45. What is the product of two parts of
    20 such that the product of one part
    and the cube of the other is maximum?
    (a) 75 (b) 91 (c) 84 (d) 96


46. What is the maximum slope of the
    curve
    y= - +2x-27?
    (a) 1 (b) 2 (c) 5 (d) – 23


47. What is/are the critical point (s) of
    the function f(x)= ⁄^ (5-2x) on the
    interval [-1, 2]?

(a) 1 only (b) 0 and^ (c)^ only (d) 0

and^

48. What is the x-coordinate of the
    point on the curve f(x)= √ (7x-6)
    where the tangent is parallel to x- axis?
    (a) - (b)^ (c)^ (d)^


49. What is the minimum value of cos Ѳ

• cos 2Ѳ?
  (a) – 2 (b) - (c) 0 (d) -

DIFFERENTIAL EQUATION

1. The degree of the differential
   equation

.
/

.^

(^)
/, is:^
(a) 1 (b) 2 (c) 3 (d) None of these

2. If y= a cos 2x + b sin 2x, then:

(a)^

(^)

• y= 0 (b)


• 2y= 0 (c)


• 
  

  3y= 0
  (d)^
  (^)

  
  


• 4y= 0^

3. The solution of the differential

equation^ is:

(a) xy= ( ) (b) xy=
(c) xy= c
(d) xy= ( )

4. The degree of the differential
   equation

[.^

(^)
/

].^ /

is:

(a) 4 (b) 2 (c) 1 (d) 3

5. y= a + b satisfies the differential
   equation:
   (a)^

(^)

-^ y= 0 (b)

• y= 0 (c)

(d)

6. The degree of the differential
   equation^. /
   is:
   (a) 2 (b) 3 (c) 4 (d) 5


7. y= A cos ωt + B sin ωt is a solution of
   the differential equation:
   (a)^

(^)
(^) (b)^
(c)^
(^)
(d)
(^)

8. The general solution of^ + y= sin x
   is:
   (a) y=

(b) y=

(c) y= + sinx

(d) y=