Unit-3: Algebra
(a) Polynomials, factorisations and expansions
(b) Algebraic identities
(c) Linear equations in two variables
Q1.
Which of the following is not a polynomials.
(a) 3x2 + 6x (b) √x + 4x2 (c) 2x2 + 6
(d) 2x2 - 1/x-2 + 6
Solution.
(b) √x + 4x2
Power of variable should be non-negative integer.
Solution
Q2.
If x = 2,then find the value of p(x) = x4 - x2 - 2 .
(a) 12 (b) 10 (c) 8 (d) 6
Solution.
p(2) = (2)4 - (4)2 - 2
= 16 - 4 - 2 = 10
Solution
Q3.
Find the degree of the polynomial given . 3y4 - 2(y2)5/2 + 6
(a) 3 (b) 4 (c) 5 (d) 6
Solution.
(c) 5
Solution
Q4.
Examine whether x - 1 is a factor of the polynomials. 4x3 - 5x2 - 2x + 3
(a) yes (b) no (c) can't say
Solution.
(a) yes
Solution
Q5.
The cost of table is five times the cost of a chair.
(a) x + 3y = 0 (b) x = 0 (c) x - 5y = 0 (d) 5y = 0
Solution.
Let the cost of table is Rs. x and the cost of a chair is Rs.y.
x = 5y
x - 5y = 0
Solution
Q6.
If the point (4,3) lies on the linear equation.
3x - ky = 9,find k.
(a) 1 (b) 2 (c) 3 (d) 4
Solution.
Point (4,3) lies on the linear equation so it will satisfy the equation.
3(4) - k(3) = 9
12 - 3k = 9
-3k = 9 - 12
k = 1
Solution
Q7.
Line 3x + 2y = 12 cuts ______________
(a) x-axis (b) neither x axis nor y axis (c) y-axis (d) cut both axis
Solution.
Equation contains pure constant (12) so it will cuts both axis.
Solution
Q8.
factorize 25x2 - 10x + 1 - 49x2
(a) (5x - 1 - 7y)(5x - 1 + 7y) (b) (5x - 7y)2
(c) (5x - 1)(7y - 1) (d) (7y + 1)
Solution.
= (5x - 1)2 - (7y)2
= (5x - 1 - 7y)(5x - 1 + 7y)
Solution
Q9.
Factorize x4 + 6x2 + 5
(a) (x2 + 3 - 2x) (b) (x2 + 1) (x2 + 5)
(c) (x2 + 1) (d) (x2 + 6)
Solution.
(x2 + 3)2
= x4 + 6x2 + 9 - 4
= (x2 + 3)2 - (2)2
(x2 + 3 - 2) (x2 + 3 + 2)
= (x2 + 1)(x2 + 5)
Solution
Q10.
(x - 2) is a factor of P(x) = x2 - 4x + k, find k.
(a) 1 (b) 2 (c) 4 (d) 3
Solution.
4 - 8 + k = 0
-4 + k = 0
k = 4
Solution
