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BITSAT Application of Derivatives PYQs with Solutions

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

67 questionsMathematics2009–2024Answers + solutions

About Application of Derivatives PYQs

Application of Derivatives has 67 previous year questions in the Quantrex Academy BITSAT Mathematics bank. The 67 questions in this list come from BITSAT (67), spanning 2009 to 2024. Each question opens on its own page with the options, the correct answer and the worked solution where available.

BITSAT Application of Derivatives PYQs with Solutions

About Application of Derivatives PYQs

Questions by year (this list)

Application of Derivatives questions with solutions

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

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

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

If the angle made by the tangent at the point (x_0, y_0) on the curve x=12(t+ t t), y=12(1+ t)^2, 0 t (π)/(2) , with the positive x -axis is (π)/(3) , then y_0 is equal to

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

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

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

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

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

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

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

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

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

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

The points at which the tangent passes through the origin for the curve y=4 x^ 3 -2 x^ 5 are

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.

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

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

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

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

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

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

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)

The least value of the function f ( x ) = ∫ _ 0 ^ x (3sinx + 4cosx)dx in the interval [(5π)/(4), (4π)/(3)] is

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

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

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

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

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

Rolle&#39;s theorem is not applicable for the function f ( x ) = | x | in the interval [ - 1, 1 ] because

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

The maximum value of f ( x ) = x + sin2x, x ∈ [ 0, 2π ] is

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

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

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

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?

Consider the following statements in respect of the function f(x)=x^ 3 -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

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

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

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

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

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

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

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

If \(0< x< (π)/(2) \), then

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)

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

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

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

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

If a^ 2 x^ 4 +b^ 2 y^ 4 =c^ 4 , then the maximum value of xy is

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

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

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

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

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

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

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

Let \(f(x)= \(\ array l a x²+1, x > 1 x+a, x ≤ 1 array .\). Then \(f(x)\) is derivable at \(x=1\), if

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

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

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

If \(M(α)=[ array ccc α & - α & 0 α & α & 0 0 & 0 & 1 array ]\); \(M(β)=[ array ccc β & 0 & β 0 & 1 & 0 - β & 0 & β array ]\) then \([M(α) M(β)]^ -1 \) is equal to -

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

The minimum value of the function \(y=x⁴-2 x²+1\) in the interval \( [(1)/(2), 2]\) is

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

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

Related BITSAT Mathematics chapters

Application of Derivatives in other exams

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