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JEE Questions for Maths Applications Of Derivatives Quiz 15 - MCQExams.com
JEE
Maths
Applications Of Derivatives
Quiz 15
If a st. line is tangent to one point and normal to another point on the curve y = 8t
3
− 1, x = 4t
2
+ 3, then the equation of such line is :
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0%
0%
2)
0%
0%
None of these
Let f(
x
) = 1 + 2
2
x
2
+ 3
2
x
4
+ 4
2
x
6
…. + n
2
x
2n–2
= + (n+1)
2
x
2n
, then f(
x
) has :
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0%
exactly one minimum
0%
exactly one maximum
0%
at least one maximum
0%
None of these
Kamal has
x
children by hist first wife. Ritu has (
x
+children by her first busband. They marry and have children of their own. The whole family has 24 children. Assuming the two children of the same parents do not fight, then the maximum possible number of fights that can take place is :
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0%
190
0%
191
0%
200
0%
52
A given right circular cone has a volume p and the longest right circular cylinder that can be inscribed in the cone has a volume q. Then p : q is :
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0%
9 : 4
0%
4 : 5
0%
7 : 3
0%
none of these
Let h(
x
) = f(
x
) − (f(
x
))
2
+ (f(
x
))
3
for every real number
x
. Then :
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0%
h is increasing whenever f is increasing
0%
h is increasing whenever f is decreasing
0%
h is decreasing whenever f is increasing
0%
nothing can be said in general
The function f(
x
) = sin
4
x
+ cos
4
x
increases in
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0%
0%
2)
0%
0%
Let f(
x
) =
x
e
x
(1−
x
)
, then f(
x
) is :
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0%
0%
decreasing on R
0%
increasing on R
0%
Let f(
x
) = (1 + b
2
)
x
2
+ 2b
x
+ 1 and let m(b) be the minimum value of f(
x
). As b varies the range of m(b) is
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0%
[0, 1]
0%
2)
0%
0%
(0,1]
A particle moves in a straight line in such a way that its velocity at any point is given by v
2
= 2 – 3
x
, where
x
is measured from a fixed point. The acceleration is
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0%
Uniform
0%
Zero
0%
Non – uniform
0%
Non – uniform
The radius of a sphere is measured to be 20 cm with a possible error of 0.02 of a cm. The consequent error in the surface of the sphere is
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0%
10.5 sq.cm
0%
5.025 sq.cm
0%
10.05 sq.cm
0%
None of these
An edge of a variable cube is increasing at the rate of 10 cm/sec. How fast the volume of the cube will increase when the edge is 5 cm long
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0%
750 cm3/sec
0%
75 cm3/sec
0%
300 cm3/sec
0%
150 cm3/sec
0%
25 cm3/sec
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0%
0
0%
2)
0%
0%
The equation of motion of a particle moving along a straight line is s = 2t
3
– 9t
2
+ 12t, where the units of s and t are cm and sec. The acceleration of the particle will be zero after
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0%
0%
2)
0%
0%
Never
If by dropping a stone in a quiet lake a wave moves in circle at a speed of 3.5 cm/sec, then the rate of increases of the enclosed region when the radius of the circular wave is 10 cm, is (π = 22/7)
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0%
220 sq. cm/sec
0%
110 sq. cm/sec
0%
35 sq. cm/sec
0%
350 sq. cm/sec
If the edge of a cube increases at the rate of 60 cm per second, at what rate the volume is increasing when the edge is 90 cm
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0%
48600 cu cm per sec
0%
1458000 cu cm per sec
0%
4374000 cu cm per sec
0%
None of the above
A particle moves along a straight line so that is distance s in time t sec is s = t + 6t
2
– t
3
. After what time is the acceleration zero
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0%
2 sec
0%
3 sec
0%
4 sec
0%
6 sec
The distance s metre covered by a body in t seconds is given by s = 3t
2
– 8t + 5, the body will stop after
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0%
1 sec
0%
2)
0%
0%
4 sec
The diagonal of a square is changing at the rate of 0.5 cm/sec. Then the rate of change of area, when the area is 400 cm
2
, is equal to
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0%
0%
2)
0%
0%
0%
The radius of a cylinder is increasing at the rate of 3 m/sec and its altitude is decreasing at the rate of 4 m/sec. the rate of change of volume when radius is 4 meters and altitude is 6 metres is
