CBSE Class XII Mathematics Sample Question Paper 2024-25
Organisation : Central Board of Secondary Education (CBSE)
Class Name : 12th/HSC (Class XII)
Subject : Mathematics
Download : Sample Question Paper 2024-25
Website : https://cbseacademic.nic.in//SQP_CLASSXII_2024-25.html
CBSE Class XII Mathematics Sample Question Paper
Central Board of Secondary Education (CBSE) Class XII Mathematics Sample Question Paper 2024-25.
Related / Similar Question Paper : CBSE Class XII Sociology Sample Question Paper 2024-25
1. The probability that it rains today is 0.4. If it rains today, the probability that it will rain tomorrow is 0.8. If it does not rain today, the probability that it will rain tomorrow is 0.7. If
𝑃1: denotes the probability that it does not rain today.
𝑃2: denotes the probability that it will not rain tomorrow, if it rains today.
𝑃3: denotes the probability that it will rain tomorrow, if it does not rain today.
𝑃4: denotes the probability that it will not rain tomorrow, if it does not rain today.
(i) Find the value of p1xp4-p2xp3
(ii) Calculate the probability of raining tomorrow
2. A kite is flying at a height of 3 metres and 5 metres of string is out. If the kite is moving away horizontally at the rate of 200 cm/s, find the rate at which the string is being released
3. Consider the following Linear Programming Problem:
Minimise Z=x+2y
Subject to 2x+y>=3, x+2y>+6,x,y>=0
Show graphically that the minimum of Z occurs at more than two point
4. The equation of the path traversed by the ball headed by the footballer is 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐; (𝑤ℎ𝑒𝑟𝑒 0 ≤ 𝑥 ≤ 14 𝑎𝑛𝑑 𝑎, 𝑏, 𝑐 ∈ 𝑅 𝑎𝑛𝑑 𝑎 ≠ 0) with respect to a XY-coordinate system in the vertical plane. The ball passes through the points (2,15) , (4, 25) and (14,15) . Determine the values of a, b and c by solving the system of linear equations in a, b and c, using matrix method. Also find the equation of the path traversed by the ball
5. Ramesh, the owner of a sweet selling shop, purchased some rectangular card board sheets of dimension25 by 40cm cm to make container packets without top. Letx 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.
(i) Express the volume (V) of each container as function ofx only.
(ii) Find 𝑑𝑉/𝑑𝑥
(iii) (a) For what value of,x the volume of each container is maximum?
OR
(iii) (b) Check whether V has a point of inflection at x = 65/6 or not?
6. An organization conducted bike race under 2 different categories-boys and girls. In all, there were 250 participants. Among all of them finally three from Category1 and two from Category2 were selected for the final race. Ravi forms two setsB andG with these participants for his college project. Let B={b1,b2,b3}, G={g1,g2} where B represents the set of boys selected andG the set of girls who were selected for the final race. Ravi decides to explore these sets for various types of relations and functions.
On the basis of the above information, answer the following questions:
(i) Ravi wishes to form all the relations possible fromB toG . How many such relations are possible?
(ii) Write the smallest equivalence relation on G.
(iii) (a) Ravi defines a relation from B to B as 𝑹𝟏 = {(𝒃𝟏, 𝒃𝟐), (𝒃𝟐, 𝒃𝟏)}. Write the minimum ordered pairs to be added in 𝑹𝟏 so that it becomes (A) reflexive but not symmetric, (B) reflexive and symmetric but not transitive.
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