CAT Algebra questions from Linear equations and Quadratic equations that appear in the Quantitative Aptitude section of the CAT Exam consists of concepts from Equations and Algebra. Get as much practice as you can in these two topics because the benefits of being good at framing equations can be enormous and useful in other CAT topics as well. In CAT Exam, one can generally expect to get 1~2 questions from Linear Equations and Quadratic Equations. 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.
3x + 4|y| = 33. How many integer values of (x, y) are possible?
(|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?
x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?
What is the number of real solutions of the equation x^{2} - 7|x| - 18 = 0?
x^{2} - 9x + |k| = 0 has real roots. How many integer values can 'k' take?
x^{2} - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?
2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.
Consider three numbers a, b and c. Max (a,b,c) + Min (a,b,c) = 13. Median (a,b,c) - Mean (a,b,c) = 2. Find the median of a, b, and c.
a_{1}x + b_{1}y + c_{1}z = d_{1}, a_{2}x + b_{2}y + c_{2}z = d_{2}, a_{3}x + b_{3}y + c_{3}z = d_{3}.
Which of the following statements if true would imply that the above system of equations does not have a unique solution?
i. \\frac{a_{1}}{a_{2}}\\) = \\frac{b_{1}}{b_{2}}\\) = \\frac{c_{1}}{c_{2}}\\) ≠ \\frac{d_{1}}{d_{2}}\\)
ii. \\frac{a_{1}}{a_{2}}\\) = \\frac{ a_{2} }{ a_{3} }\\) ; \\frac{ b_{1} }{ b_{2} }\\) = \\frac{ b_{2} }{ b_{3} }\\)
iii. a_{1}, a_{2}, a_{3} are integers; b_{1}, b_{2}, b_{3} are rational numbers, c_{1}, c_{2}, c_{3} are irrational numbers
Equation x^{2} + 5x – 7 = 0 has roots a and b. Equation 2x^{2} + px + q = 0 has roots a + 1 and b + 1. Find p + q.
Sum of the roots of a quadratic equation is 5 less than the product of the roots. If one root is 1 more than the other root, find the product of the roots?
How many real solutions are there for the equation x^{2} – 7|x| - 30 = 0?
If (3x+2y-22)^{2} + (4x-5y+9)^{2} = 0 and 5x-4y = 0. Find the value of x+y.
Let x^{3}- x^{2} + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true
(3 + 2√2)^{(x2 - 3)} + (3 - 2√2)^{(x2 - 3)} = b which of the following can be the value of b?
If f(y) = x^{2} + (2p + 1)x + p^{2} - 1 and x is a real number, for what values of ‘p' the function becomes 0?
A merchant decides to sell off 100 articles a week at a selling price of Rs. 150 each. For each 4% rise in the selling price he sells 3 less articles a week. If the selling price of each article is Rs x, then which of the below expression represents the rupees a week the merchant will receive from the sales of the articles?
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One-fifth of a number is equal to \\frac{5}{8}\\)^{th} of another number. If 35 is added to the first number, it becomes four times of the second number. Find the second number.
John's present age is one fourth of his father's age two years ago. John's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago, then what is John's present age?
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 + 1 = x^{2} and x > 0, then 2x^{4} is:
The minimum possible value of the sum of the squares of the roots of the equation x^{2} + (a + 3)x - (a + 5) = 0 is
If u^{2} + (u-2v-1)^{2} = -4v(u + v), then what is the value of u + 3v?
The number of solutions of the equation |x|(6x^{2} + 1) = 5x^{2} is [TITA]
The product of the distinct roots of ∣x^{2} - x - 6∣ = x + 2 is
What is the largest positive integer such that \\frac{n^2+7n+12}{n^2-n-12}) is also positive integer?
Let A be a real number. Then the roots of the equation x^{2} - 4x – log_{2}A = 0 are real and distinct if and only if
The quadratic equation x^{2} + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b^{2} + c?
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