QUESTION PAPER
2025 BOARD EXAM
CBSE CLASS 12-PCM MATHEMATICS Board Paper 2025 — Set 2
2025
MATHEMATICS
CLASS 12-PCM
CBSE EXAMINATION PAPER-2025
MATHEMATICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 43 questions. All questions are compulsory.
- This question paper is divided into 7 sections.
- Section A – questions number 1 to 1 are case based questions
-
Section B –
questions number
2 to 2
are
assertion (a) : common difference of the ap : 5, 1, 3, 7,... is 4.
reason (r): common difference of the ap : a1, a2, a3 an is obtained
by d = an an 1.
-
Section C –
questions number
3 to 5
are
assertion (a) : common difference of the ap : 5, 1, 3, 7,... is 4
reason (r): common difference of the ap : a₁, a₂, a₃,...., aₙ is obtained by d = aₙ aₙ₋₁
- Section D – questions number 6 to 23 are multiple choice questions
- Section E – questions number 24 to 29 are very short answer
- Section F – questions number 30 to 37 are short answer
- Section G – questions number 38 to 43 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
A school is organizing a grand cultural event to show the talent of its students. To accommodate the guests, the school plans to rent chairs and tables from a local supplier. It finds that rent for each chair is ₹50 and for each table is ₹200. The school spends ₹30,000 for renting the chairs and tables. Also, the total number of items (chairs and tables) rented are 300.
If the school 'x' chairs and 'y' tables, answer the following questions:
(1) Find the number of chairs and number of tables rented by the school.
[2 Marks](2) What is maximum number of tables that can be rented in ₹30,000 if no chairs are rented?
[1 Marks](3) Write down the pair of linear equations representing the given information.
[1 Marks](4) If the school wants to spend a maximum of Rs 27,000 on 300 items (tables and chairs), then find the number of chairs and tables it can rent.
Section B
Section C
Section D
The probability of drawing an even prime number out of numbers from 1 to 30 is:
The quadratic equation whose roots are 7 and 1/7 is:
The least number which is a perfect square and is divisible by each of 16, 20 and 50 is:
The coordinates of the end points of a diameter of a circle are (5, -2) and (5, 2). The length of the radius of the circle is:
The points (−5,0), (5,0) and (0,4) are the vertices of a triangle which is a/an:
In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If ∠NML = 30°, then ∠RLM is:
In the given figure, PQ || BC. If AP/ PB = 4 /13 and AC = 20.4 cm, then the length of AQ is:
In a cricket match, a batsman hits the boundary 7 times out of the 42 balls he plays. The probability of his not hitting a boundary is:
If sin 30° tan 45° = sec 60° / k, then the value of k is:
If - 4 is a zero of the polynomial p(x) = x² - x - (2 + 2k), then the value of k is:
Assertion (A) : The pair of linear equations px + 3y + 59 = 0 and 2x + 6y + 118 = 0 will have infinitely many solutions if p = 1.
Reason (R): If the pair of linear equations px + 3y + 19 = 0 and 2x + 6y + 157 = 0 has a unique solution, then p≠1.
Section E
If p and q are zeroes of the polynomial p(y) = 21y² – y – 2, then find the value of (1 - p).(1 - q).
If tan A = √3, where A is an acute angle, then find the value of sin² A / 1 + cos² A
In the given figure, D is a point on side BC of ΔABC such that ∠ADC = ∠BAC. Show that CA² = CD.CB.
In the given figure, OA.OB = OC.OD. Show that ∠A = ∠C and ∠B = ∠D.
Section F
Prove that : ( 1+ 1/tan²θ)(1 + 1/ cot²θ)= 1 / sin²θ - sin⁴θ
Prove that : √cosecθ-1/√cosecθ + 1 + √cosecθ + 1/√cosecθ -1 = 2sec θ
Prove that √3 is an irrational number.
A sum of ₹ 2,000 is invested at 7% per annum simple interest. Calculate the interests at the end of 1ˢᵗ, 2ⁿᵈ and 3ʳᵈ year. Do these interests form an AP? If so, find the interest at the end of the 27th year.
Section G
Two ships are sailing in the sea on either side of a lighthouse. The angles of depression to the two ships as observed from the top of the lighthouse are 60° and 45°, respectively. If the distance between the ships is 100 (1 + √3 / √3) m, then find the height of the lighthouse.
The time taken by a person to travel an upward distance of 150 km was 2x1/2 hours more than the time taken in the downward return journey. If he returned at a speed of 10 km/h more than the speed while going up, find the speeds in each direction.
Prove that a line drawn parallel to one side of a triangle to intersect the other two sides in distinct points divides the other two sides in the same ratio. Hence, in the figure given below, prove that AM/ MB= AN / ND where LM || CB and LN || CD.
Find the Mean and Mode of the following frequency distribution:
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