Differential Equations

141 CBSE Class 12 Mathematics past-year questions from 5 papers, 2022 to 2026, with answers and worked solutions.

Difficulty: 51 easy · 67 moderate · 23 hard.
Most-asked subtopics: Linear Differential Equations (38), Homogeneous Differential Equations (35), Variables Separable (31).
Updated 19 August 2026.

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#1Order and Degree of a Differential Equation
#2Order and Degree of a Differential Equation
#3Order and Degree of a Differential Equation
#4Order and Degree of a Differential Equation
#5Order and Degree of a Differential Equation
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#6Order and Degree of a Differential Equation
#7Order and Degree of a Differential Equation
#8Order and Degree of a Differential Equation
#9Order and Degree of a Differential Equation
#10Order and Degree of a Differential Equation
#11Order and Degree of a Differential Equation
#12Order and Degree of a Differential Equation
#13Order and Degree of a Differential Equation
#14Order and Degree of a Differential Equation
#15Order and Degree of a Differential Equation
#16Order and Degree of a Differential Equation
#17Order and Degree of a Differential Equation
#18Order and Degree of a Differential Equation
#19Order and Degree of a Differential Equation
#20Order and Degree of a Differential Equation
#21Order and Degree of a Differential Equation
#22Order and Degree of a Differential Equation
#23Order and Degree of a Differential Equation
#24Order and Degree of a Differential Equation
#25Order and Degree of a Differential Equation
#26Order and Degree of a Differential Equation
#27Order and Degree of a Differential Equation
#28Order and Degree of a Differential Equation
#29Order and Degree of a Differential Equation
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature. (Cylindrical-shaped Camphor tablets) A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that the rate of reduction of its volume is proportional to its total surface area. Thus, $\dfrac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours. Based upon the above information, answer the following questions :
#30Order and Degree of a Differential Equation
#31General and Particular Solutions
#32General and Particular Solutions
#33General and Particular Solutions
#34General and Particular Solutions
A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential growth model, the rate of growth of this sample of bacteria is calculated. The differential equation representing the growth of bacteria is given as : $\dfrac{dP}{dt} = kP$ , where P is the population of bacteria at any time 't'. Based on the above information, answer the following questions :
#35General and Particular Solutions
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature. (Cylindrical-shaped Camphor tablets) A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that the rate of reduction of its volume is proportional to its total surface area. Thus, $\dfrac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours. Based upon the above information, answer the following questions :
#36General and Particular Solutions
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature. (Cylindrical-shaped Camphor tablets) A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that the rate of reduction of its volume is proportional to its total surface area. Thus, $\dfrac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours. Based upon the above information, answer the following questions :
#37General and Particular Solutions
Camphor is a waxy, colourless solid with strong aroma that evaporates through the process of sublimation, if left in the open at room temperature. (Cylindrical-shaped Camphor tablets) A cylindrical camphor tablet whose height is equal to its radius (r) evaporates when exposed to air such that the rate of reduction of its volume is proportional to its total surface area. Thus, $\dfrac{dV}{dt} = kS$ is the differential equation, where V is the volume, S is the surface area and t is the time in hours. Based upon the above information, answer the following questions :
#38Variables Separable
#39Variables Separable
#40Variables Separable
#41Variables Separable
#42Variables Separable
#43Variables Separable
#44Variables Separable
#45Variables Separable
#46Variables Separable
#47Variables Separable
#48Variables Separable
#49Variables Separable
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
#50Variables Separable

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Differential Equations

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