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JEE Advanced Level Test: Maxima and Minima- 2 - Question 1

The lower corner of a leaf in a book is folded over so as to just reach the inner edge of the page. The fraction of width folded over if the area of the folded part is minimum is

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

If x_{1} and x_{2} are abscissa of two points on the curve f(x) = x – x^{2} in the interval [0, 1], then maximum value of the expression (x_{1} + x_{2}) – is

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JEE Advanced Level Test: Maxima and Minima- 2 - Question 3

Least value of the function, f(x)= is

Detailed Solution for JEE Advanced Level Test: Maxima and Minima- 2 - Question 3

JEE Advanced Level Test: Maxima and Minima- 2 - Question 4

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 5

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 6

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

(where [*] denotes the greatest integer function)

JEE Advanced Level Test: Maxima and Minima- 2 - Question 7

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)

JEE Advanced Level Test: Maxima and Minima- 2 - Question 8

A function is defined as f(x) = ax^{2} – b|x| where a and b are constants then at x = 0 we will have a maxima of f(x) if

JEE Advanced Level Test: Maxima and Minima- 2 - Question 9

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 10

The maximum value of f(x) = 2bx^{2} – x^{4} – 3b is g(b), where b > 0, if b varies then the minimum value of g(b) is

JEE Advanced Level Test: Maxima and Minima- 2 - Question 11

Number of solution(s) satisfying the equation, 3x^{2} – 2x^{3} = log_{2} (x^{2} + 1) – log_{2} x is

JEE Advanced Level Test: Maxima and Minima- 2 - Question 12

If a^{2}x^{4} + b^{2} y^{4} = c^{6}, then the maximum value of xy is

JEE Advanced Level Test: Maxima and Minima- 2 - Question 13

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 14

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 15

The maximum slope of the curve y=–x^{3}+3x^{2}+2x–27 will be

JEE Advanced Level Test: Maxima and Minima- 2 - Question 16

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 17

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 18

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

JEE Advanced Level Test: Maxima and Minima- 2 - Question 19

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

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