) Divisibility (c) Cube and cube roots (d) Square and square roots
(e)Surds, indices and rationalisation
Q1.
(6 ÷ 3 ÷ 2) + {(5 x 22 + 2)x 1/2}
Solution.
6 x 1/3 x 1/2 + {22 x 1/2}
1 + 11 = 12
Solution
Q2.
Solve 28/9 ÷ {5/4 - 1/2} ÷ (1/2 of 28/3) .
Solution.
28/9 ÷ {3/4} ÷ 28/6
28/9 x 4/3 x 6/28 = 8/9
Solution
Q3.
Which is divisible by 7.
(a)82196 (b)21459 (c)48960 (d)598514
Solution.
(d)
Difference between the number formed by last 3 digits and rest of the digits should be divisible by 7, the whole number will also be divisible by 7.
Solution
Q4.
Which number is divisible by 13 .
(a)419617 (b)21489 (c)218960 (d)96345
Solution.
(b)
Difference between the number formed by last 3 digits and rest of the digits should be divisible by 13, the whole number will also be divisible by 13.
Solution
Q5.
If x = (3)1/2 + 1/(3)1/2 -1 and y = 1/x so, find (x+y/x-y)2 .
Solution.
(x+y/x-y) = 2/(3)1/2
(x+y/x-y)2 = 4/3
Solution
Q6.
Find the number of digits in the square root of 1915456.
Solution.
In this number there are 7 digits (odd)
Formula = (k+1)/2 = (7 + 1)/2 = 4
Solution
Q7.
xm= yn= zp and y4 = x2z3 find n.
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
Q8.
If ax = b and by = a , find xy ?
Solution.
b = a1/y
ax = a1/y
x = 1/y
xy = 1.
Solution
Q9.
find x, (x)2.3/8 = 2/(x)1.7
Solution.
x4 = 16
x = 2
Solution
Q10.
If (5)1/2 = 2.236
(3)1/2 = 1.732
find the value of 1/(5)1/2 + (3)1/2
Solution.
(5)1/2 - (3)1/2/2 = 2.236 - 1.732/2
0.504/2 = 0.252
Solution
