List of top Quantitative Ability and Data Interpretation Questions on Quadratic Equations

Consider the quadratic function \( f(x) = ax^2 + bx + a \) having two irrational roots, with \( a \) and \( b \) being two positive integers, such that \( a, b \leq 9 \). If all such permissible pairs \( (a, b) \) are equally likely, what is the probability that \( a + b \) is greater than 9?

If \(2x^2 - 7x + 6 = 0\), what is the largest value of \(x\) which satisfies the equation?

Raj Travels has the following revenue model for a group package. The owner charges Rs. 20,000 per person for a group size up to 200. For every additional traveller beyond 200, he starts offering a discount of Rs. 50 to ALL members of the group.

The maximum possible income for Raj Travels from the package is:

Questions 43 and 44 are based on the following instructions: each question gives a statement followed by three conclusions, I, II and III. Pick the option that tells you which of the three conclusions can be derived from the statement alone.

Statement: Let \(A\), \(B\), \(C\) be real numbers satisfying \(A < B < C\), \(A + B + C = 6\), and \(AB + BC + CA = 9\).

Conclusion I: \(1 < B < 3\)
Conclusion II: \(2 < A < 3\)
Conclusion III: \(0 < C < 1\)

The number of possible real solution(ss) of \(y\) in the equation \(y^2 - 2y\cos x + 1 = 0\) is:

If \(0 < p < 1\), then the roots of the equation \((1-p)x^2 + 4x + p = 0\) are:

\(a\), \(b\) and \(c\) are the sides of a triangle. The equations \(ax^2 + bx + c = 0\) and \(3x^2 + 4x + 5 = 0\) have a common root. Then angle C is equal to