CAT Question Bank - Maxima & Minima
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Number of Questions - 30
Topic - Maxima & Minima
Answer key available? - No
Source - Curated Content
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Q1) If ax^2 + bx + 6 = 0 has no distinct real roots then find the minimum value of 3a + b, if a & b are real.
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Q2) Find the minimum value of a + b + c if a * b * c = 90 and a, b and c are natural numbers.
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Q3) If x and y are real numbers such that x^2 + 2xy − y^2 = 2, what is the minimum value of x^2 + y^2
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Q4) Find the maximum and minimum values of |x+1| + 3|x-2| + 4|x-6| = 20
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Q5) If x and y are positive integers satisfying 17x + 8y = 3051. What will be the difference between maximum and minimum values of x and y?
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Q6) Find the maximum value of 2^(1/(x^2 - x + 1))
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Q7) Find the maximum and minimum values of (x^2 + 14x + 9) / (x^2 + 2x + 3) (given x is a real number)
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Q8) Find the maximum and minimum values of 3x + 4y if x^2 + y^2 = 14x + 6y + 6 and x, y are positive real numbers.
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Q9) f(x) = max (2x + 1, 3 - 4x). Find minimum value of f(x), if x belongs to [3,7]
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Q10) f(x) = minimum (4x + 3, x + 4) for x belongs to 0 to 2. What is the maximum value of f(x)?
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Q11) if x * y * z = 2002 and x > y > z ≥ 2 then find the maximum and minimum values of x + y + z
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Q12) If (x + 2)^2 = 9 and (y + 3)^2 = 25, then the sum of maximum and minimum values of x/y is ?
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Q13) Find the sum of maximum and minimum values of x^2/(1 + x^4) where x is real
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Q14) If |x| + |y| = 10, then what is the sum of minimum and maximum values of x + y ?
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Q15) a, b, c and d are four positive real numbers such that a^2 + b^2 + c^2 + d^2 = 100. What is the maximum
possible value of a + b + c + d ?
(a) 30
(b) 10
(c) 20
(d) None of these
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Q16) Find the maximum value of x * y * z, if x^2 + y^3 + z^4 = 26
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Q17) If a * b * c * d * e = 32 then minimum value of the expression (a + 1) * (b + 1) * (c + 1) * (d + 1) * (e + 1)
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Q18) Find the maximum and minimum value of sin³x + cos³x
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Q19) If minimum value of A is -1 then find the minimum value of A + (1/A)
