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
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