Calculus

Application of Derivatives

Easy

core

The approximate volume of a cube of side a meters on increasing the side by 4% is:

$1.04 a^3$ m $^3$

$1.004 a^3$ m $^3$

$1.12 a^3$ m $^3$

$1.12 a^2$ m $^3$

✅ Correct Option: 3

$V = a^3$ . Using $dV = 3a^2\,da$ with $da = 0.04a$ : $dV = 3a^2(0.04a) = 0.12a^3$ . New volume $\approx a^3 + 0.12a^3 = 1.12a^3$ m $^3$ .

2025: 15 May Shift 1

Which of the following functions are increasing on $x \in \left(0, \frac{\pi}{2}\right)$ ?

(A) $f(x) = \sin x$

(B) $f(x) = \cos x$

(D) $f(x) = \cos 3x$

Choose the correct answer from the options given below:

2026: 14 May Shift 2

In a sphere the rate of change of volume with respect to(w.r.t) time is

2025: 30 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The maximum value of $f(x) = \sin(3x) + 6$	(I) 2
(B) The maximum value of $f(x) = -\vert x + 2\vert + 4$	(II) 5
(C) The minimum value of $f(x) = (3x + 1)^2 + 5$	(III) 7
(D) The minimum value of $f(x) = 2 \cos x + 4$	(IV) 4

Choose the correct answer from the options given below:

2025: 14 May Shift 1

The rate of change of area of a circle with respect to its circumference when radius is 4cm, is

2026: 21 May Shift 1

The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

2026: 22 May Shift 1

The interval for which the function $f(x)=\frac{x}{x^2+x+1}$ is an increasing function, is:

Solution