Practice Question On Application of derivative for NDA , Airforce and IIT-JEE

Application of derivative

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Question no. 1

The curve y = xe^x has minimum value equal to

looks_one - 1/e

looks_two 1/e

looks_3 -e

looks_4 e

Option looks_3 0

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Question no. 2

What is the minimum value of |x| ?

looks_one -1

looks_two 0

looks_3 1

looks_4 2

Option looks_two q

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Question no. 3

The radius of a circle is uniformly increasing at the rate of 3 cm/s . What is the rate of increase in area , when the radius is 10 cm ?

looks_one 6π

looks_two 10π

looks_3 30π

looks_4 60π

Option looks_3 5: 7

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Question no. 4

What is the slope of the tangent to the curve x =t² + 3t - 8 , y =2t² - 2t - 5 at t=2 ?

looks_one 7/6

looks_two 6/7

looks_3 1

looks_4 5/6

Option looks_4 x-y+101=0

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Question no. 5

A ballon is pumped at the rate of 4 cm³ per second. What is the rate at which its surface area increases and radius is 4 cm ?

looks_one 1 cm² per second

looks_two 2 cm² per second

looks_3 3 cm² per second

looks_4 4 cm² per second

Option looks_two 5

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Question no. 6

The largest value of 2 x³ - 3x² - 12x + 5 for -2 ≤ x ≤ 2 occurs when

looks_one x =-2

looks_two x =-1

looks_3 x = 2

looks_4 x = 0

Option looks_one 6 sq. unit

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Question no. 7

The function f(x) = k sinx + (sin3x)/ 3 has maximum value at x = π/3 , what is the value of k ?

looks_one 3

looks_two 1/3

looks_3 2

looks_4 1/2

Option looks_two

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Question no. 8

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 ?

looks_one

looks_two

looks_3

looks_4

Option looks_two not cross each other

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Question no. 9

What is the maximum point on the curve x = e^xy ?

looks_one (1, e )

looks_two (1 , e^-1)

looks_3 (e,1)

looks_4 (e^-1 , 1)

Option looks_3 3

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Question no. 10

for a point of infection of y = f(x) , which one of the following is correct ?

looks_one must be zero

looks_two must be zero

looks_3 must be non zero

looks_4 must be non zero

Option looks_two 2 sq. unit

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Question no. 11

If f and g are two increasing function such that fog is defined , then whihc one of the following is correct ?

looks_one fog is always an increasing function

looks_two fog is always a decreasing function

looks_3 fog is neither an increasing nor a decreasing function

looks_4 None of the above

Option looks_4 x² + a² = b² - y²

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Question no. 12

What is the interval over which the function f(x) = 6x - x² , x > 0 is increasing ?

looks_one (0 ,3)

looks_two (3,6)

looks_3 (6,9)

looks_4 None of these

Option looks_4 1/3

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Question no. 13

What is the least value of f(x) = 2x³ - 3x² - 12x + 1 on [-2 , 2.5] ?

looks_one -3

looks_two 8

looks_3 -19

looks_4 -16.5

Option looks_3 X=2

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Question no. 14

Given two squares of sides x and y such that y = x + x². What is the rate of change of area of the second square with respect to the area of the first square ?

looks_one 1 + 3x + 2x²

looks_two 1 + 2x + 3x²

looks_3 1 - 2x + 3x²

looks_4 1 - 2x - 3x²

Option looks_3 Y=-8

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Question no. 15

If f(x) = Kx³ - 9x +3 is monotonically increasing in every interval , then which of the following is correct ?

looks_one K < 3

looks_two K ≤ 3

looks_3 K > 3

looks_4 K ≥ 3

Option looks_one never intersect

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