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Name of the Board : Central Board of Secondary Education (CBSE)
Class : XII STD
Document Type : Sample Question Paper
Subject : Mathematics
Year : 2022-23
Website : https://cbseacademic.nic.in/SQP_CLASSXII_2022-23.html

CBSE XII Mathematics Sample Question Paper

CBSE Students can download the Mathematics Sample Question Paper for the year 2022-23 from the website of CBSE Academic.

Mathematics Sample Question Paper

Section A
1. If A is a square matrix of order 3, |𝐴′| = −3, then |𝐴𝐴′| =
(a) 9 (b) -9 (c) 3 (d) -3

2. The solution set of the inequality 3x + 5y < 4 is
(a) an open half-plane not containing the origin.
(b) an open half-plane containing the origin.
(c) the whole XY-plane not containing the line 3x + 5y = 4.
(d) a closed half plane containing the origin.

3. The corner points of the shaded unbounded feasible region of an LPP are (0, 4), (0.6, 1.6) and (3, 0) as shown in the figure. The minimum value of the objective function Z = 4x + 6y occurs at
(a)(0.6, 1.6) 𝑜𝑛𝑙𝑦
(b) (3, 0) only
(c) (0.6, 1.6) and (3, 0) only
(d) at every point of the line-segment joining the points (0.6, 1.6) and (3, 0)

4. P is a point on the line joining the points 𝐴(0,5, −2) and 𝐵(3, −1,2). If the x-coordinate of P is 6, then its z-coordinate is
(a) 10
(b) 6
(c) -6
(d) -10

5. ASSERTION-REASON BASED QUESTIONS
In the following questions, a statement of assertion (A) is followed by a statement of Reason (R). Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true

6. A man 1.6 m tall walks at the rate of 0.3 m/sec away from a street light that is 4 m above the ground. At what rate is the tip of his shadow moving? At what rate is his shadow lengthening?

7. Three friends go for coffee. They decide who will pay the bill, by each tossing a coin and then letting the “odd person” pay. There is no odd person if all three tosses produce the same result. If there is no odd person in the first round, they make a second round of tosses and they continue to do so until there is an odd person. What is the probability that exactly three rounds of tosses are made?
OR
8. Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.

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