Skip to main content
Back to QUADRATIC EQUATIONS

Your Progress

0 / 914 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • QUADRATIC EQUATIONS

Quadratic equations practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 61-90 of 914 questions

Preparing practice and saved progress…

61 Medium
61 of 914
Analyzing +4 | -1
Let α,β\alpha ,\beta be the roots of the equation ax2+2bx+c=0a{x^2} + 2bx + c = 0 and γ,δ\gamma ,\delta be the roots of the equation px2+2qx+r=0p{x^2} + 2qx + r = 0. If α,β,γ,δ\alpha ,\beta ,\gamma ,\delta are in GP, then
View answer and explanation
Correct option: A
q2ac=b2pr{q^2}ac = {b^2}pr
Option A (q2ac=b2pr{q^2}ac = {b^2}pr) is correct because the relationship between the roots of the two quadratic equations, when they are in GP, leads to this condition.
62 Medium
62 of 914
Application +4 | -1
If roots of the equation (a2+b2)x2−2(ac+bd)x+c2+d2=0\left(a^2+b^2\right) x^2-2(a c+b d) x+c^2+d^2=0 are equal then :
View answer and explanation
Correct option: D
ad=bca d=b c
Option D (ad=bca d=b c) is correct because it is derived from the condition that the roots of the quadratic equation are equal, which implies the discriminant is zero.
63 Medium
63 of 914
Analyzing +4 | -1
The sum of the roots of the equation, x2+∣2x−3∣−4=0\mathrm{x}^{2}+|2 \mathrm{x}-3|-4=0, is:
View answer and explanation
Correct option: C
2\sqrt{2}
The sum of the roots of the equation is 2\sqrt{2} because we need to consider two cases for the absolute value and then check which roots satisfy the initial conditions.
64 Easy
64 of 914
Application +4 | -1
The solution set of the inequation 0<∣3x+1∣<13  ,0 < \left| {3x + 1} \right| < \frac{1}{3}\;, is
View answer and explanation
Correct option: C
(−4/9  ,−2/9)−{−1/3}\left( { - 4/9\;, - 2/9} \right) - \left\{ { - 1/3} \right\}
The correct answer is C ((−4/9  ,−2/9)−{−1/3}\left( { - 4/9\;, - 2/9} \right) - \left\{ { - 1/3} \right\}) because it represents the interval where the absolute value of 3x+13x+1 is greater than 0 but less than 1/3, excluding the point where 3x+1=03x+1 = 0.
65 Medium
65 of 914
Application +4 | -1
If α\alpha and β\beta are the roots of the equation x2−6x+a=0{x^2} - 6x + a = 0 and satisfy the relation 3α+2β=163\alpha + 2\beta = 16, then the value of aa is
View answer and explanation
Correct option: B
8
The correct answer is B (8) because by using the given relation 3α+2β=163\alpha + 2\beta = 16 and the properties of roots of a quadratic equation, we can solve for the value of 'a'.
66 Easy
66 of 914
Analyzing +4 | -1
Real roots of the equation x2+5∣x∣+4=0{x^2} + 5\left| x \right| + 4 = 0 are
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the equation has no real roots, as the left-hand side is always positive for real x.
67 Medium
67 of 914
Application +4 | -1
If α\alpha and β\beta are the roots of x2−2x+4=0{x^2} - 2x + 4 = 0, then the value of α6+β6{\alpha ^6} + {\beta ^6} is
View answer and explanation
Correct option: C
128
Option C (128) is correct because by finding the roots α\alpha and β\beta of the quadratic equation and substituting them into the expression α6+β6\alpha^6 + \beta^6, we get 128.
68 Medium
68 of 914
Application +4 | -1
If an angle AA of a △ABC\triangle A B C satisfies 5cos⁡A+3=05 \cos A+3=0, then the roots of the quadratic equation, 9x2+27x+20=09 x^{2}+27 x+20=0 are.
View answer and explanation
Correct option: B
sec⁡A,tan⁡A\sec A, \tan A
Option B (sec⁡A,tan⁡A\sec A, \tan A) is correct because the roots of the quadratic equation are equal to the secant and tangent of angle A, derived from the given cosine value.
69 Easy
69 of 914
Application +4 | -1
If the equation x2−3kx+2e2log⁡k−1=0{x^2} - 3kx + 2{e^{2\log k}} - 1 = 0 has real roots such that the product of roots is 7, then the value of kk is
View answer and explanation
Correct option: B
2
Option B (2) is correct because solving the equation with the product of roots equal to 7 yields k = 2, considering k > 0.
70 Medium
70 of 914
Application +4 | -1
If the equation (log⁡16x)2−(log⁡16x)+log⁡16k=0\left(\log _{16} x\right)^2-\left(\log _{16} x\right)+\log _{16} k=0 has a unique solution (where kk is constant), then the value of kk is
View answer and explanation
Correct option: B
2
The correct answer is B (2) because setting the discriminant of the quadratic equation to zero and solving for k gives k=2.
71 Easy
