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Assertion and Reason Questions Class 10 Maths Chapter 4 Quadratic Equations
1.) Assertion: Equation of (x+1)^2-x^2=0 has number of real roots equal to 1
Reason: (x+1)^2-x^2=0
X^2+2x+1-x^2 = 0
2x+1=0
x=-½
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2.) Assertion: A quadratic equation in the variable x is an equation of the form ax^2 + bx + c = 0, where a, b, c are real numbers, a ≠ 0.
Reason: 2x^2 + x – 300 = 0 is a quadratic equation
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
3.) Assertion: (x – 2)^2 + 1 = 2x – 3 is not quadratic equation
Reason: it is not in the form of ax2 +bx+c
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for assertion.
4.) Assertion: the discriminant of the quadratic equation 2x^2 – 4x + 3 = 0, is -8and
hence the nature of its roots is no real roots .
reason: if b^2-4ac<0the nature of root is no real roots.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
5.) Assertion: x^2+x3+2 has no quadratic equation.
Reason: it has degree 3
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
6.) Assertion: If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, the value of k is -1
Reason: x = 2 is a root of the equation 2x² + kx -6 = 0
∴ 2(2)² +k(2) – 6 = 0
⇒ 8 + 2k – 6 = 0
⇒ 2k = -2
∴ k = -1
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
7.) Assertion: The roots of the equation 7x² + x – 1 = 0 are real and distinct
Reason : if b^2-4ac >0 then roots are real and distinct.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
8.) Assertion: Every quadratic equation has at most two root
Reason: Every quadratic equation has atleast one real root.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
9.) Assertion: 4x^2 – 12x+ 9= 0 has repeated roots.
Reason : The quadratic equation ax^2+ bx^2 + c = 0 have repeated roots if discriminant D > 0.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: c) Assertion is correct but reason is false
10.) Assertion: Any equation of the form ax^2+ bx+c = 0
where a not equal to 0, is called a quadratic equation
Reason: The equation x^2 +3x+1=(x-2)^2 is a quadratic equation .
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
11.) Assertion: If discriminant D= b^2- 4ac< 0 then the roots of quadratic equation ax^2× bx +c+ = 0 are imaginary.
Reason: The roots of the quadratic equation x^2 +2x+ 2 = 0 are imaginary
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both assertion and reason are correct and reason is the correct explanation for Assertion.
12.) Assertion: The equation 9x^2+3kx + 4 = 0 has equal roots for k =9.
Reason : If discriminant ‘D’ of a quadratic equation is equal to zero then the roots of equation are real and equal.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: a) Both assertion and reason are correct and reason is the correct explanation for assertion.
13.) Assertion: Sum of roots of 2x^2-3x+5=0 are 7/9
Reason: if a and b are the roots of ax^2+ bx + c= 0 then sum of roots a+b= b/a
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: d) Both assertion and reason are false.
14.) Assertion: product of roots of 2x^2-3x+5=0 are 7/9
Reason: : If a and b are the roots of ax^2+bx+c =0 then the product of ab=-c/a
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: d) Both assertion and reason are false.
15.) Assertion: The root of quadratic equation x^2+3x+3=0 are imaginary
Reason: if discriminant is less than zero then the roots if quadratic equation are imaginary.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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.
16.) Assertion: If the discriminant is equal to zero then the roots of quadratic equation are real and equal
Reason : the roots of quadratic equation 3x^2−2×6^1/2x+2=0 are same
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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: Roots of the quadratic equation 3x^2−2 × 6^1/2 x+2=0 are same.
Reason: A quadratic equation ax^2 +bx=c=0 has two distinct real roots, if b^2 −4ac>0
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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.
18.) Assertion: the discriminant D of a quadratic equation ax^2+bx+c=0 is D=b^2−4ac
Reason : The discriminant of 2x^2+5x+7=0 is -31
a)Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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.
- ) Assertion : If f(x)=ax^2+bx+c, where a>0,c<0 and b∈R, then roots of f(x)=0 must be real and distinct .
Reason: If f(x)=ax^2 +bx+c, where a>0,b∈R,b=0 and the roots of f(x)=0 are real and distinct, then c is necessarily negative real number .
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the reason is false.
d.) both assertion and reason are false.
Ans: c) Assertion is correct but reason is false.
- ) Assertion: The discriminant of ax^2 -(a+b)x+b=0 is (a-b)^2
Reason: D= b^2−4ac=[(a+b)] ^2−4ab=(a+b)^2−4ab=a^2 +b^2−2ab=(a−b) ^2
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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
- ) Assertion: If a=0, then it will nullify x^2 , making it a linear equation
Reason: only if a =0, the equation remains quadratic.
- a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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.
22.) Assertion: quadratic equation in which the term containing x raised to the
power of 1 is not present is called a pure quadratic equation.
Reason: ax^2 + c = 0 is a pure quadratic equation.
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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
23.)Assertion: a quadratic equation as an equation of degree 2
reason: The standard form of a quadratic is y = ax^2+bx+c=0
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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
24.) Assertion: The equation x^+(2m+1)x+(2n+1)=0 where m,n are integers cannot have any rational roots.
Reason: the quantity of (2m+1)^2-4(2n+1) where m,n belongs to integers can never be perfect square
a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
c.) assertion is true but the 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
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