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JEE Questions for Maths Applications Of Derivatives Quiz 7 - MCQExams.com
JEE
Maths
Applications Of Derivatives
Quiz 7
Let P(
x
) be a polynomial of degree 4, with P(= − 1, and . Then is equal to : P'(= 0, P (= 2, P '(= –12 , P (= 24, P''(is equal to :
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0%
20
0%
22
0%
24
0%
26
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0%
0%
2)
0%
0%
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0%
20
0%
14
0%
18
0%
12
Let f : R → R be a function defined by f(x) = Max {
x
,
x
3
}. The set of all points where f(x) is not differentiable is :
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{–1, 1}
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{-1, 0}
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{0, 1}
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{–1, 0, 1}
The left−handed derivative of f(
x
) = [
x
] sin (π
x
) at
x
= K, K is an integer, is
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(–1)K (K – 1)π
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(–1)K–1 (K –π
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(–1)K K π
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(–1)K – 1 K π
If m is the slope of a tangent to the curve e
y
= 1 +
x
2
, then :
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| m | < 1
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| m | ≤ 1
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| m | > 1
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m < 1
The curve given by
x
+ y = e
x
y
has a tangent parallel to the y − axis at the point :
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(0,
0%
(1, 1)
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(0, 0)
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(1, 0)
The equation of the tangent to the curve y = e
|-
x
|
at the point where the curve cuts the line
x
= 1 is :
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x + y = e
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y + ex = 1
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0%
x + ey = 2
If the tangent at (1,on y
2
=
x
(2 –
x
)
2
meets the curve again at P, then P is :
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(–4, 4)
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(1, –2)
0%
0%
None of these
The area of the triangle formed by the positive x−axis and the normal and tangent to the circle
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0%
2)
0%
0%
none of these
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0%
2)
0%
0%
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0%
0%
2)
0%
0%
None of these
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0%
0%
2)
0%
0%
None of these
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(2,–1)
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(1,2)
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(0,1)
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None of these
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(–∞,0)
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(0,∞)
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(–∞,∞)
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(1,∞)
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0%
2)
0%
0%
None of these
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0%
2)
0%
0%
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0%
2)
0%
0%
None of these
Let f(
x
) = (
x
2
−
n
(
x
2
+
x
+ 1), then f(
x
) has local extremum at
x
= 1 when least value of n :
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2
0%
3
0%
5
0%
7
The number of solutions of the equation a
f(
x
)
+ g(
x
) = 0, where a > 0, g(
x
) ≠ 0 and has minimum value ½ is
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1
0%
2
0%
0
0%
∞
A curve passes through the point (2,and the slope of the tangent at any point (
x
, y) is
x
2
− 2
x
for all values of
x
. The point of maximum ordinate on the curve is :
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0%
2)
0%
0%
Let f(
x
) = |
x
− 1 | + a if
x
≤ 1 = 2x + 3 if
x
> 1. If f(
x
) has local minimum at
x
= 1, then :
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a = 7
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a = 8
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a = 9
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a ≤ 5
The set of all
x
for which log (1 +
x
) ≤
x
is :
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(0, ∞)
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(−1, ∞)
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(−∞, ∞)
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(1, ∞)
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1
0%
0
0%
2
0%
None of these
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0%
2)
0%
0%
The points of contact of the tangent drawn from (0,to the curve y = sin
x
lies on the curve :
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0%
2)
0%
0%
None of these
The point on the curve y
2
=
x
, the tangent at which makes an angle of 45° with x−axis will be given by :
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0%
2)
0%
0%
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0%
1
0%
2
0%
3
A cylindrical gas contained is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius of the height of the cylinder using minimum material for the same capacity is :
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0%
2)
0%
0%
The number of solutions of the equation
x
3
+ 2
x
2
+ 5
x
+ 2 cos
x
= 0 in [0, 2π ] is :
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3
0%
0
0%
1
0%
2
Which one of the following curves cuts the parabola y
2
= 4a
x
at right angles :
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0%
2)
0%
0%
If the line joining the points (0,and (5,is a tangent to the curve
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0%
2)
0%
0%
Two men are walking on a path
x
3
+ y
3
= a
3
. When the first man arrives at a point (
x
1
, y
1
), he finds the second man in the direction of his own instantaneous motion. If the co−ordinates of the second man are (
x
2
, y
2
) then :
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0%
2)
0%
0%
On the curve
x
3
= 12y, the abscissa changes at a faster rate than the ordinate. Then x belongs to the interval :
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(−2,
0%
(−3,
0%
(0,
0%
none of these
A balloon is pumped at the rate of a cm
3
/minute. The rate of increase of its surface area when the radius is b cm, is :
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0%
0%
2)
0%
0%
None of these
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f(x) has a local maxima at x = 1
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f(x) has a local minima at x = 1
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f(x) does not have any local extrema at x = 1
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None of these
The function f(
x
) = | p
x
− q| + r |
x
|,
x
∈ (− ∞, ∞), where p > 0, q > 0, r > 0, assumes its minimum value only at one point if :
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p ≠ q
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r ≠ q
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r ≠ p
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p = q = r
The normal to the curve y = (1 + 2
x
)
x
+ sin
−1
(sin
3
x
) at
x
= 0 is :
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y = 0
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x + y = 1
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x = 0
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None of these
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0%
2
0%
0%
None of these
The co−ordinates of the point M(
x
, y) of y = e
−|
x
|
so that the area formed by the co−ordinate axes and the tangent at M is the greatest, are :
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(e,or (1,e)
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2)
0%
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(0,π)
Let C be the curve y
3
− 3
x
y + 2 = 0. If H is the set of points on the curve C where the tangent is horizontal and V is the set of points where the tangent is vertical, then H and V are respectively given by :
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{(0, 0)}, {(0, 1)}
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φ, {(1, 1)}
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{(1, 1)}, {(0, 0)}
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None of these
Tangent at a point P
1
, (other tan (0, 0)) on the curve y =
x
3
meets the curve again at P
2
. The tangent at P2 meets the curve at P3 and so on. Then the abscissa of P
1
, P
2
,P
3
, …. are in :
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A.P.
0%
G.P.
0%
H.P
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None of these
If the normal to the curve
x
2/3
+ y
2/3
= a
2/3
makes an angle φ with the x−axis, then its equation is :
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x sin φ + y cos φ = a
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y cos φ − x sin φ = a cos 2φ
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x cos φ + y sin φ = a sin 2 φ
0%
none of these
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both f(x) and g(x) are increasing functions
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both f(x) and g(x) are decreasing functions
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f(x) is increasing function and g(x) is an increasing function
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None of these
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0
0%
1
0%
2
0%
infinite
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does not exist because f is unbounded
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is not attained even though f is bounded
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is equal to 1
0%
is equal to − 1
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0, 4
0%
1, 3
0%
0, 2
0%
2, 4
If f’(
x
)= g(
x
) (
x
− a)
2
, where g(a) ≠ 0 and g is continuous at
x
= a, then : f\'(
x
)
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f is increasing in the nbd. of a if g(a) > 0 and f is decreasing in the nbd. of a if g(a) < 0
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f is increasing in the nbd. of a if g(a) < 0
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f is decreasing in the nbd. of a if g(a) > 0
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f is increasing in the nbd. of a if g(a) < 0 and f is decreasing in the nbd. of a if g(a) > 0
The function f(
x
) defined by f(
x
) = (
x
+e
−
x
is :
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decreasing for all x
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decreasing in (−∞, −and increasing in (−1, ∞)
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increasing for all x
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decreasing in (−1, ∞) and increasing in (− ∞, −1)
The angle between tangents to 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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