71 of 914
Application +4 | -1
The quadratic equation with rational coefficients whose one root is 2+32−3\frac{2+\sqrt{3}}{2-\sqrt{3}}, is
View answer and explanation
Correct option: A
x2−14x+1=0x^2-14 x+1=0
Option A (x2−14x+1=0x^2-14 x+1=0) is correct because the quadratic equation is formed by finding the other root and then constructing the equation using the sum and product of the roots.
72 Easy
72 of 914
Application +4 | -1
If p,q∈Rp, q \in \mathbf{R} and 2+3i2+\sqrt{3} i a foot of x2+px+x^2+p x+ q=0q=0, then
View answer and explanation
Correct option: B
p=−4,q=7p=-4, q=7
Option B (p=-4, q=7) is correct because if 2+3i2 + \sqrt{3}i is a root, then its conjugate 2−3i2 - \sqrt{3}i is also a root, and we can find p and q using Vieta's formulas.
73 Medium
73 of 914
Analyzing +4 | -1
If the quadratic equation ax2−bx+12=0a x^2-b x+12=0 where a,ba, b are positive integers not exceeding 10 has roots both greater than 2 , then number of possible ordered pair (a,b)(a, b) is
View answer and explanation
Correct option: A
1
Option B (1) is correct because there is only one possible ordered pair (a, b) that satisfies the given conditions.
74 Easy
74 of 914
Application +4 | -1
If the roots of the equation ax2−4x+a2=0a{x^2} - 4x + {a^2} = 0 are imaginary and the sum of the roots is equal to their product, then a=a =
View answer and explanation
Correct option: C
2
Option C (2) is correct because it satisfies both conditions: the roots are imaginary (discriminant < 0) and the sum of the roots equals their product.
75 Easy
75 of 914
Application +4 | -1
The number of solutions of ∣x+2∣=2(3−x)|x+2|=2(3-x) is
View answer and explanation
Correct option: A
1
Option A (1) is correct because there is only one solution to the equation, which is x = 4/3.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
76 Easy
76 of 914
Application +4 | -1
If a,b,ca, b, c are rational and ax2+bx+c=0a x^2+b x+c=0 and 3x2+3 x^2+ x−5=0x-5=0 have a common root, then 3a+b+2c=3 a+b+2 c=
View answer and explanation
Correct option: A
0
Option A (0) is correct because the equations must be the same, leading to a relationship where 3a + b + 2c = 0.
77 Easy
77 of 914
Application +4 | -1
If sin⁡θ+cos⁡θ=h\sin \theta + \cos \theta = h, then the quadratic equation having sin⁡θ\sin \theta and cos⁡θ\cos \theta as its roots, is
View answer and explanation
Correct option: B
2x2−2hx+(h2−1)=02{x^2} - 2hx + \left( {{h^2} - 1} \right) = 0
Option B (2x2−2hx+(h2−1)=02{x^2} - 2hx + \left( {{{h^2} - 1}} \right) = 0) is correct because it is the quadratic equation formed using the given sum of roots and calculated product of roots.
78 Medium
78 of 914
Analyzing +4 | -1
If a,ba, b and cc are three distinct positive real numbers, then the number of real roots of ax2+2b∣x∣−c=0a x^2+2 b|x|-c=0 is
View answer and explanation
Correct option: B
2
Option B (2) is correct because the equation can be transformed into a quadratic in ∣x∣|x|, which yields one positive solution for ∣x∣|x|, resulting in two real roots for xx.
79 Medium
79 of 914
Analyzing +4 | -1
The values of λ\lambda such that sum of the squares of the roots of the quadratic equation, x2+(3−λ)x+2=λ\mathrm{x}^2+(3-\lambda) \mathrm{x}+2=\lambda has the least value is :
View answer and explanation
Correct option: A
2
Option A (2) is correct because completing the square for the sum of squares of roots results in a minimum value when lambda equals 2.
80 Medium
80 of 914
Analyzing +4 | -1
The values of ' aa ' for which x2+ax+sin⁡−1(x2−4x+5)+cos⁡−1(x2−4x+5)=0x^2+a x+\sin ^{-1}\left(x^2-4 x+5\right)+\cos ^{-1}\left(x^2-4 x+5\right)=0 has atleast one solution, is
View answer and explanation
Correct option: D
−2−π4-2-\frac{\pi}{4}
Option D (−2−π4-2-\frac{\pi}{4}) is correct because it's the value of 'a' that satisfies the given equation when x=2, which is the only possible solution.
81 Medium
81 of 914
Application +4 | -1
Let α,β\alpha ,\beta are the roots of equation 2x2−(p+1)x+(p−1)=02{x^2} - \left( {p + 1} \right)x + \left( {p - 1} \right) = 0. If α−β=αβ\alpha - \beta = \alpha \beta, then what is the value of pp?
View answer and explanation
Correct option: B
2
Option B (2) is correct because it is the value of p that satisfies the given condition α−β=αβ\alpha - \beta = \alpha \beta.
82 Easy
82 of 914
Application +4 | -1
