# 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. 7
2. 8
3. 9
4. 13

7. #### CAT 2020 Question Paper Slot 2 - Linear & quadratic equations

The number of integers that satisfy the equality (x2 - 5x + 7)x + 1 = 1 is

1. 5
2. 4
3. 3
4. 2

8. #### CAT 2020 Question Paper Slot 2 - Linear & quadratic equations

In how many ways can a pair of integers (x , a) be chosen such that x2 − 2 | x | + | a - 2 | = 0 ?

1. 7
2. 6
3. 4
4. 5

9. #### CAT 2020 Question Paper Slot 2 - Linear & quadratic equations

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

1. 33
2. 27
3. 30
4. 36

10. #### CAT 2020 Question Paper Slot 1 - Linear & quadratic equations

The number of distinct real roots of the equation

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

1. #### 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

2. #### 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?

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

4. #### CAT 2017 Question Paper Slot 1 - Algebra

If x + 1 = x2 and x > 0, then 2x4 is:

1. 6 + 4√5
2. 3 + 5√5
3. 5 + 3√5
4. 7 + 3√5

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.

1. #### XAT 2018 Question Paper - QADI

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

1. The common root is 29.
2. The smallest among the roots is 1.
3. One of the roots is 5.
4. Product of the roots of the other equation is 5.
5. All of the above are possible, but none are definitely correct.

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.

1. #### IPMAT 2019 Question Paper - IPM Indore Quants

If $|x| < 100$\$ and $|y| < 100\\$, then the number of integer solutions of$x, y) satisfying the equation 4x + 7y = 3 is

2. #### IPMAT 2019 Question Paper - IPM Indore Quants

If a, b, c are real numbers a2 + b2 + c2 = 1, then the set of values ab + bc + ca can take is:

1. [-1,2]
2. [-$$frac{1}{2}\\$, 2] 3. [-1,1] 4. [-$\frac{1}{2}\\$, 1] 3. #### IPMAT 2019 Question Paper - IPM Indore Quants Let $\alpha, \beta\\$ be the roots of x2 - x + p = 0 and $\gamma, \delta\\$ be the roots of x2 - 4x + q = 0 where p and q are integers. If $\alpha, \beta, \gamma, \delta\\$ are in geometric progression then p + q is 1. -34 2. 30 3. 26 4. -38 ###### 🎉Get Upto ₹10,000 off on our CAT 23/24 courses.🎉Flat ₹6000 off on IPM courses.Valid till 30th September 2023! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2023 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ##### 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
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com