# CAT Questions | CAT Algebra Questions

###### CAT Quantitative Aptitude | CAT Algebra: Linear Equations; Quadratic Equations

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.

1. #### CAT Linear Equations - Counting

3x + 4|y| = 33. How many integer values of (x, y) are possible?

1. 6
2. 3
3. 4
4. More than 6

2. #### CAT Linear Equations - Counting

(|x| - 3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation?

1. 4
2. 6
3. 10
4. 8

3. #### CAT Linear Equations - Integer Values; Modulus

x + |y| = 8, |x| + y = 6. How many pairs of x, y satisfy these two equations?

1. 2
2. 4
3. 0
4. 1

4. #### CAT Quadratic Equations - Counting.

What is the number of real solutions of the equation x2 - 7|x| - 18 = 0?

1. 2
2. 4
3. 3
4. 1

5. #### CAT Quadratic Equations - Counting

x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

1. 40
2. 21
3. 20
4. 41

6. #### CAT Quadratic Equations - Integer Roots

x2 - 11x + |p| = 0 has integer roots. How many integer values can 'p' take?

1. 6
2. 4
3. 8
4. More than 8

7. #### CAT Linear Equations - Integer Solutions

2x + 5y = 103. Find the number of pairs of positive integers x and y that satisfy this equation.

1. 9
2. 10
3. 12
4. 20

8. #### CAT Linear Equations - Maximum, Minimum

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.

1. 11.5
2. 9
3. 9.5
4. 12

9. #### CAT Linear Equations - Unique Solutions

a1x + b1y + c1z = d1, a2x + b2y + c2z = d2, a3x + b3y + c3z = d3.

Which of the following statements if true would imply that the above system of equations does not have a unique solution?

1. 7
2. 9
3. 11
4. 13

14. #### CAT Cubic Equations - AP and roots of an equation

Let x3- x2 + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true

1. b=2,c=2
2. b=1,c=1
3. b= -1,c = 1
4. b= -1,c= -1

15. #### CAT Linear Quadratic Equations - Roots of an Equation

(3 + 2√2)(x2 - 3) + (3 - 2√2)(x2 - 3) = b which of the following can be the value of b?

1. 2
2. √2
3. -√2
4. All of the above

16. #### CAT Quadratic Equations - Real roots

If f(y) = x2 + (2p + 1)x + p2 - 1 and  x is a real number, for what values of ‘p' the function becomes 0?

1. p > 0
2. p > -1

1. 1
2. 2
3. 3
4. 4

3. #### CAT 2018 Question Paper Slot 1 - Linear and Quadratic Equations

If u2 + (u-2v-1)2 = -4v(u + v), then what is the value of u + 3v?

5. #### CAT 2019 Question Paper Slot 1 - Quadratic equations

The product of the distinct roots of ∣x2 - x - 6∣ = x + 2 is

1. -4
2. -16
3. -8
4. -24

6. #### CAT 2019 Question Paper Slot 2 - Linear & quadratic equations

What is the largest positive integer such that $$frac{n^2+7n+12}{n^2-n-12}$ is also positive integer? 1. 6 2. 8 3. 16 4. 12 7. #### CAT 2019 Question Paper Slot 2 - Linear & quadratic equations Let A be a real number. Then the roots of the equation x2 - 4x – log2A = 0 are real and distinct if and only if 1. A < $\frac{1}{16}$ 2. A > $\frac{1}{8}$ 3. A > $\frac{1}{16}$ 4. A < $\frac{1}{8}$ 8. #### CAT 2019 Question Paper Slot 2 - Linear & quadratic equations The quadratic equation x2 + bx + c = 0 has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of b2 + c? 1. 3721 2. 549 3. 361 4. 427 ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2021Enroll at 49,000/- 44,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 4000/- Attend a Demo Class ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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