A CAT Algebra question from Inequalities that appears in the Quantitative Aptitude section of the CAT Exam consists of concepts: Range of Inequalities, Modulus functions, Possible solutions and so on. The topic also involves linear and quadratic equations, finding roots, polynomials, functions and more. Inequalities is a crucial topic for CAT. Having a good foundation in this subject can help a student tackle questions in Coordinate Geometry, Functions. In CAT Exam, one can generally expect to get 2~3 questions from Inequalities. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.
How many positive integer values can x take that satisfy the inequality (x - 8) (x - 10) (x - 12).......(x - 100) < 0?
Solve the inequality: x^{3} – 5x^{2} + 8x – 4 > 0?
Find the range of x for which (x + 2) (x + 5) > 40?
How many integer values of x satisfy the inequality x( x + 2)(x + 4)(x + 6) < 200?
Find the range of x where ||x - 3| - 4| > 3?
The sum of three distinct natural numbers is 25. What is the maximum value of their product?
If x (x + 3) (x + 5) (x + 8) < 250, how many integer values can x take?
(|x| - 2) (x + 5) < 0. What is the range of values x can take?
a and b are roots of the equation x^{2} - px + 12 = 0. If the difference between the roots is at least 12, what is the range of values p can take?
If a, b, c are distinct positive integers, what is the highest value a × b × c can take if a + b + c = 31?
a, b, c are distinct natural numbers less than 25. What is the maximum possible value of |a – b| + |b – c| – |c – a|?
Consider integers p, q such that – 3 < p < 4, – 8 < q < 7, what is the maximum possible value of p^{2} + pq + q^{2}?
For how many integer values does the following inequality hold good? (x + 2) (x + 4) (x + 6)........(x + 100) < 0?
If a, b, c are integers such that – 50 < a, b, c < 50 and a + b + c = 30, what is the maximum possible value of abc?
Solve x^{2} - |x + 3| + x > 0?
Find range of f(x) = x^{2} – 6x + 14?
Solve :\\frac{(x – 4) (x+3)}{(x + 4) ( x +5)}\\) > 0?
Consider three distinct positive integers a, b, c all less than 100. If |a - b| + |b - c| = |c – a|, what is the maximum value possible for b?
Consider integers m, n such that -5 < m < 4 and -3 < n < 6. What is the maximum possible value of m^{2} - mn + n^{2}?
Consider integers p, q, r such that |p| < |q| < |r| < 40. P + q + r = 20. What is the maximum possible value of pqr?
What is the minimum value of f(x) = x^{2} – 5x + 41?
x^{4} – 4x^{3} + ax^{2} – bx = 1 = 0 has positive real roots. What is the maximum possible value of a + b?
|x^{3} – 3x + 5| > -4. What range of x satisfies this?
What are the maximum and minimum possible values for \\frac{|x+y|}{|x|+|y|}\\) + \\frac{|z+y|}{|z|+|y|}\\) + \\frac{|z+x|}{|x|+|z|}\\)?
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The set of all real numbers x for which x^{2} - |x + 2 |+ x > 0, is
For all real values of x, \\frac{3x^{2} - 6x + 12}{x^{2} + 2x + 4}\\) lies between 1 and k, and does not take any value above k. Then k equals
If \|x| < 100\\) and \|y| < 100\\), then the number of integer solutions of (x, y) satisfying the equation 4x + 7y = 3 is
If x ∈ (a, b) satisfies the inequality \\frac{x - 3}{x^{2} + 3x + 2} \geq 1,\\) then the largest possible value of b - a is
If a, b, c are real numbers a^{2} + b^{2} + c^{2} = 1, then the set of values ab + bc + ca can take is:
The inequality \\log _{2} \frac{3x - 1}{2 - x} < 1\\) holds true for
The set of values of x which satisfy the inequality 0.7^{2x2 - 3x + 4} < 0.343 is
Determine the greatest number among the following four numbers
The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.
If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals
The smallest integer n for which 4^{n} ＞ 17^{19} holds, is closest to
The smallest integer n such that n^{3} - 11n^{2} + 32n - 28 ＞ 0 is (TITA)
If a and b are integers such that 2x^{2} - ax + 2 ＞ 0 and x^{2} - bx + 8 ≥ 0 for all real numbers x, then the largest possible value of 2a - 6b is (TITA)
For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? (TITA)
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