CAT Previous Year Questions: Linear and Quadratic Equations

Linear Equations CAT Previous Year Questions with Answer PDF

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:If x and y are real numbers such that x+ (x − 2y − 1)2 = −4y(x + y), then the value x−2y is

[2023]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:If then is equal to

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:The number of integer solutions of equation 2 |x| (x2 + 1)= 5x2 is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Let & and β be the two distinct roots of the equation 2x- 6x + k = 0, such that (α + β) and αβ are the distinct roots of the equation x2 + px + p = 0. Then, the value of 8(k - p) is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:The equation x3 + (2r + 1)x2 + (4r - 1)x + 2 = 0 has -2 as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of r is

[2023]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:The sum of all possible values of x satisfying the equation 24x2 - 22x2 + x + 16 + 22x + 30 = 0, is

[2023]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:If r is a constant such that ∣x2 − 4x − 13∣ = r has exactly three distinct real roots, then the value of r is

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:If x0 = 1, x1 = 2 , and  n=0,1,2,3,......, then x2021 is equal to

[2021]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself: is negative if and only if

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:If f (5 + x) = f (5 - x) for every real x, and f(x) = 0 has four distinct real roots, then the sum of these roots is

[2020]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:How many distinct positive integer-valued solutions exist to the equation ?

[2020]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:The number of distinct real roots of the equation  equals

[2020]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself: Let f ( x) = x2 + ax + b and g ( x) = f ( x + 1) - f ( x - 1) . If f ( x) ≥ 0 for all real x, and g (20) = 72 , then the smallest possible value of b is

[2020]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

[2020]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Let m and n be natural numbers such that n is even and  . Then m - 2n equals

[2020]

*Answer can only contain numeric values
Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick's age is 1 year less than the average age of all three, then Harry's age, in years, is

[2020]

Question for CAT Previous Year Questions: Linear and Quadratic Equations
Try yourself:In the final examination, Bishnu scored 52% and Asha scored 64%. The marks obtained by Bishnu is 23 less, and that by Asha is 34 more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored 84%, is

[2020]

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FAQs on Linear Equations CAT Previous Year Questions with Answer PDF

 1. What are linear and quadratic equations?
Ans. Linear equations are equations that involve only variables raised to the power of 1, such as x or y. They can be represented by a straight line on a graph. Quadratic equations, on the other hand, involve variables raised to the power of 2, such as x^2 or y^2. They can be represented by a curved line on a graph.
 2. How do you solve a linear equation?
Ans. To solve a linear equation, you need to isolate the variable on one side of the equation. This can be done by applying inverse operations, such as addition, subtraction, multiplication, and division, to both sides of the equation until the variable is alone.
 3. How do you solve a quadratic equation?
Ans. Quadratic equations can be solved using various methods, such as factoring, completing the square, or using the quadratic formula. Factoring involves breaking down the equation into two binomials that multiply to give the original equation. Completing the square involves manipulating the equation to create a perfect square trinomial. The quadratic formula is a formula that gives the solutions for any quadratic equation.
 4. What are the applications of linear and quadratic equations?
Ans. Linear and quadratic equations are used in various fields, such as physics, engineering, finance, and computer science. Linear equations are often used to model relationships between variables that have a constant rate of change. Quadratic equations are used to model situations involving projectiles, parabolic paths, and optimization problems.
 5. Can linear and quadratic equations have multiple solutions?
Ans. Yes, linear and quadratic equations can have multiple solutions. In the case of linear equations, if the equation represents a line, it can intersect with the x-axis at multiple points, indicating multiple solutions. Similarly, quadratic equations can have two, one, or no real solutions depending on the discriminant value. The discriminant is the part of the quadratic formula inside the square root sign and determines the nature of the solutions.

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