Classical

Calculus - Calculus MCQ

26:  

The minimum value of | x2-5x+21 | is

A.

-5

B.

0

C.

-1

D.

-2

 
 

Option: B

Explanation :

Since the value of a mod function cannot be less than zero, therefore
   f(x) = | x2-5x+2 | is zero.


27:  

 Sum of the perimeters of a circle and a square is 1. If sum of the area is least, then

A.

side of the square is double the radius of circle 

B.

side of the square is 1/2 of the radius of the circle 

C.

side of the square is equal to radius of the circle

D.

none of these 

 
 

Option: A

Explanation :

mcq calculus


28:  

The maximum slope of the curve
-x3 + 6x3 + 2x + 1 is 

A.

14

B.

16

C.

19

D.

-13

 
 

Option: A

Explanation :

Let f(x) = -x3 + 6x2 + 2x + 1

Slope of the function is,       f'(x)  =  -3x2 + 12x + 2 = F(x) (say)
Now to find minimum or maximum of F(x)
Therefore                  F'(x) = - 6x + 12
                                  F"(2) = -6
For maxima and minima, F'(x) = 0
⇒                                x = 2 
Therefore                   F"(2) = -6 
Hence F(x) (slope) is maximum at x = 2
  Maximum slope = F(2) = -3(2)2 + 12(2) + 2 = 14

 


29:  

Limit of the following series as x approaches is 

A.

2Π / 3

B.

Π / 2

C.

Π / 3

D.

1

 
 

Option: D

Explanation :

mcq for calculus


30:  

 Directional derivative of f ( x,  y,  z ) = x2 + y2 + z2 at the point (1, 1, 1) in the direction i - k is

A.

0

B.

1

C.

√2

D.

2√2

 
 

Option: A

Explanation :

calculus questions




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