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Application of Derivatives — BITSAT Mathematics PYQs

67 previous year questions from Application of Derivatives with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

67 questionsMathematicsSolutions on every page
1

The maximum area of rectangle inscribed in a circle of diameter R is

BITSAT 2024 Solution View → 2

Consider the function f(x)= |x-1| x^2 , then f(x) is

BITSAT 2024 Solution View → 3

The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is

BITSAT 2024 Solution View → 4

If the angle made by the tangent at the point (x₀, y₀ ) on the curve x=12(t+ t t), y=12(1+ t)^2, 0 t 2 , with the positive x -axis is 3 , then y₀ is equal to

BITSAT 2024 Solution View → 5

The altitude of a cone is 20 cm and its semivertical angle is 30^ . If the semi-vertical angle is increasing at the rate of 2^ per second, then the radius of the base is increasing

BITSAT 2024 Solution View → 6

The point of inflexion for the curve y=(x-a)^n , where n is odd integer and n 3 is

BITSAT 2024 Solution View → 7

The population p(t) at time t of a certain mouse species satisfies the differential equation d p(t) d t =0.5 p ( t )-450 . If p(0)=850 , then the time at which the population becom

BITSAT 2024 Solution View → 8

The function f(x)= (1+x)- 2 x 2+x is increasing on

BITSAT 2023 Solution View → 9

If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x)= x , then which of the following option is correct?

BITSAT 2023 Solution View → 10

The interval in which the function f(x)= 4 x^2+1 x is decreasing is :

BITSAT 2023 Solution View → 11

The curve given by x+y=e^ x y has a tangent parallel to the Y-axis at the point

BITSAT 2023 Solution View → 12

The function f(x)= ⁻¹( x+ x) is an increasing function in

BITSAT 2023 Solution View → 13

A running track of 440 ft is to be laid out enclosing a football field, the shape of which is a rectangle with a semi-circle at each end. If the area of the rectangular portion is

BITSAT 2022 Solution View → 14

A spherical balloon is filled with 4500 ~ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 ~ cubic meters per minute then the rate (i

BITSAT 2022 Solution View → 15

The points at which the tangent passes through the origin for the curve y=4 x³-2 x⁵ are

BITSAT 2021 Solution View → 16

If the radius of a sphere is measured as 9 ~cm with an error of 0.03 ~cm , then find the approximating error in calculating its volume.

BITSAT 2021 Solution View → 17

f(x)= ( e^ 2 x -1 e^ 2 x +1 ) is

BITSAT 2021 Solution View → 18

If the tangent at P(1,1) on y²=x(2-x)² meets the curve again at Q , then Q is

BITSAT 2021 Solution View → 19

Consider the function f(x)=|x-1| /x², then f(x) is

BITSAT 2020 Solution View → 20

Let x+y=3- 4 and x-y=4 2 then the greatest of x y is

BITSAT 2020 Solution View → 21

The equation of the tangent to the curve y=b e^ -x/a at the point where it crosses the y -axis is

BITSAT 2020 Solution View → 22

Suppose that f(0)=-3 and f^ (x) 5 for all values of x Then, the largest value which f(2) can attain is

BITSAT 2020 Solution View → 23

If f and g are differentiable function in 0 , 1 satisfying f 0 = 2 = g 1 , g 0 = 0 and f 1 = 6 , then for some c ∈ 0 , 1

BITSAT 2019 Solution View → 24

The least value of the function f ( x ) = ∫ 0 x 3 sin x + 4 cos x d x in the interval 5 π 4 , 4 π 3 is

BITSAT 2019 Solution View → 25

The difference of maximum and minimum values of f ( x ) = x 2 e - x is

BITSAT 2019 Solution View → 26

The distance between the origin and the normal to curve y = e 2 x + x 2 at x = 0 is

BITSAT 2019 Solution View → 27

An inverted conical flask is being filled with water at the rate of 3 cm 3 sec - 1 . The height of the flask is 10 cm and the radius of the base is 5 cm . How fast is the water lev

BITSAT 2018 Solution View → 28

For which interval the given function f x = - 2 x 3 - 9 x 2 - 12 x + 1 is decreasing?

BITSAT 2018 Solution View → 29

Let f x = - 2 x 3 + 21 x 2 - 60 x + 41 , then

BITSAT 2017 Solution View → 30

Rolle's theorem is not applicable for the function f ( x ) = | x | in the interval [ - 1 , 1 ] because

BITSAT 2017 Solution View → 31

If the curve y = a x and y = b x intersect at angle α , then tan α is equal to

BITSAT 2017 Solution View → 32

The maximum value of f ( x ) = x + sin 2 x , x ∈ [ 0 , 2 π ] is

BITSAT 2017 Solution View → 33

Line joining the points ( 0 , 3 ) and ( 5 , - 2 ) is a tangent to the curve y = a x 1 + x , then

BITSAT 2017 Solution View → 34

The shortest distance between the parabolas y 2 = 4 x and y 2 = 2 x - 6 is

BITSAT 2017 Solution View → 35

The set of all values of a for which the function f(x)= (a²-3 a+2 ) ( ² x / 4- ² x / 4 )+(a-1) x+ 1 does not possess critical points is

BITSAT 2016 Solution View → 36

What is the x -coordinate of the point on the curve f(x)= x (7 x-6), where the tangent is parallel to x -axis?

