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) $ \sqrt {y} + 1$
(b) $\sqrt {2} + x +x^2$
(c) $y+ \frac {1}{y} + y^2$
(d) $\frac {5 \sqrt x + 6x^3/2}{\sqrt x}$
(e) $\frac {x+1}{x-1} $
(f) $x \sqrt {2}$
Answer
Polynomials : b,d,f
Non -Polynomial: a,c,e as exponent of variable is not non-negative integer
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)3pqr
(c)2pqr
(d)pqr
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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