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JEE Questions for Maths Applications Of Derivatives Quiz 14 - MCQExams.com
JEE
Maths
Applications Of Derivatives
Quiz 14
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2
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Infinite
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1
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0
x
and y be two variables such that
x
> 0 and
x
y = 1. Then the minimum value of
x
+ y is
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2
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3
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4
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0
What are the minimum and maximum values of the function
x
5
– 5
x
4
+ 5
x
3
– 10
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–37, –9
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10, 0
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It has 2 min. and 1 max.values
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It has 2 max. and 1 min. values
The minimum value of 2
x
+ 3y, where
x
y = 6 is
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12
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9
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8
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6
The maximum and minimum values of
x
3
– 18
x
2
+ 96
x
in interval (0,are
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160, 0
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60, 0
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160, 128
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120, 28
The maximum value of sin
x
(1 + cos
x
) will be at the
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None of these
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0%
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2)
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0%
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2)
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1
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The real number
x
when added to its inverse gives the minimum value of the sum at
x
equal to
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–2
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2
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1
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–1
The denominator of a fraction number is greater than 16 of the square of numerator, then least value of the number is
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2)
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The real number which most exceeds its cube is
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None of these
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A one of maximum value is inscribed in a given sphere, then ration of the height of the cone to diameter of the sphere is
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2)
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0%
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More than one minimum
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Exactly one minimum
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At least one maximum
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None of the above
The function f(
x
) =
x
+ sin
x
has
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A minimum but no maximum
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A maximum but no minimum
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Neither maximum nor minimum
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Both maximum and minimum
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If P = (1,1), Q = (3, and R is a point on
x
- axis then the value of PR + RQ will be minimum at
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Given, P(
x
) =
x
4
+ b
x
2
+ c
x
+ d such that
x
= 0 is the only real root of P’(
x
) = 0. If P(–< P(1), then in the interval [–1, 1]
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P(–is not minimum and P(is the maximum of P
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P(–is not minimum but P(is the maximum of P
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P(–is the minimum but P(is not the maximum of P
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Neither P(–is the minimum nor P(is the maximum of P
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0
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12
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16
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32
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No maxima and minima
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One maximum and one minimum
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Two maxima
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Two minima
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2)
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1
0%
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–2
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0
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3
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None of these
The perimeter of a sector is p. The area of the sector is maximum when its radius is
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No extrema
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One extremum
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Two extrema
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Four extrema
On [1, e] the greatest value of
x
2
log
x
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2)
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None of these
The maximum value of
x
y = 8 is
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20
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16
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24
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8
0%
4
If ab = 2a + 3b, a > 0, b > 0 then the minimum value of ab is
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12
0%
24
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0%
None of these
If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is
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0%
2)
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0%
The function y = a(1 – cos
x
) is maximum when
x
=
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2)
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0%
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50
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25
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75
0%
55
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Two maximum and two minimum value
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Two maximum and one minimum value
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One maximum and one minimum value
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None of the above
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1
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0
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–1
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1
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–1
0%
0
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2
The minimum value of f(
x
) = |3 –
x
| + 7 is
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0
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6
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7
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8
0%
10
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1
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–1
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2
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–2
The displacement of a particle at time t is
x
, where
x
= t
4 – kt
3
. If the velocity of the particle at time t = 2 is minimum, then
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k = 4
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k = – 4
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k = 8
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k = – 8
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2)
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Local maxima
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Local minima
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Point of inflexion
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None of these
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1
0%
–1
0%
0
0%
None of these
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2)
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1
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2)
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None of these
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None of these
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