JEE Advanced Level Test: Maxima and Minima- 2 - JEE MCQ

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

The co-ordinate of the point for minimum value of z = 7x – 8y subject to the conditions x + y – 20 £ 0, y ³ 5, x ³ 0, y ³ 0

 The equation x³ – 3x + [a] = 0, will have three real and distinct roots if

(where [*] denotes the greatest integer function)

Let f(x) = . Then the set of values of a for which f can attain its maximum values is

(where a>0 and { * } denotes the fractional part function)

A function is defined as f(x) = ax² – b|x| where a and b are constants then at x = 0 we will have a maxima of f(x) if

 A and B are the points (2, 0) and (0, 2) respectively. The coordinates of the point P on the line 2x+3y+1=0 are

The maximum value of f(x) = 2bx² – x⁴ – 3b is g(b), where b > 0, if b varies then the minimum value of g(b) is

 Number of solution(s) satisfying the equation, 3x² – 2x³ = log₂ (x² + 1) – log₂ x is

 If a²x⁴ + b² y⁴ = c⁶, then the maximum value of xy is

Maximum and minimum value of f(x) = max (sin t), 0 < t < x, 0 £ x £ 2p are

The function `f' is defined by f(x) = x^p (1 – x)^q for all x Î R, where p, q are positive integers, has a maximum value, for x equal to

The maximum slope of the curve y=–x³+3x²+2x–27 will be

Two points A(1, 4) & B(3, 0) are given on the ellipse 2x² + y² = 18. The co-ordinates of a point C on the ellipse such that the area of the triangle ABC is greatest is

The lateral edge of a regular hexagonal pyramid is 1 cm. If the volume is maximum, then its height must be equal to

 Let f(x) = 5x – 2x² + 2; x ∈ N then the maximum value of f(x) is

The maximum value of f(x), if f(x) + , x ∈ domain of f