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Class 11 Maths Practice Test - Applications of Quadratic Equations
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Class 11 Maths Practice Test - Applications of Quadratic Equations
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15 Questions

1. A real number ‘a’ is called a good number if the inequality (2x2 – 2x – 3) / (x2 + x + 1) ≤ a is satisfied for all real x. What is the set of all real numbers?
2. Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x2 ≥ log1/2 (x + 2) is the solution of the inequality 49x2 – 4a4 ≤ 0. What is the value of S?
3. A real number ‘a’ is called a good number if the inequality (2x2 – 2x – 3) / (x2 + x + 1) ≤ a is satisfied for all real x. What is the set of all real numbers?
4. Which is the largest negative integer which satisfies (x2 – 1)/(x – 2)(x – 3)?
5. What is the value of x if (a + 2b – 3c)x2 + (b + 2c – 3a)x + (c + 2a – 3b) = 0 where a, b, c are in A.P?
6. What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax2 + Bx + C = 0?
7. If x1, x2 are real roots of ax2 – x + a = 0. Then, find the set of all values of parameter ‘a’ for which |x1 – x1| < 1?
8. If, (a + 1)x2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have imaginary roots?
9. What will be the sum of the real roots of the equation x2 + 5|x| + 6 = 0?
10. For what value of θ, 1 lies between the roots of the quadratic equation 3x2 – 3sinθ x – 2cos2θ = 0?
11. What is the set of values of p for which the roots of the equation 3x2 + 2x + p(p – 1) = 0 are of opposite sign?
12. If, (a + 1)x2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have imaginary roots?
13. For what value of θ, 1 lies between the roots of the quadratic equation 3x2 – 3sinθ x – 2cos2θ = 0?
14. What is the number of solution(s) of the equation |√x – 2| + √x(√x – 4) + 2 = 0?
15. If x1, x2 are real roots of ax2 – x + a = 0. Then, find the set of all values of parameter ‘a’ for which |x1 – x1| < 1?

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