The Central Board of Secondary Education (CBSE) is conducting the Class 10 and 12 board exams for the 2025 academic year. The Class 10 exams began with English, while the Class 12 exams started with Entrepreneurship. The Mathematics exam for Class 12 is scheduled for March 8, 2025. Students can visit the official CBSE website to check sample papers.

Here are some of the important questions from the Mathematics Class 12 sample paper: 

Q) Arka bought two cages of birds: Cage-I contains 5 parrots and 1 owl and Cage –II contains 6 parrots. One day Arka forgot to lock both cages and two birds flew from Cage-I to Cage-II (simultaneously). Then two birds flew back from cage-II to cage-I(simultaneously).
Assume that all the birds have equal chances of flying.
On the basis of the above information, answer the following questions:-
When two birds flew from Cage-I to Cage-II and two birds flew back from Cage-II to Cage-I then find the probability that the owl is still in Cage-I.
When two birds flew from Cage-I to Cage-II and two birds flew back from Cage-II to Cage-I, the owl is still seen in Cage-I, what is the probability that one parrot and the owl flew from Cage-I to Cage-II?

Q) Ramesh, the owner of a sweet selling shop, purchased some rectangular card board sheets of dimension 25 by 40 cm cm to make container packets without top. Let x cm be the length of the side of the square to be cut out from each corner to give that sheet the shape of the container by folding up the flaps.
Based on the above information answer the following questions:
Express the volume (V) of each container as function of x only.
Find 𝑑𝑉/𝑑𝑥
For what value of x, the volume of each container is maximum?
OR
Check whether V has a point of inflection at x = 65/6 or not?

Q) If 𝑓: 𝑅 → 𝑅 is defined by 𝑓(𝑥) = |𝑥|3, show that 𝑓”(𝑥) exists for all real x and find it.

Q) Draw the rough sketch of the curve 𝑦 = 20 𝑐𝑜𝑠 2 𝑥; (where 𝜋/6 ≤ 𝑥 ≤ 𝜋/3 ).
Using integration, find the area of the region bounded by the curve y = 20 cos2x from the ordinates
𝑥 =𝜋/6 to 𝑥 = 𝜋/3 and the x-axis. 

The complete list of questions is available on the official website.