Q1: If x/y + y/x = 1 and (xy, ≠ 0), the value of x^{3} – y^{3} is
(a) 1
(b) 1
(c) 0
(d) 2
Ans: (c)
x/y + y/x = 1
x^{2} + y^{2} = − xy
or
x^{2} + y^{2} + xy = 0
Now x^{3} – y^{3} = (x − y) (x^{2} + y^{2} + xy) = (x − y) × 0 = 0
Hence (c) is the correct answer
Q2: If p + q + r = 0 ,then the value of
(a) 1
(b) 3
(c) 1
(d) 0
Ans: (b)
Now we know that p^{3} + q^{3} + r^{3} − 3pqr = (p + q + r) (p^{2} + q^{2} + r^{2} − pq − qr − pr)
as p + q + r = 0
p^{3} + q^{3} + r^{3} − 3pqr = 0 or p^{3} + q^{3} + r^{3} = 3pqr
Now
Hence (b) is the correct answer.
Q3: The product of (x + a) (x + b) is
(a) x^{2} + (a + b)x + ab
(b) x^{2}  (a  b)x + ab
(c) x^{2} + (a  b)x + ab
(d) x^{2} + (a  b)x + ab
Ans: (a)
Q4: The value of (x + 2y + 2z)^{2} + (x  2y  2z)^{2} is
(a) 2x^{2} + 8y^{2} + 8z^{2}
(b) 2x^{2} + 8y^{2 }+ 8z^{2} + 8xyz
(c) 2x^{2} +8y^{2} + 8z^{2}  8yz
(d) 2x^{2} + 8y^{2} + 8z^{2} + 16yz
Ans: (d)
Q5: Find the value of (a^{3} b^{3} c^{3}  3abc)/(ab + bc + c  a^{2}  b^{2}  c^{2 }), when a = 5, b = 6 c = 10.
(a) 1
(b) 1
(c) 2
(d) 2
Ans: (a)
Q1: P(x) = x  1 and g(x) =x^{2 } 2x + 1 . p(x) is a factor of g(x)
Ans: True, as g(1) = 0
Q2: The factor of 3x^{2} – x  4 are (x + 1)(3x  4)
Ans: True, we can get this by split method
Q3: Every linear polynomial has only one zero
Ans: True
Q4: Every real number is the zero’s of zero polynomial
Ans: True
Q5: A binomial may have degree 4
Ans: True, example x^{4} + 1
Q6: 0, 2 are the zeroes of x^{2} 2x
Ans: True
Q7: The degree of zero polynomial is not defined
Ans: True
Q1: Is 3x^{1/2}  4x + 15 a polynomial of one variable?
Ans: No. it is not a polynomial
Q2: Is ∛x  √2x a polynomial
Ans: No. It is not a polynomial
Q3: What will be the degree of polynomials 30x^{5}  15x^{2} + 40
Ans: Degree of Polynomial is 5
Q4: Is (y^{2})^{1/2} + 2√3 a polynomial of one variable?
Ans: Yes it is a polynomial of one variable
Q5: What will be the coefficient of x^{3 }in 9x^{3}  5x + 20.
Ans: Coefficient of x^{3} is 9
Q6: Show that x = 1 is a root of the polynomial 3x^{3}  4x^{2} + 8x  7
Ans: On putting x = 1
X = 1 is root of polynomial
3x^{3}  4x^{2} + 8x  7
3(1)^{3}  4(1)^{2} + 8(1)  7
3  4 + 8  7 = 0
X = 1 is root of polynomial
48 videos387 docs65 tests

Practice Questions: Polynomials Doc  2 pages 
Previous Year Questions : Polynomials Doc  8 pages 
NCERT Exemplar Solutions: Polynomials  1 Doc  35 pages 
1. What is a polynomial? 
2. How do you determine the degree of a polynomial? 
3. What are the different types of polynomials? 
4. How do you add or subtract polynomials? 
5. Can a polynomial have negative exponents? 
48 videos387 docs65 tests

Practice Questions: Polynomials Doc  2 pages 
Previous Year Questions : Polynomials Doc  8 pages 
NCERT Exemplar Solutions: Polynomials  1 Doc  35 pages 

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