Test: Maxima And Minima (Competition Level) - 2


19 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Maxima And Minima (Competition Level) - 2


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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

Solution:
QUESTION: 2

 If x1 and x2 are abscissa of two points on the curve f(x) = x – x2 in the interval [0, 1], then maximum value of the expression (x1 + x2) –  is

Solution:
QUESTION: 3

Least value of the function, f(x)= is

Solution:

 (2x2 - 1) + 2/(2x2 + 1)
AM ≥ GM
f(x) = (2x2 + 1) + 2/(2x2 + 1) - 2
[(2x2 - 1) + 2/(2x2 + 1)]/2
⇒ [(2x2 - 1) * 2/(2x2 + 1)]^½
⇒ [(2x2 - 1) * 2/(2x2 + 1)]^½ ≥ 2(2)^½ - 2
⇒ f(x) ≥ 2(2)^½ - 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

Solution:
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

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QUESTION: 6

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

(where [*] denotes the greatest integer function)

Solution:
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)

Solution:
QUESTION: 8

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

Solution:
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

Solution:
QUESTION: 10

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

Solution:
QUESTION: 11

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

Solution:
QUESTION: 12

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

Solution:
QUESTION: 13

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

Solution:
QUESTION: 14

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

Solution:
QUESTION: 15

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

Solution:
QUESTION: 16

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

Solution:
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

Solution:
QUESTION: 18

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

Solution:
QUESTION: 19

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

Solution:

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