- A balloon is pumped at the rate of 4
/s. What is the rate at which its
surface area increases when its radius
is 4cm?
(a) 1 /s (b) 2 /s (c) 3 /s
(d) 4 /s - Given two squares of sides x and y
such that y= x+. What is the rate of
change of the area of the second square
with respect to the area of the first
square?
(a) 1+3x+2 (b) 1+2x+3
(c) 1-2x+3 (d) 1-2x- 3
- The function y= x-x
(a) is always decreasing (b) is always
increasing (c) first increases and then
decreases (d) first decreases and then
increases - The velocity of telegraphic
communication is given by v= log
.^ / where x is the displacement. For
maximum velocity, x is equal to
(a) ⁄^ (b) ⁄^
(c) ( )^ (d) 2 ⁄^
- The function f(x)= - 2x increases
for all
(a) x>-1 only (b) x<-1 only (c) x>1
only
(d) x<1 only - The profit function, in rupees, of a
firm selling x items (x 0) per week is
given by P(x)= -3500+(400-x) x. How
many items should the firm sell so that
the firm has maximum profit?
(a) 400 (b) 300 (c) 200 (d) 100
37. If f(x)= 3 +6x-9, then
(a) f(x) in increasing in (-1, 3) (b) f(x)
is decreasing in (3, ) (c) f(x) is
increasing in (- , -1) (d) f(x) is
decreasing in (- , -1)
38. What is the maximum value of the
function log x-x?
(a) -1 (b) 0 (c) 1 (d)
39. f(x)= cos x is monotonic decreasing
under which one of the following
conditions?
(a) 0<x<^ only (b)^ <x<π only (c)
0<x<π
(d) 0<x<2π
40. Find the minimum value of 2 -
3x+5?
(a) 0 (b)^ (c)^ (d)^
41. What is the area of the largest
rectangular field which can be enclosed
with 200 m of fencing?
(a) 1600 (b) 2100 (c) 2400
(d) 2500
42. What is the maximum value of x. y
subject to the condition x + y= 8?
(a) 8 (b) 16 (c) 24 (d) 32
43. The function f(x)= (x-1) +1 is
(a) negative for all x>0 (b) positive for
all x>0
(c) increasing for all x (d) decreasing
for all x
44. The motion of the particle is
described as s= 2-3t+4. What is the
acceleration of the particle at the point
where its velocity is zero?
(a) 0 (b) 4 unit (c) 8 unit (d) 12 unit