Competency Based Questions for Class 10 Maths Chapter 2 Polynomials

Competency Based Questions are new type of questions asked in CBSE Board exam for class 10. Practising the following Competency Based Questions will help the students in facing Board Questions.

Hint: Recall degree of polynomial in order to find the number of zeroes of polynomial.

Question.1. Which of the following statements is correct?

(a) A polynomial of degree 2 has three zeroes
(b) A polynomial of degree 3 has two zeroes
(c) A polynomial of degree 4 has four zeroes
(d) A polynomial of degree 5 has ten zeroes

Answer. (c) A polynomial of degree 4 has four zeroes

Question.2. Ravi claims that the polynomial p(x)=mx^{a}+x^{2b} has 4b zeroes. For Ravi’s claim to be correct, which of these must be true?

(a) a = 2b or a = 4b
(b) a = 2 or a = 4b
(c) m = 2b
(d) m = 4b

Answer. (a) a = 2b or a = 4b

Hint: Analyse the graph of the polynomials in order to find the number of zeroes of polynomial.

Question.3. Which of the following graphs could be for the simple polynomial x^{2} ?

(a)
(b)
(c)
(d)

Answer. (b)

Question.4. Consider the expression x^{m^{2}-1}+3x^{\frac{m}{2}}, where m is a constant. For what value of m, will the expression be a cubic polynomial?

(a) -2
(b) -1
(c) 1
(d) 2

Answer. (d) 2

Hint: Compute zeroes of the polynomials in order to verify the relationship between zeroes and the coefficients.

Question.5. Consider the polynomial in z, p(z)=z^{4}-2z^{3}+3. What is the value of the polynomial at z=-1?

(a) 2
(b) 3
(c) 5
(d) 6

Answer. (d) 6

Question.6. The polynomial in x, is x^{2}+kx+5, where k is a constant. At x=2, the value of the polynomial is 15.
What is the value of the polynomial at x=5?

(a) 3
(b) 18
(c) 35
(d) 45

Answer. (d) 45

Hint: Compute the sum and product of zeroes of the polynomial in order to find the quadratic polynomial.

Question.7. Which of these is a zero of the polynomials P(y)=3y^{3}-16y-8?

(a) -8
(b) -2
(c) 0
(d) 2

Answer. (b) -2

Question.8. Given that m+2, where m is a positive integer, is a zero of the polynomial q(x)=x^{2}-mx-6.
Which of these is the value of m?

(a) 1
(b) 2
(c) 3
(d) 4

Answer. (a) 1

Hint: Divide the two given polynomials in order to verify the division algorithm.

Question.9. The polynomial q(z)=z^{3}-4z+a when divided by the polynomial (z-3) leaves remainder 5. What is the value of a?

(a) –10
(b) –3
(c) 3
(d) 10

Answer. (a) –10

Question.10. The polynomial p(x)=x^{m}+x, where m>1, when divided by (x-a), leaves remainder 6. Given that a is a positive integer, what is the value of m?

(a) 2
(b) 3
(c) 5
(d) 6

Answer. (a) 2

Hint: Divide the given polynomial with its known zero in order to find all the other zeroes of that polynomial.

Question.11. Which of these is a factor of the polynomial p(x)=x^{3}+4x+5 ?

(a) (x-1)
(b) (x+1)
(c) (x-2)
(d) (x+2)

Answer. (b) (x+1)

Question.12. The polynomial (x-a), where a>0, is a factor of the polynomial q(x)=4 \sqrt{2} x^{2}-\sqrt{2}. Which of these is a polynomial whose factor is (x-\frac{1}{a})?

(a) x^{2}+x+6
(b) x^{2}-5x+4
(c) x^{2}+4x-3
(d) x^{2}+x-6

Answer. (d) x^{2}+x-6