If the total cost function is given by $C(x)=\frac{x^3}{3}-2x^2+9x-70$ and the selling price per unit is ₹6, then for what value of $x$ will the profit be maximum?

Rate of change of area of a circle with respect to radius

(A) When r = 2 cm is $4\pi$ cm²/cm.

(B) When r = 6 cm is $12\pi$ cm²/cm.

(C) When r = 12 cm is $6\pi$ cm²/cm.

(D) When r = 16 cm is $8\pi$ cm²/cm.

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The equation of tangent to the curve $x = a \cos^3 t, y = a \sin^3 t$ at t is :

If the maximum value of the function $f(x) = \frac{\log_ex}{x}$, $x > 0$ occurs at $x = a$, then $a^2f''(a)$ is equal to

A ring is dropped into a quiet pond and waves move in circles at a speed of 2 cm/second. At the instant, when the radius of the circular wave is 12 cm, how fast is the enclosed area increasing?

Which of the following are NOT correct regarding the equation of tangent and normal to the curve $y = \frac{x-11}{(x-2)(x-3)}$ at the point, where it cuts the $x$-axis?

(A) The point of contact is (11, 0).

(B) The equation of tangent is $x - 72y - 11 = 0$

(C) The equation of normal is $72x + y - 11 = 0$

(D) The slope of the tangent at the given point of contact is $\frac{1}{88}$

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Consider the function $f(x) = x^3 - 3x$. Then

Match List-I with List-II

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