If rr be the ratio of the roots of the equation ax2+bx+c=0a x^2+b x+c=0, then (r+1)2r=\frac{(r+1)^2}{r}=
View answer and explanation
Correct option: B
b2ca\frac{b^2}{c a}
Option B (b2ca\frac{b^2}{c a}) is correct because it is derived from the relationship between the roots and coefficients of the quadratic equation.
83 Easy
83 of 914
Application +4 | -1
The solutions of the inequation 2x2+3x−9≤02 x^2+3 x-9 \leq 0 are given by
View answer and explanation
Correct option: B
−3≤x≤32-3 \leq x \leq \frac{3}{2}
Option B (−3≤x≤32-3 \leq x \leq \frac{3}{2}) is correct because it represents the solution to the quadratic inequality obtained by factoring and finding the interval where the expression is less than or equal to zero.
84 Easy
84 of 914
Analyzing +4 | -1
If xx is real, then expression x+22x2+3x+6\frac{{x + 2}}{{2{x^2} + 3x + 6}} takes all values in the interval
View answer and explanation
Correct option: B
[−113,13]\left[ { - \frac{1}{{13}},\frac{1}{3}} \right]
Option B ([−113,13]\left[ { - \frac{1}{{13}},\frac{1}{3}} \right]) is correct because it represents the range of the given expression when x is real, found by analyzing the discriminant of the quadratic equation.
85 Medium
85 of 914
Analyzing +4 | -1
The equation x2−4x+[x]+3=x[x]x^{2}-4 x+[x]+3=x[x], where [x][x] denotes the greatest integer function, has
View answer and explanation
Correct option: D
A unique solution in (−∞,∞)(-\infty, \infty)
Option D (A unique solution in (−∞,∞)(-\infty, \infty)) is correct because the equation simplifies to having only one solution, which is x=1.
86 Medium
86 of 914
Analyzing +4 | -1
The value of x,log⁡1/2x≥log⁡1/3xx, \log _{1 / 2} x \geq \log _{1 / 3} x is
View answer and explanation
Correct option: A
(0,1](0,1]
Option A ((0,1])((0,1]) is correct because the inequality holds for x in this interval, including x=1.
87 Medium
87 of 914
Application +4 | -1
If a1,a2,…,ana_1, a_2, \ldots, a_n are positive real numbers whose product is a fixed real number cc, then the minimum value of a1+a2+…+an−1+2ana_1+a_2+\ldots+a_{n-1}+2 a_n is
View answer and explanation
Correct option: A
n(2c)1/nn(2 c)^{1 / n}
The correct answer is A (n(2c)1/nn(2 c)^{1 / n}) because it is derived using the AM-GM inequality to find the minimum value of the given expression.
88 Medium
88 of 914
Analyzing +4 | -1
If a,b,c are real numbers such that a + b + c = 0, then the
quadratic equation 3ax2+2bx+c=03a{x^2} + 2bx + c = 0 has:
View answer and explanation
Correct option: A
At least one root in [0, 1]
Option A (At least one root in [0, 1]) is correct because applying Rolle's theorem to the function f(x)=ax3+bx2+cxf(x) = ax^3 + bx^2 + cx on the interval [0, 1] shows that there must be at least one root of 3ax2+2bx+c=03ax^2 + 2bx + c = 0 in the interval [0, 1].
89 Medium
89 of 914
Application +4 | -1
The roots of the equation (b−c)x2+(c−a)x+(a−b)(b-c) x^2+(c-a) x+(a-b) =0=0 are
View answer and explanation
Correct option: C
a−bb−c,1\frac{a-b}{b-c}, 1
The correct answer is C (a−bb−c,1\frac{a-b}{b-c}, 1) because 1 is a root and the product of the roots equals a−bb−c\frac{a-b}{b-c}.
90 Easy
90 of 914
Analyzing +4 | -1
If one root of the equation ax2+bx+c=0a{x^2} + bx + c = 0 is reciprocal of the one root of the equation a1x2+b1x+c1=0,{a_1}{x^2} + {b_1}x + {c_1} = 0, then
View answer and explanation
Correct option: A
(aa1−cc1)2=(bc1−b1a)(b1c−a1b){\left( {a{a_1} - c{c_1}} \right)^2} = \left( {b{c_1} - {b_1}a} \right)\left( {{b_1}c - {a_1}b} \right)
Option A ((aa1−cc1)2=(bc1−b1a)(b1c−a1b){\left( {a{a_1} - c{c_1}} \right)^2} = \left( {b{c_1} - {b_1}a} \right)\left( {{b_1}c - {a_1}b} \right)) is correct because it represents the condition derived when one root of the first quadratic equation is the reciprocal of a root of the second quadratic equation.
Revision notes and key takeaways

Review QUADRATIC EQUATIONS in your textbook or class notes, then use this set to check your understanding.

Showing 61-90 of 914 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Easy) 528 MCQs → ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Hard) 24 MCQs → ENGINEERING MATHEMATICS - QUADRATIC EQUATIONS MCQs (Medium) 362 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs

Your practice

0 / 914 answered · 914 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Answer feedback and difficulty
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →