Quadratic Equation JEE Questions PDF with Solution, Practice Now

Quadratic Equation JEE Questions: Quadratic Equations are an important topic in Mathematics for both JEE Main and JEE Advanced exams. It is part of Algebra, one of the most asked areas in JEE. Every year, questions from quadratic equations appear in the exam, and they test both concepts and problem-solving skills. The weightage of quadratic equations in JEE is usually around 6 to 8 marks, which can make a big difference in your rank.

Practicing quadratic equations questions JEE Mains helps you build speed, accuracy, and confidence. Many times, quadratic equations also connect with other topics like progressions, inequalities, and complex numbers, making it even more important for your preparation.

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Quadratic Equation JEE Questions Overview

Quadratic equation means an equation of the form ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0. In JEE exams, quadratic equations are not just about solving equations, but also about:

• Nature of roots (real, equal, distinct, imaginary)

• Relation between coefficients and roots

• Formation of quadratic equations from given conditions

• Graphical understanding of quadratic functions

• Mixed problems with inequalities and modulus

In JEE Main, you will usually get direct formula-based and concept-based questions, while in JEE Advanced quadratic problems, the focus is on application, tricky conditions, and combined concepts.

Practice Quadratic Equation JEE Questions

Practicing questions is the right way to master the Quadratic Equation JEE Questions topic. Below are a few practice problems following the JEE exam pattern:

1. Suppose a, b denote the distinct real roots of the quadratic polynomial x^2 + 20x - 2020 = 0 and suppose c, d denote the distinct complex roots of the quadratic polynomial x^2 - 20x + 2020 = 0. Then the value of ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) is

A. 0
B. 8000
C. 8080
D. 16000

2. Let -π/6 < θ < -π/12. Suppose α1 and β1 are the roots of the equation x^2 - 2x sec θ + 1 = 0, and α2 and β2 are the roots of the equation x^2 + 2x tan θ - 1 = 0. If α1 > β1 and α2 > β2, then α1 + β2 equals

A. 2 (sec θ - tan θ)
B. 2 sec θ
C. -2 tan θ
D. 0

3. Number of solution of the equation (x^2 - 5|x| + 5)^(x^2 - 11|x| + 30) = 1 is

A. 12
B. 14
C. 7
D. 2

4. If the equation 5x^2 - 10x + log_1/5 a = 0 has real roots then the minimum value of a is

A. 1/5^5
B. 1/10^10
C. 1/5^10
D. 1/5^20

5. All possible quadratic equation a x^2 + b x + 1 = 0 taking a in {1, 2, 3, …, n}, b in {-1, -2, …, -n} and if (a_i, b_j), i = 1, 2, 3, …, n represent solution set of these equations then ∑ 1/α_i + ∑ 1/β_j equals

A. n(n+1)/2
B. n^2(n+1)/2
C. n^3(n+1)/2
D. n^2

6. The equation tan^4 x - 2sec^2 x + k^2 = 0 will have at least one solution if

A. |k| ≤ 4
B. |k| ≤ 2
C. |k| ≤ √3
D. None of these

7. Number of real solution of the equation 5(√(1+x) + √(1-x)) = 6x + 8√(1-x^2) is

A. 1
B. 2
C. 4
D. infinite

8. If exactly one root of the equation k x^2 + k√3(x - 1) + 1 = 0 lies in (0, 1) then

A. k < -1, k > 1/√3
B. -1 < k < 1/√3
C. k > √3
D. k > 2√3

9. Let S be the set of value of k for which (k-4) sec^4 x + (k-3) sec^2 x + 1 = 0 has real solution. Then S is

A. R
B. (-∞, 3]
C. (4, ∞)
D. [3, 4)

10. The set of real values of a for which the equation (2a^2 + x^2)/(a^3 - x^3) = 2x/(a x + a^2 + x^2) + 1/(x - a) is

A. (-∞, 1)
B. (-∞, 0)
C. (1, ∞)
D. (0, ∞)

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Quadratic Equation JEE Questions PDF with Solution

To help aspirants, PW provides a practice question PDF with answer and solution. This PDF covers all varieties of problems including formula-based, tricky MCQs, and advanced-level questions. The PDF is structured as per the JEE exam pattern, where each question has 4 options (A, B, C, D). Detailed step-by-step solutions are given for better understanding. Students can download the PDF and use it for daily practice and revision.