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Assertion and Reason Questions Class 10 Maths Chapter 2 Polynomials
1) Assertion: A quadratic polynomial can have at the most two zeroes.
Reason: x^2+7x+12 has no real zeroes.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is true but reason is false.
2) Assertion: If the sum of the zeroes of the quadratic polynomial x^2-2kx+8 is 2 then value of k is 1.
Reason: Sum of zeroes of a quadratic polynomial ax^2+bx+c is-b/a
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.
3) Assertion: The highest power of x in the polynomial P(x) is the degree of the polynomial.
Reason: P(x) = 4x^3-x^2+5x^4+3x-2 is a polynomial of degree 3.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false.
4) Assertion: x3+x has only one real zero.
Reason: A polynomial of nth degree must have n real zeroes
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false.
5) Assertion: If one zero of polynomial p(x) = (k^2+4)x^2+13x+4k is reciprocal of the other, then k=2.
Reason: If (x-a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion.
6) Assertion: A quadratic polynomial can have at the most two zeroes.
Reason: : x^2+4x+5 has two zeroes.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
7) Assertion: Degree of aa zero polynomial is not defined.
Reason: Degree of a non-zero constant polynomial is 0.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion.
8) Assertion: If the product of the zeroes of the quadratic polynomial ax^2+3x+5k is -10 then value of k is -2.
Reason: Sum of zeroes of a quadratic polynomial ax^2+bx+c is -b/a
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for assertion.
9) Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.
Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
10) Assertion: 3-2√5 is one zero of the quadratic polynomial then other zero will be 3+2√5.
Reason: Irrational zeros (roots) always occurs in pairs.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.
11) Assertion: y^2+6y+9 has two zeros
Reason (R): A quadratic Polynomial can have at most two zeros.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.
12) Assertion:x+1is a Linear Polynomial
Reason (R): The polynomials of degree 1 are called linear polynomials.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.
13) Assertion: 3x^3+3x^2+3x+3 is a cubic polynomial.
Reason: If the number ‘3’ is multiplied in all the terms of a polynomial then it is called a cubic polynomial.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
14) Assertion: -1& -4 are the zeroes of polynomial x^2-3x-4
Reason: a real number k is said to be a zero of polynomial P(x) if P(K)= 0
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion.
15) Assertion: The number of zeros that a polynomial can have is equal to the degree of the polynomial.
Reason: the polynomial x^5-x^4-2x^3+x^2-1 has four zeroes
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
16) Assertion: the graph of linear polynomial intersect the x-axis at point
Reason: for polynomial P(x) of degree n the graph of y=P(x) intersect x-axis at most points.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
17) Assertion: the graph of quadratic polynomial P(x) intersect x-axis at two point
Reason: degree of quadratic polynomial is 2
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
18) Assertion: the graph of polynomial intersect xaxis at 3 points and y-axis at 1 points the polynomial has 3 zeroes
Reason: the number of zeroes that a polynomial P(x) can have is the number of times polynomial intersect x and y axis
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
19) Assertion: The graph of a polynomial p(x) is a straight line parallel to x axis. The polynomial has no zeros.
Reason (R): If a polynomial P(x) does not intersect the x-axis at any point, it does not have any zero.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
20) Assertion: The graph of a quadratic polynomial P(x)intersects the x-axis at two points.
Reason (R): The graph of a quadratic polynomial is a parabola.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: b ) both Assertion and reason are correct but reason is not correct explanation for assertion
21) Assertion: if a,b,c are the zeroes of x^3-2x ^2+qx-r and a+b=0 then 2q=r
Reason: if a,b,c are the zeroes of px^3+qx^2+rx+s then a+b+c=- q/p, ab+bc+ca=r/s, abc=-s/p
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
22) Assertion: (2-√3 ) is one zero of quadratic polynomial then other zero will be 2+√3
Reason: irrational zeroes always occur in pair
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
23) Assertion: zeroes of f(x)= x^2-4z-5 are5,-1
Reason: the polynomial whose zeroes are 2+√3, 2-√3 is x^2-4x+7
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
24) Assertion: a quadratic polynomial can have at most two zeroes.
Reason: x^2+4x+5 has two zeroes
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
25) Assertion: P(x)=14x^3-2x^2+8x^4+7x-8 is a polynomial of degree 4
Reason: the highest power of x in the polynomial P(x) is the degree of polynomial.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
26) Assertion: the sum and product of zeroes of quadratic polynomial are 1/4 and -1/4 then the quadratic polynomial is 4x^2+4x+1
Reason: the quadratic polynomial whose sum and product of zeroes are given x^2-(sum of zeroes)x+ product of zeroes
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
27) Assertion: The graph y =f(x) is shown in figure, for the polynomial f( x) The number of zeros of f( x) =4.
Reason : The number of zero of the polynomial f (x) is the number of point of which f (x)cuts or touches the axes.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
28) Assertion: the degree of polynomial 2x-1 is 1
Reason: polynomial the degree is the value of highest power of the variable.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
29) Assertion: 5t− √7 is a linear polynomial
Reason: A polynomial of degree 1 is called a linear polynomial.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
30) Assertion: 3x^3 is a cubic polynomial
Reason: whose highest power of polynomial is 3 it is a type of cubic polynomial
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
31) Assertion: t^2 is a quadratic polynomial
Reason: The degree of the given expression is 2. So, it is a quadratic polynomial.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
32) Assertion: x^20+1 is a binomial
Reason: If an expression contains two unlike terms, then it is called as a binomial.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
33) Assertion: a polynomial having variable with two constant value is called constant polynomial
Reason: a constant polynomial has highest degree is 2
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: d) both Assertion and reason are false
34) Assertion: A term of the expression having no literal factors is called a constant term
Reason: 5+4x here 5 is the constant term
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
35) Assertion: The polynomials in which the highest power of the variable is two are known as Quadratic polynomials.
Reason: P(x)=ax^2 +bx+c is a quadratic polynomial
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
36) Assertion: x^2 +x is a quadratic polynomial
Reason: in this polynomial the highest power of x is 2. Hence, the given polynomial is quadratic.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
37) Assertion: in linear polynomial t+5 , t is a variable
Reason: Since in a polynomial x+a, x is a variable and a is a constant term
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
38) Assertion: the polynomial p(x)= 3/2 x− 10/7 is a linear polynomial
Reason the general form of linear polynomial is ax+b
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
39) Assertion: If the graph of polynomial intersect the x-axis at only pont it be a quadratic polynomial.
Reason: Because every quadratic has at most two zeroes.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
40) Assertion: the cofficent of x in the expansion of (x+3)^3 is 27
Reason: (a+b)^3= a^3+b^3+3a^2+3ab^2
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
41) Assertion : A polynomial of degree n has at most n zeroes
Reason: Maximum number of zeroes of a polynomial = degree of the polynomial.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion amd reason are correct and reason is correct explanation for assertion
42) Assertion: if x^6 + 1 is divided by x – 1, then the remainder is 2.
Reason: p(x) = x^6 + 1 when divided by x – 1, then remainder = p(1)
p(1) = 1^6 + 1 = 2
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
43) Assertion: Zeroes of p(z) = z² – 27 are √3and -√3
Reason:For zeroes z² – 27 = 0, z² = 27
z = ±√27
z = ± 3√3
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
44) Assertion: x = 3 is a zero of the polynomial. p(x) = 2x^3 – 5x² – 4x + 3
Reason: p(x) = 2x^3 – 5x² – 4x + 3
∴ p{3) = 2(3)^3 – 5 x (3)² -4 x 3 + 3
= 54 – 45- 12 + 3 = 0
P(3) = 0
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
45) Assertion: The graph of y =f(x) is given below. Number of zeroes of F(x)=1
Reason: Graph of y = f(x) intersect x-axis in one point only.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
46) Assertion: The graph of y = f(x) is given, number of zeroes of f(x)=0
Reason: Graph y =f(x) does not intersect x-axis.
a) Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
c) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
47) Assertion: product of the zeroes of – 2x² + kx + 6. is -3
Reason: product of zeroes =c/a
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
48) Assertion: the sum of the zeroes of the given quadratic polynomial -3x² + k is 0
Reason: sum of zeroes=-b/a
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
49) Assertion: A polynomial of degree five is divided by a quadratic polynomial. If it leaves a remainder, then the degree of remainder is 1 or 0
Reason: Degree of remainder is always less than divisor.
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
50) Assertion: The graph of x = p(y) is given below, for some polynomial p(y). the number of zeroes of p(y) is 4
Reason: Graph of p(y) intersects y-axis in four different points
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
51) Assertion: (100+2)^2= 10404
Reason: (a+b)^2=a^2+b^2+2ab
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
52) Assertion: (a^2-b^2)=(a-b)(a+b)
Reason: (5^2-4^2)=9
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion
53) Assertion: 4x^2+9x+79 here 4,9 are the cofficent in this polynomial.
Reason: in above polynomial 79 is constant term
a)Both assertion and reason are true and reason is the correct explanation of assertion
b) Both assertion and reason are true but reason is not the correct explanation of assertion
C) Assertion is true but reason is false.
d) both Assertion and reason are false
Ans: a ) both Assertion and reason are correct and reason is correct explanation for assertion