- A body moves in a straight line
according to the law s= - 3t.
What are the values of time and
acceleration: (time, acceleration) ; each
time when velocity of the body is zero?
(a) (3, -10) (b) (3, 10) (c) (2, - 10) (d)
(2, 10) - What is the rate of change of
volume of a given sphere of radius r
with respect to its surface area?
(a) r (b) r/2 (c) π r (d) πr/2 - Under which conditions are the two
curves y= +ax+b and y= cx-
tangent to each other at the point (1,
0)?
(a) a= 2, b= - 3, c= -1 (b) a= 3, b= -4, c=
- 1
(c) a= -1, b= 0, c= 1 (d) a= -3, b= 2, c= 1
- A particle P moves along the curve
= 27.
= 10 at the time when P is at the
point (1, 3). What is the value of^ at
that instant?
(a) 5 (b) – 10 (c) 10 (d) – 5
- If the rate of change in volume of
spherical soap bubble is uniform, then
the rate of change surface area varies
as:
(a) square of radius
(b) square root of radius
(c) inversely proportional to radius
(d) cube of the radius
- If f(x)= x In x, then f(x) attains the
minimum value at which one of the
following points?
(a) x= (b) x= e
(c) x= (d) x= 2- What are the points on the curve
- 2x-3=0 where the tangents are
parallel to x-axis?
(a) (1, 2) and (1, -2) (b) (0, √ and 0, -
√ )
(c) (3, 0) and (-3, 0) (d) (2, 1) and (2, -
- 2x-3=0 where the tangents are
- The function f(x)= k sin x+^ sin 3x
has maximum value at x=^. What is the
value of k?
(a) 3 (b)^ (c) 2 (d)^ - The largest value of
for - 2 , occurs when
(a) x= -2 (b) x= -1 (c) x= 2 (d) x= 0 - What is the interval over which the
function f(x)= 6x- , x>0 is increasing?
(a) (0, 3) (b) (3, 6) (c) (6, 9) (d) None
of these - If at any instant t, for a sphere, r
denotes the radius, S denotes the
surface area and V denotes the volume,
then what is^ equal to?
(a)^ (b)^ (c) (d)^ - What is the maximum point on the
curve x= y?
(a) (1, e) (b) (1, ) (c) (e, 1) (d)
( , 1)