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0%
80 π cu. m/sec
0%
144 π cu. m/sec
0%
80 cu. m/sec
0%
64 cu. m/sec
0%
–80 π cu. m/sec
If the displacement, velocity and acceleration of a particle at time t be
x
, v and f respectively, then which one is true
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0%
0%
2)
0%
0%
The area of the triangle formed by the coordinate axes and a tangent to the curve
x
y = a
2
at the point (
x
1
,y
1
) on it is
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0%
0%
2)
0%
0%
The point of the curve y
2
= 2(
x
–at which the normal is parallel to the line y – 2
x
+ 1 = 0
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0%
(5, 2)
0%
2)
0%
0%
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0%
(0, 0)
0%
(0, a)
0%
(0, b)
0%
(b, 0)
The tangent to the curve y = a
x
2
+ b
x
at (2, –is parallel to
x
- axis. Then
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a = 2, b = –2
0%
a = 2, b = – 4
0%
a = 2, b = – 8
0%
a = 4, b = – 4
The angle of intersection of intersection of the curves y =
x
2
and
x
= y
2
at (1,is
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
The equation of tangent at (–4, –on the curve
x
2
= – 4y is
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0%
2x + y + 4 = 0
0%
2x – y – 6 = 0
0%
2x + y – 4 = 0
0%
2x – y + 4 = 0
The length of the normal at point ‘t’ of the curve
x
= a(t + sin t), y = a(1 – cos t) is
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0%
a sin t
0%
2)
0%
0%
The angle between the curves y
2
= 4
x
+ 4 and y
2
= 36(9 –
x
) is
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0%
30o
0%
45o
0%
60o
0%
90o
If the normal to the curve y
2
= 5
x
–1, at the point (1, –is of the form a
x
– 5y + b = , then a and b are
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0%
4, –14
0%
4, 14
0%
–4, 14
0%
–4, –14
The equation of the tangent to the curve
x
= 2 cos
3
θ and y = 3 sin
3
θ at the point θ = π/4 is
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0%
0%
2)
0%
0%
The tangent and the normal drawn to the curve y =
x
2
–
x
+ 4 at P(1,cut the X – axis at A and B respectively. If the length of the subtangent drawn to the curve at P is equal to the length of the subnormal then the area of the triangle PAB is sq. units is
Report Question
0%
4
0%
32
0%
8
0%
16
The normal to the curve at P(
x
, y) meets the
x
- axis at G. If the distance of G from the origin is twice the abscissa of P, then the curve is a
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0%
Ellipse
0%
Parabola
0%
Circle
0%
Hyperbola
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-1
0%
2)
0%
0%
The point on the curve y
2
=
x
, the tangent at which makes an angle 45
o
with
x
- axis is
Report Question
0%
0%
2)
0%
0%
If slope of tangent to curve y =
x
3
at a point is equal to ordinate of a point, then point is
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0%
(27, 3)
0%
(3, 27)
0%
(1, 2)
0%
(–1, 3)
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0%
0%
2)
0%
0%
The co – ordinates of the points on the curve y =
x
2
– 3
x
+ 2 where the tangent is perpendicular to the straight line y =
x
are
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0%
(0, 2)
0%
(1, 0)
0%
(–1, 6)
0%
(2, –2)
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0%
[–1, 1]
0%
[0, 1]
0%
[–1, 0]
0%
[–1, 2]
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0%
cos x
0%
cos 2x
0%
cos 3x
0%
cot x
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0%
0%
2)
0%
0%
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0%
0%
2)
0%
0%
0%
Report Question
0%
0%
Increasing for every value of x
0%
Decreasing for every value of x
0%
None of the above
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0%
0%
2)
0%
0%
For which value of
x
, the function f(
x
) =
x
2
– 2
x
is decreasing
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0%
x > 1
0%
x > 2
0%
x < 1
0%
x < 2
The values of ‘a’ for which the function (a + 2)
x
3
– 3a
x
2
+ 9a
x
– 1 decreases monotonically throughout for all real
x
, are
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0%
a < –2
0%
a > –2
0%
–3 < a < 0
0%
– ∞ a ≤ – 3
For all real values of
x
, increasing function f(
x
) is
Report Question
0%
x–1
0%
x2
0%
x3
0%
x4
The function f(
x
) = 1 – e
–
x
2
/2
is
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0%
Decreasing for all x
0%
Increasing for all x
0%
Decreasing for x < 0 and increasing for x > 0
0%
Increasing for x < 0 and decreasing for x > 0
The function f(
x
) = 1 –
x
3
–
x
5
is decreasing for
Report Question
0%
1 ≤ x ≤ 5
0%
x ≤ 1
0%
x ≥ 1
0%
All values of x
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