Unit-5:Algebra
(a) Exponents and powers
(b) Simplification of algebraic expressions
(c) Factorisation
Q1.
Find m so that (3/4)3 x (9/16) = (3/4)2m + 3
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
(3/4)3 x (3/4)2 = (3/4)2m + 3
(3/4)5 = (3/4)2m + 3
5 = 2m + 3
2 = 2m
m = 1
Solution
Q2.
Evaluate (101 - 60) x 50
(a) 3 (b) 6 (c) 9 (d) 5
Solution.
= (101 - 60) x 1
= (10 - 1) x 1
= 9
Solution
Q3.
x = 2m , y = 2m+1. find the value of 2x/y
(a) 2 (b) 1 (c) 3 (d) 4
Solution.
2.2m/2m+1 = 2m+1/2m+1 = 1
Solution
Q4.
Evaluate {(5/3)6}0
(a) 2 (b) 3 (c) 0 (d) 1
Solution.
(d) 1
Solution
Q5.
Find the H.C.F of 20x2 y9 z, 16x5 y3, 12x3 y10
(a) 4x2 y3 (b) 2xy (c) 2 (d) 1
Solution.
H.C.F of 20, 16, 12 = 4
Highest power of x common to all = x2
Highest power of y common to all = y3
z is not common so omit it
HCF is 4x2 y3
Solution
Q6.
Find the H.C.F of x2 + x - 2, x3 + 6x2 + 8x
(a) (x+2) (b) (x+2) (c) x (d) (x-1)
Solution.
x2 + x - 2 = (x-1)(x+2)
x3 + 6x2 + 8x = x(x2 + 6x + 8)
= x (x+4)(x+2)
Common factor is (x+2)
HCF is (x+2)
Solution
Q7.
Find the LCM of x2 - 5x + 6, x2 + 3x + 2
(a) (x-3)(x+1) (b) (x-3)(x+1)(x2-4) (c) x+y (d) (x+1)(x-1)
Solution.
x2 - 5x + 6 = x2 - 3x - 2x + 6
= x(x-3) - 2(x-3)
= (x-2)(x-3)
x2 + 3x + 2 = x2
+ 2x + x + 2
= x(x+2) + 1(x+2)
So, LCM = (x-3)(x+1)(x2 - 2)
Solution
Q8.
Reduce (4x+20)/(x2 - 25) to simplest form.
(a) 4/(x-5) (b) (x-5) (c) (x+5) (d) (x-5)/4
Solution.
4(x+5)/(x-5)(x+5) = 4/(x-5)
Solution
Q9.
Factorise 4x2 - 9y2
(a) (2x-3y)(2x+3y) (b) (2x-3y)(2x-3y) (c) (2x+3y) (d) (2x-3y)
Solution.
(a) (2x-3y)(2x+3y)
Solution
Q10.
Factorise x2/25 - y2/9
(a) (x/4 - y/3) (b) (x/5 - y/3)(x/5 + y/3) (c) (x/5 + y/3) (d) (x/5 - y/3)
Solution.
(b) (x/5 - y/3)(x/5 + y/3)
Solution
