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Maxima minima || Quantitative Aptitude || CAT 2021 || 20 May (App update required to attempt this test)
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Question 1
The minimum value of ax2+bx+c is 0 at x=2. Find the expression at x=4 if the value of expression is 2 at x=3.
Question 2
A quadratic function ƒ(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value ƒ(x) at x = 10
Question 3
The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is
Question 4
The quadratic equation 
has non-real roots. If a and b are integers and a < b < 5, what is the minimum possible value of a?
has non-real roots. If a and b are integers and a < b < 5, what is the minimum possible value of a?Question 5
If x, y, z are any real numbers then the minimum possible value of x2 + 2y2 + z2 + 2yz subject to x + 2y + z = –6 is
Question 6
Let f(x)=min{2x2, 52 - 5x}, where x is any positive real number. Then the maximum possible value of f(x) is [TITA]
Question 7
Let g(x) = max(5 − x, x + 2). The smallest possible value of g(x) is
Question 8
The maximum of 3x + 10y, subject to 3x + 5y ≤ 15, 5x + 2y ≤ 10, where x and y are nonnegative, is
Question 9
A, B and C are 3 distinct natural numbers such that their product is 6!. If Y is the minimum possible sum of A, B and C, then find the value of (Y2 – 2). (TITA)
Question 10
If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is
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