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Rate of Measure
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A water tank has the shape of a right circular cone with axis vertical and vertex
downwards. Its semi vertical angle is tan-1 3/4. Water is poured in it at a constant rate of 6
cubic meter per hour . The rate (in square meter per hour), at which the wet curved surface
area of the tank is increasing, when the depth of water in the tank is 4 meters, is_.
JEE M 2022
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Tangents and Normals
Normal
Tangent
Curve
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Let the tangent to the curve x2 + 2x − 4y + 9 = 0 at the point P (1, 3) on it
meet the y − axis at A. Let the line passing through P and parallel to the line
x − 3y = 6 meet the parabola y2 = 4x at B. If B lies on the line 2x − 3y = 8, then
(AB)2 is equal to _ _ _ _ .
JEE M 2023
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JEE M 2023
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Shortest Distance between two curves
Shortest Distance is always along Common Normal
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The shortest distance between the line x - y = 1 and the curve x2 = 2y is
A. 1/2
B. 0
C. 1/2√2
D. 1/√2
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Monotonic Functions
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A.
JEE M 2022
B.
C.
D.
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Let f be a real valued function, defined on
Then in which of the following intervals, function f(x) is increasing ?
A. (-∞, -1) U ([1/2 , ∞) - {1})
B. (-∞, ∞) - {-1, 1}
C. (-1, 1/2]
D. (-∞, 1/2] - {-1}
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Let f(x) = 2x + tan−1 x and g (x) = loge , x ∈ [0, 3]. Then
(A) There exists x ∈ [0, 3] such that f ′ (x) < g′(x)
(B) max f(x) > max g(x)
(C) There exist 0 < x1 < x2 < 3 such that f(x) < g (x), ∀ x ∈ (x1, x2)
JEE M 2023
(D) min f′(x) = 1 + max g′(x)
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Maxima and Minima
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If the total maximum value of the function
is equal to
(A) e3 +e6 + e11
(B) e5 + e6 + e11
(C) e3 + e6 + e10 JEE M 2023
(D) e3 + e5 + e11
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A square piece of tin of side 30 cm is to be made into a box without top by
cutting a square from each corner and folding up the flaps to form a box. If
the volume of the box is maximum, then its surface area (in cm2) is equal to
(A) 800
(B) 675
(C) 1025 JEE M 2023
(D) 900
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The sum of the absolute maximum and minimum values of the function
f(x) = |x2 − 5 x + 6| − 3x + 2 in the interval [−1, 3] is equal to :
(A) 10
(B) 12
(C) 13
JEE M 2023
(D) 24
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A wire of length 20 m is to be cut into two pieces. A piece of length ℓ1 is bent to make a
square of area A1 and the other piece of length ℓ2 is made into a circle of area A2. If 2 A1 + 3
A2 is minimum then (π ℓ1) : ℓ2 is equal to:
(A) 6:1
(B) 3:1
(C) 1:6
JEE M 2023
(D) 4:1
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Thank You #VCians