BITSAT 2016 Solution View → 37

Consider the following statements in respect of the function f(x)=x³-1, x [-1,1] I. f(x) is increasing in [-1,1] II. f(x) has no root in (-1,1) . Which of the statements given abov

BITSAT 2016 Solution View → 38

At an extreme point of a function f(x), the tangent to the curve is

BITSAT 2016 Solution View → 39

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

BITSAT 2016 Solution View → 40

The line which is parallel to X-axis and crosses the curve y= x at an angle of 45^ , is

BITSAT 2015 Solution View → 41

The number of real roots of the equation e e ^ (x-1) + x -2=0 is

BITSAT 2015 Solution View → 42

Tangents are drawn from the origin to the curve y = x . Their points of contact lie on

BITSAT 2015 Solution View → 43

The slope of the tangent to the curve y=e^ x cos x is minimum at x= , 0 a 2 , then the value of is

BITSAT 2015 Solution View → 44

The function f ( x )= x 2 + 2 x has a local minimum at

BITSAT 2015 Solution View → 45

If (0<x< 2 ), then

BITSAT 2015 Solution View → 46

Let f(x) be a polynomial of degree three satisfying f (0)=-1 and f (1)=0 . Also , 0 is a stationary point of f(x) If f(x) does not have an extremum at x=0 , then the value of f(x)

BITSAT 2015 Solution View → 47

The interval in which the function 2 x ³+15 increases less rapidly than the function 9 x²-12 x, is -

BITSAT 2014 Solution View → 48

The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs ' 48 per hour at 16 miles per hour. The most economical speed

BITSAT 2014 Solution View → 49

The equation of all lines having slope 2 which are tangent to the curve y= 1 x-3 , x 3, is

BITSAT 2013 Solution View → 50

The function f ( x )=( x ( x -2))² is increasing in the set

BITSAT 2013 Solution View → 51

If a² x⁴+b² y⁴=c⁴ , then the maximum value of xy is

BITSAT 2013 Solution View → 52

If f(x)=x^ x and f(0)=0, then the value of for which Rolle's theorem can be applied in [0,1] is

BITSAT 2012 Solution View → 53

If f ( x )= a ²-1 a ²+1 x ³-3 x +5 is a decreasing function of x in R , then the set of possible values of a (independent of x ) is

BITSAT 2012 Solution View → 54

If the normal to the curve y=f(x) at the point (3,4) makes an angle 3 / 4 with the positive x -axis, then f ^ (3)=

BITSAT 2012 Solution View → 55

The function (f(x)= x-k x-c ), where (k ) and (c ) are constants, decreases always when

BITSAT 2011 Solution View → 56

The minimum value of (f(x)= ^4 x+ ^4 x ) in the interval ( (0, 2 ) ) is

BITSAT 2011 Solution View → 57

The curve (y-e^ x y +x=0 ) has a vertical tangent at

BITSAT 2011 Solution View → 58

The function ( f ( x )=2 x ^3-3 x ^2-12 x +4 ), has

BITSAT 2011 Solution View → 59

Let ( f ( x )= ) ( array l a x^2+1, x > 1 x+a, x 1 array . ). Then (f(x) ) is derivable at (x=1 ), if

BITSAT 2010 Solution View → 60

If a circular plate is heated uniformly, its area expands (3 c ) times as fast as its radius, then the value of (c ) when the radius is 6 units, is

BITSAT 2010 Solution View → 61

The function ( f ( x )= x -4 x ) is strictly decreasing on

BITSAT 2010 Solution View → 62

If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of (2 3 ) metres along the ground, then the angle (in degrees) that the sun makes with the ground is

BITSAT 2010 Solution View → 63

If (M( )= [ array ccc & - & 0 & & 0 0 & 0 & 1 array ] ); (M( )= [ array ccc & 0 & 0 & 1 & 0 - & 0 & array ] ) then ([M( ) M( )]⁻¹ ) is equal to -

BITSAT 2009 Solution View → 64

The set of points of discontinuity of the function (1 / | x | ) is -

BITSAT 2009 Solution View → 65

The minimum value of the function (y=x^4-2 x^2+1 ) in the interval ( [ 1 2 , 2 ] ) is

BITSAT 2009 Solution View → 66

The value of (a ) in order that (f(x)= x- x-a x+b ) decreases for all real values is given by

BITSAT 2009 Solution View → 67

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is (60^ ). when he retreats 20 feet from the bank, he finds the angle to b

BITSAT 2009 Solution View →
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