MCQs For NCERT Class 12 Mathematics Chapter 12 Linear Programming

Please refer to the MCQ Questions for Class 12 Mathematics Chapter 12 Linear Programming with Answers. The following Linear Programming Class 12 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 12. Our experts have designed MCQ Questions for Class 12 Mathematics with Answers for all chapters in your NCERT Class 12 Mathematics book.

Linear Programming Class 12 MCQ Questions with Answers

See below Linear Programming Class 12 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

Question. Refer to question 27. Maximum of Z occurs at
(a) (5, 0)
(b) (6, 5)
(c) (6, 8)
(d) (4, 10)

Question. Refer to question 7, maximum value of Z + minimum value of Z is equal to
(a) 13
(b) 1
(c) -13
(d) -17

Question. The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y. Compare the quantity in column A
and column B.

(a) The quantity in column A is greater
(b) The quantity in column B is greater
(c) The two quantities are equal
(d) The relationship cannot be determined on the basis of the information supplied.

Question. Refer to question 32, maximum of F- minimum of F is equal to
(a) 60
(b) 48
(c) 42
(d) 18

Question. The feasible region for an LPP is shown in the following figure. Let F =3x -4y be the objective function. Maximum value of F is

(a) 0
(b) 8
(c) 12
(d) -18

Question. The feasible solution for a LPP is shown in following figure. Let Z =3x – 4y be the objective function. Minimum of Z occurs at

(a) (0,0)
(b) (0,8)
(c) (5,0)
(d) (4,10)

Question. Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F =4x + 6y be the objective function. The minimum value of F occurs at
(a) Only (0, 2)
(b) Only (3, 0)
(c) the mid-point of the line segment joining the points (0, 2) and (3, 0)
(d) any point on the line segment joining the points (0, 2) and (3, 0)

Question. Refer to question 30. Minimum value of F is
(a) 0
(b) -16
(c) 12
(d) Does not exist

Question. Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q, so that the minimum of Z occurs at (3, 0) and (1, 1) is
(a) p = 2q
(b) p = q/2
(c) p = 3q
(d) p = q

A window of fixed perimeter (including the base of the arch) is in the form of a rectangle surmounted by a semi-circle. The semi-circular portion is fitted with coloured glass, while the rectangular portion is fitted with clear glass. The clear glass transmits three times as much light per square metre as the coloured glass.
Suppose that y is the length and x is the breadth of the rectangular portion and Pis the perimeter.
On the basis of above information, answer the following questions.

Question. If µ is the amount of light per square metre for the coloured glass and L is the total light transmitted, then

Question. The ratio of the sides y x: of the rectangle so that the window transmit the maximum light is
(a) 3: 2
(b) 6: 6 + π
(c) 6 +π :6
(d) 1:2 

Assertion and Reason
Each of these questions contains two statements : Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select one of the codes( a), ( b), (c )  and (d) given below.
(a) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.
(b) Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(c) Statement I is true; Statement II is false.
(d) Statement I is false; Statement II is true.

Question. If f’ (x)=(x-1)³ (x-2)⁸, then
Statement I f (x) has neither maximum nor minimum at x = 2.
Statement II f’ (x) changes sign from negative to positive at x = 2.

Question. Consider the cubic expression y=x³+ax²+bx+c 
 Statement I a²<3b,  then function y have no any critical points.
Statement II Either y is increasing function ordecreasing function for all x∈R .

Question. Statement I The minimum distance of the fixed point (0,y₀), where 0≤ y₀ ≤1/2,from the curve y=x2 is y₀·
Statement II Maxima and minima of a function is always a root of the equation f’ (x) =0.

Question. Consider the function f (x)= -x²+4x+1+sin^-1)(x/2) 
Statement I Minimum value of interval [ -1,1]  is (-4,-π/6).
Statement II Minimum value of f (x) in interval [-1,1] is min {f ( -1), f( 1)}.

Question. A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a Δ OPQ, where, O is the origin, if the area of the Δ OPQ is least, then the slope of the line PQ is 
(a) – 1 /4
(b) – 4
(c) – 2
(d) -1 /2

Question. Statement I The local maximum of the function x x cos will occur between π/4 and π/3.
Statement II The function x tan x is increasing in (0,π/4 and decreasing in (π/4, π/2).

Question. Let a, b ∈ R  be such that the function f given by f (x)= log|x | +bx²+ax, x≠ 0 has extreme values at x = – 1 and x = 2.
Statement I f has local maximum at x = – 1 and at x = 2.
Statement II a = 1/2 and b = – 1/4 .

Question. Statement I The minimum value of the expression x²+2bx+c is c-b²·
Statement II The first order derivative of the expression at x= -b =  is zero.

Question. Let f be a function defined by f (x)

Statement I x = 0 is point of minima of f.
Statement II f'(0)=0 

True/False

Question. Maximum value of the objective function Z =ax + by in a LPP always occurs at only one corner point of the feasible region.

Question. If the feasible region for a LPP is unbounded, maximum or minimum of the objective function Z = ax + by may or may not exist.

Question. In a LPP, the maximum value of the objective function Z =ax + by is always finite.

Question. In a LPP, the minimum value of the objective function Z = ax + by is always 0, if origin is one of the corner point of the feasible region.