Application of Integrals

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

Difficulty: 9 easy · 28 moderate · 37 hard.
Most-asked subtopics: Area Bounded by a Curve and a Line (41), Area Under Simple Curves (33).
Updated 19 August 2026.

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#1Area Under Simple Curves
#2Area Under Simple Curves
#3Area Under Simple Curves
#4Area Under Simple Curves
#5Area Under Simple Curves
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#6Area Under Simple Curves
#7Area Under Simple Curves
#8Area Under Simple Curves
#9Area Under Simple Curves
#10Area Under Simple Curves
A racing track is build around an elliptical ground whose equation is given by $9x^2 + 16y^2 = 144$ . The width of the track is 3 m as shown below : Based on given information, answer the following questions :
#11Area Under Simple Curves
A racing track is build around an elliptical ground whose equation is given by $9x^2 + 16y^2 = 144$ . The width of the track is 3 m as shown below : Based on given information, answer the following questions :
#12Area Under Simple Curves
#13Area Under Simple Curves
Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by $C_1$ ; $x^2 + y^2 = 64$ . There is a circular pond with a fountain in the middle of the roundabout whose equation is given by $C_2 : x^2 + y^2 = 4$ . Based on the given information, answer the following questions :
#14Area Under Simple Curves
Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by $C_1$ ; $x^2 + y^2 = 64$ . There is a circular pond with a fountain in the middle of the roundabout whose equation is given by $C_2 : x^2 + y^2 = 4$ . Based on the given information, answer the following questions :
#15Area Under Simple Curves
Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by $C_1$ ; $x^2 + y^2 = 64$ . There is a circular pond with a fountain in the middle of the roundabout whose equation is given by $C_2 : x^2 + y^2 = 4$ . Based on the given information, answer the following questions :
#16Area Under Simple Curves
Roundabouts are often made on busy roads to ease the traffic and avoid red lights. One such round-about is made such that equation representing its boundary is given by $C_1$ ; $x^2 + y^2 = 64$ . There is a circular pond with a fountain in the middle of the roundabout whose equation is given by $C_2 : x^2 + y^2 = 4$ . Based on the given information, answer the following questions :
#17Area Under Simple Curves
#18Area Under Simple Curves
#19Area Under Simple Curves
#20Area Under Simple Curves
#21Area Under Simple Curves
#22Area Under Simple Curves
#23Area Under Simple Curves
#24Area Under Simple Curves
#25Area Under Simple Curves
#26Area Under Simple Curves
#27Area Under Simple Curves
#28Area Under Simple Curves
#29Area Under Simple Curves
#30Area Under Simple Curves
#31Area Under Simple Curves
#32Area Under Simple Curves
#33Area Under Simple Curves
#34Area Bounded by a Curve and a Line
#35Area Bounded by a Curve and a Line
#36Area Bounded by a Curve and a Line
#37Area Bounded by a Curve and a Line
#38Area Bounded by a Curve and a Line
#39Area Bounded by a Curve and a Line
#40Area Bounded by a Curve and a Line
#41Area Bounded by a Curve and a Line
#42Area Bounded by a Curve and a Line
#43Area Bounded by a Curve and a Line
#44Area Bounded by a Curve and a Line
#45Area Bounded by a Curve and a Line
#46Area Bounded by a Curve and a Line
#47Area Bounded by a Curve and a Line
There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are $A(0, 4)$ , $B(-2, 0)$ and $C(3, 0)$ . Based on the above information, answer the following questions :
#48Area Bounded by a Curve and a Line
There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are $A(0, 4)$ , $B(-2, 0)$ and $C(3, 0)$ . Based on the above information, answer the following questions :
#49Area Bounded by a Curve and a Line
There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are $A(0, 4)$ , $B(-2, 0)$ and $C(3, 0)$ . Based on the above information, answer the following questions :
#50Area Bounded by a Curve and a Line
There is a triangular park in the society. The park is divided into two sections as shown in the figure. In the region OAC, children are allowed to play games like cricket, football, while in the region AOB, activities which involve running are not allowed. The vertices of the triangular park ABC are $A(0, 4)$ , $B(-2, 0)$ and $C(3, 0)$ . Based on the above information, answer the following questions :

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Application of Integrals

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