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Here we are trying to give the Test Paper for Polynomial. It tests the basic concepts and at the same makes the student comfortable with the questions

**Question 1**
Which of these is a polynomial

a) √ y + 1

b) √ 2 + x +x

^{2}
c) y+ 1/y + y

^{2}
d) $\frac {5 \sqrt x + 6x^3/2}{\sqrt x}$

e) $\frac {x+1}{x-1} $

f) x&radic 2

Answer
Polynomials : b,d,f

Non -Polynomial: a,c,e

**Question 2**
True and false
a) The degree of non-zero constant polynomail is zero

b) The degree of the zero polynomial is well defined

c) A binomial can have atmost two terms

d) A binomial may have degree 6

e) A polynomial cannot have more than one zero

f) The degree of the sum of two polynomials each of degree 6 is always 6.

g) 0 and 2 are the zeroes of y

^{2}- 2y

Solution
a) True

b) False

c) False

d) True

e) False

f) False

g) True

## Multiple choice Questions

**Question 3**
If p + q+ r = 0, then p

^{3} + q

^{3} + r

^{3} is equal to
a)0

b)3abc

c)2abc

d)abc

Solution
Solution (b)

**Question 4**
Which of these identities is not true?

Solution
Solution (d)

**Question 5**
Find the coefficent of x

^{2} in (x –1)(9x

^{2} – 3x + 1)

a)12

b)-3

c) 9

d) -12

Solution
Solution (d)

**Question 6**
Factorize the below expression
a) 49x

^{2} + 70xy + 25y

^{2}
b) 4y

^{2}+ 20y + 25

c) 16x

^{2}+ 4y

^{2} + 9z

^{2}– 16xy – 12yz + 24xz

d) 2x

^{3}– 3x

^{2}– 17x + 30

**Question 7**
If x

^{61} + 61 is divided by x + 1, the remainder is

a) 0

b) 1

c) 60

d) 59

Solution
Putting x=-1, we get the remainder
x^{61} + 61= (-1)^{61} + 61=-1 +61=60
Solution (c)

**Question 8**
Find the value of a, if x – a is a factor of x

^{3}– ax

^{2} + 2x + a – 1

a) 2/3

b) 1/3

c) 1

d) 3

Solution
Let p(x) = x^{3}– ax^{2} + 2x + a – 1

Since x – a is a factor of p(x), so p(a) = 0.

i.e., a^{3}– a(a^{2}) + 2a + a – 1=0

3a = 1 or a=1/3

Solution (b)

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Class 9 Maths
Class 9 Science