Linear Equations CAT Previous Year Questions with Answer PDF

It is given that for some real numbers a and b, the system of equations x + y = 4 and (a+5)x + (b² - 15)y = 8b has infinitely many solutions for x and y.

Hence, we can say that

This equation can be used to find the value of a, and b.

Firstly, we will determine the value of b. 

Hence, the values of b are 5, and -3, respectively. 

As -50 is not in the range of b so it is the answer

n cannot be -3
 has to be an integer
And this value has to be equal to 1, for n to be high

8 = n - 4
n = 12

if we put n=16
then 8/(n-4) wont be a integer

For roots of any Quadratic equation to be real and distinct, D > 0
So, for x² − 4x - log₂A = 0,
D = (-4)² - (4 x 1 x (-log₂A)) > 0
16 + 4 log₂A > 0
4 + log₂A > 0
log₂A > -4
A > 1/2⁴
A > 1/16

Given quadratic equation is x² + bx + c = 0
Sum of roots = -b
-b = 4a + 3a
-b = 7a
Product of the roots = c
c = 4a x 3a
c = 12a²
b² = 49a² and c =12a²
b² + c = 49a² + 12a²
b² + c = 61 a²
Our answer must be a multiple of 61, which should be a perfect square 
Going through the options,
549 = 61 x 9
549 = 61 x 3²
Thus, possible value of b² + c = 549