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|}\\)?
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.
The number of distinct pairs of integers (m, n) satisfying |1+mn| < |m+n| < 5 is
For all possible integers n satisfying 2.25 ≤ 2 + 2^{n + 2} ≤ 202, the number of integer values of 3 + 3^{n + 1} is
The number of integers n that satisfy the inequalities |n - 60| < |n - 100| < |n - 20| is
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)
The Questions that follow, are from actual XAT papers. If you wish to take them separately or plan to solve actual XAT papers at a later point in time, It would be a good idea to stop here.
If 2 ≤ |x – 1|×|y + 3| ≤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.
The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.
Consider the following statements:
(i) When 0 < x < 1, then \\frac{1}{1+x}) < 1 - x + x^{2}
(ii) When 0 < x < 1, then \\frac{1}{1+x}) > 1 - x + x^{2}
(iii) When -1 < x < 0, then \\frac{1}{1+x}) < 1 - x + x^{2}
(iv) When -1 < x < 0, then \\frac{1}{1+x}) > 1 - x + x^{2}
Then the correct statements are
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
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