JEE Advanced Level Test: Maxima and Minima - JEE MCQ

 The minimum value of the function defined by f(x) = max (x, x + 1, 2 – x) is

Let f(x) =  then

The greatest and the least values of the function, f(x) = 2 – , x ∈ [–2, 1] are

Let f(x) = {x}, For f(x), x = 5 is (where {*} denotes the fractional part)

 The critical points of f(x) =  lies at

The difference between the greatest and least values of the function f(x) = sin 2x – x on [–p/2, p/2] is

The radius of a right circular cylinder of greatest curved surface which can be inscribed in a given right circular cone is

The dimensions of the rectangle of maximum area that can be inscribed in the ellipse (x/4)² + (y/3)² = 1 are

The largest area of a rectangle which has one side on the x–axis and the two vertices on the curve y =  is

The co–ordinates of the point on the curve x² = 4y, which is at least distance from the line

y = x – 4 is 

f(x) =  then

Let f(x) =  the set of values of b for which f(x) has greatest value at x = 1 is given by

 The set of values of p for which the extrema of the function, f(x) = x³ – 3px² + 3(p² – 1) x + 1 lie in the interval (–2, 4) is

Four points A, B, C, D lie in that order on the parabola y = ax² + bx + c. The co–ordinates of A, B & D are known as A(–2, 3); B(–1, 1) and D(2, 7). The co–ordinates of C for which the area of the quadrilateral ABCD is greatest is

 In a regular triangular prism the distance from the centre of one base to one of the vertices of the other base is l. The altitude of the prism for which the volume is greatest is

 Two vertices of a rectangle are on the positive x–axis. The other two vertices lie on the lines y = 4x and y = –5x + 6. Then the maximum area of the rectangle is

A variable point P is chosen on the straight line x + y = 4 and tangents PA and PB are drawn from it to circle x² + y² = 1. Then the position of P for the smallest length of chord of contact AB is

The maximum area of the rectangle whose sides pass through the angular points of a given rectangle of sides a and b is

 If p and q are positive real numbers such that p² + q² = 1, then the maximum value of (p + q) is

 The function f(x) =  has a local minimum at

 If x is real, the maximum value of  is

 If the function f(x) = 2x³ – 9ax² + 12a²x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p² = q, then a equals

The maximum value x³ – 3x in the interval [0, 2] is

Minimum value of    is

The minimum value of (x – p)² + (x – q)² + (x – r)² will be at x equals to

The number of values of x where f(x) = cos x + cos  x attains its maximum value is

The maximum value of cos a₁ . cos a₂ . cos a₃....cos a_n under the restriction 0 £ a₁, a₂,.....a_n £and cot a₁ cot a₂ .... cot a_n=1 is