Applications of Derivatives: Class 12 Previous Year Questions

Applications of Derivatives questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. For f(x) = x + x 1 (x  0) 1 (A) local maximum value is 2 (B) local minimum value is –2 (C) local maximum value is –2 (D) local minimum value < local maximum value 1 a
   Board 20261 markMCQ
2. (a) Find the sub intervals in which f(x) = cot–1 (sin x + cos x), x  (0, ) is increasing and decreasing. 5 OR (b) A rectangle of perimeter 36 cm is revolved around one of its sides to sweep out a cylinder of maximum volume. 5 Find the dimensions of the recta…
   Board 20265 markslong answer
3. { } 36. An online delivery company in a city has 5000 subscribers and collects annual subscription fees of ` 300 per subscriber for unlimited free deliveries. The company wishes to increase the annual subscription fee. It is predicted that, for every increase …
   Board 20264 marksshort answer
4. Find the absolute maximum and absolute minimum of function f(·) = 2x3 - 15x2 + 36x + 1 on [1, 5]. Page 17 of 24 34. (a) y+3 x+5 z-6 (b) (2,4,1) -9 : 3 × 4 = 12 36. Page 18 of 24 1 Z
   Board 20255 markslong answer
5. A technical company is designing a rectangular solar panel installation on a roof using 300 metres of boundary material. The design includes a partition running parallel to one of the sides dividing the area (roof) into two sections. Let the length of the side…
   Board 20254 marksshort answer
6. A small town is analyzing the pattern of a new street light installation. The lights are set up in such a way that the intensity of light at any point x metres from the start of the street can be modelled by f(x) = ex sin x, where x is in metres. Based on the …
   Board 20254 marksshort answer
7. The side of an equilateral triangle is increasing at the rate of 3 cm/s. At what rate its area increasing when the side of the triangle is 15 cm ?
   Board 20253 marksshort answer
8. l. A cylindrical tank of radius 10 cm is being filled with sugar at the rate of 100 · cm3/s. The rate, at which the height of the sugar inside the tank is increasing, is : (A) 0.1 cm/s (B) 0.5 cm/s (C)1 cm/s (D) 1.1 cm/s
   Board 20251 markMCQ
9. JJJJ Page 21 37. A tank, as shown in the figure below, formed using a combination of a cylinder and a cone, offers better drainage as compared to a flat bottomed tank. JJJJ Page 22 H$ma ^mJ nmZr go ^am h¡, _| EH$ Zb bJm`m J`m VWm Zb go 2 cm3/s H$s g_mZ Xa go n…
   Board 20234 marksshort answer
10. Engine displacement is the measure of the cylinder volume swept by all the pistons of a piston engine. The piston moves inside the cylinder bore Aluminium cylinder head Combustion chamber Cylinder head surface that is machined flat Piston The ulaue displ: The …
    Board 20234 marksshort answer
11. In the interval (1,2) the function  2 1 3 2 f x x x    is (a) Strictly Increasing (b) Strictly Decreasing (c) Neither Increasing nor Decreasing (d) Remains constant
    CBSE practice 2023-241 markMCQ
12. The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/sec. How fast is the area decreasing when the two equal sides are equal to the base? OR The volume of the cube increases at a constant rate. Prove that the increas…
    CBSE practice 2023-242 marksshort answer
13. Answer the questions based on the given information. A medicinal drug administered into a human body requires some time to produce its effect on the body. The amount (in mg) of a certain medicinal drug in the bloodstream at t hours after administering the drug…
    CBSE practice 2022-234 marksshort answer
14. Answer the questions based on the given information. Two metal rods, R1 and R2, of lengths 16 m and 12 m respectively, are insulated at both the ends. Rod R1 is being heated from a specific point while rod R2 is being cooled from a specific point. The temperat…
    CBSE practice 2023-244 marksshort answer
15. In a park, an open tank is to be constructed using metal sheet with a square base and vertical sides so that it contains 500 cubic meters of water. Using above information answer the following: (i) Find the minimum surface area of the tank. (ii) Find the perce…
    CBSE practice 2023-244 marksshort answer
16. Water is essential for life, and rivers are vital water sources across the world. The Yamuna Action Plan (YAP), one of India’s largest river restoration projects, was launched to clean the Yamuna, but its effectiveness must be measured through cost-benefit, ec…
    Sample paper 2026-274 markscase-based
17. Iqbal, a data analyst in a social media platform is tracking the number of active users on their site between 5 pm and 6 pm on a particular day. The user growth function is modelled by N(t) = 1000e0.1t, where N(t) represents the number of active users at time …
    CBSE practice 2023-242 marksshort answer

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