English Medium
Academic Year: 2024-2025
Date & Time: 10th March 2025, 10:30 am
Duration: 3h
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General Instructions:
Read the following instructions carefully and follow them:
- This question paper contains 38 questions. All questions are compulsory.
- Question Paper is divided into FIVE Sections. SECTION A, B, C, D and E.
- In Section A, question numbers 1 to 18 are Multiple Choice Questions (MCQs), and question numbers 19 & 20 are Assertion-Reason based questions of 1 mark each.
- In Section B, question numbers 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
- In Section C, question numbers 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
- In Section D, question numbers 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
- In Section E, question numbers 36 to 38 are case-based integrated units of assessment questions carrying 4 marks each. Internal choice is provided in 2 marks question in each case-study.
- There is no overall choice. However, an internal choice has been provided in 2 questions in Section B, 2 questions in Section C, 2 questions in Section D and 3 questions of 2 marks in Section E.
- Draw neat figures wherever required. Take π = `22/7` wherever required, if not stated.
- Use of calculators is NOT allowed.
In the given figure, the graph of polynomial p(x) is shown. Number of zeroes of p(x) is:
3
2
1
4
Chapter:
22nd term of the A.P. : `3/2, 1/2, (-1)/2, (-3)/2, ...` is:
`45/2`
–9
`(-39)/2`
–21
Chapter:
The line 2x – 3y = 6 intersects the x-axis at ______.
(0, –2)
(0, 3)
(–2, 0)
(3, 0)
Chapter:
Two identical cones are joined as shown in the figure. If the radius of the base is 4 cm and the slant height of the cone is 6 cm, then the height of the solid is:
8 cm
`4sqrt(5)` cm
`2sqrt(5)` cm
12 cm
Chapter:
The value of k for which the system of equations 3x – 7y = 1 and kx + 14y = 6 is inconsistent is ______.
–6
`2/3`
6
`(-3)/2`
Chapter:
Two dice are rolled together. The probability of getting a sum more than 9 is ______.
`5/6`
`5/18`
`1/6`
`1/2`
Chapter:
ABCD is a rectangle with its vertices at (2, –2), (8, 4), (4, 8) and (–2, 2) taken in order. Length of its diagonal is ______.
`4sqrt(2)`
`6sqrt(2)`
`4sqrt(26)`
`2sqrt(26)`
Chapter:
In the given figure, PA is tangent to a circle with centre O. If ∠APO = 30° and OA = 2.5 cm, then OP is equal to:
2.5 cm
5 cm
`5/sqrt(3)` cm
2 cm
Chapter:
If the probability of happening of an event is 57%, then the probability of non-happening of the event is ______.
0.43
0.57
53%
`1/57`
Chapter:
OAB is a sector of a circle with centre O and radius 7 cm. If the length of arc `bar(AB) = 22/3` cm, then ∠AOB is equal to ______.
`(120/7)^°`
45°
60°
30°
Chapter:
In ΔABC, DE || BC. If AE = (2x + 1) cm, EC = 4 cm, AD = (x + 1) cm and DB = 3 cm, then value of x is:
1
`1/2`
–1
`1/3`
Chapter:
Three coins are tossed together. The probability that exactly one coin shows heads is ______.
`1/8`
`1/4`
1
`3/8`
Chapter:
In two concentric circles centred at O, a chord AB of the larger circle touches the smaller circle at C. If OA = 3.5 cm, OC = 2.1 cm, then AB is equal to:
5.6 cm
2.8 cm
3.5 cm
4.2 cm
Chapter:
If `sqrt(3) sin θ = cos θ`, then the value of θ is ______.
`sqrt(3)`
60°
`1/sqrt(3)`
30°
Chapter:
To calculate the mean of grouped data, Rahul used the assumed mean method. He used d = (x – А), where A is the assumed mean. Then `bar(x)` is equal to ______.
`A + bar(d)`
`A + hbar(d)`
`h(A + bard)`
`A - hbar(d)`
Chapter:
If the sum of the first n terms of an A.P. is given by `S_n = n/2 (3n + 1)`, then the first term of the A.P. is ______.
2
`3/2`
4
`5/2`
Chapter:
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In ΔABC, ∠B = 90°. If `(AB)/(AC) = 1/2`, then cos C is equal to ______.
`3/2`
`1/2`
`sqrt(3)/2`
`1/sqrt(3)`
Chapter:
The volume of air in a hollow cylinder is 450 cm3. A cone of the same height and radius as that of the cylinder is kept inside it. The volume of empty space in the cylinder is:
225 cm3
150 cm3
250 cm3
300 cm3
Chapter:
Assertion (A): `(a + sqrt(b)) · (a - sqrt(b))` is a rational number, where a and b are positive integers.
Reason (R): Product of two irrationals is always rational.
Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Assertion (A): ΔАВС ~ ΔРQR such that ∠A = 65°, ∠C = 60°. Hence ∠Q = 55°.
Reason (R): Sum of all angles of a triangle is 180°.
Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Solve the equation 4x2 – 9x + 3 = 0, using the quadratic formula.
Chapter:
Find the nature of the roots of the equation `3x^2 - 4sqrt(3)x + 4 = 0`.
Chapter:
In a trapezium ABCD, AB || DC and its diagonals intersect at O. Prove that `(OA)/(OC) = (OB)/(OD)`.
Chapter:
A box contains 120 discs, which are numbered from 1 to 120. If one disc is drawn at random from the box, find the probability that:
- it bears a 2-digit number.
- the number is a perfect square.
Chapter:
Verify that sin 2A = `(2 tan A)/(1 + tan^2A)`, for A = 30°.
Chapter:
Using prime factorisation, find the HCF of 180, 140 and 210.
Chapter:
If α, β are zeroes of the polynomial 8x2 – 5x – 1, then form a quadratic polynomial in x whose zeroes are `2/α` and `2/β`.
Chapter:
Find the zeroes of the polynomial p(x) = 3x2 + x – 10 and verify the relationship between the zeroes and its coefficients.
Chapter:
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Find length and breadth of a rectangular park whose perimeter is 100 m and area is 600 m2.
Chapter:
Three measuring rods are of lengths 120 cm, 100 cm and 150 cm. Find the least length of a fence that can be measured an exact number of times, using any of the rods. How many times each rod will be used to measure the length of the fence?
Chapter:
AB and CD are diameters of a circle with centre O and radius 7 cm. If ∠BOD = 30°, then find the area and perimeter of the shaded region.
Chapter:
Prove that `tan θ/(1 - cot θ) + cot θ/(1 - tan θ) = sec θ "cosec" θ + 1`.
Chapter:
Find the A.P. whose third term is 16 and seventh term exceeds the fifth term by 12. Also, find the sum of first 29 terms of the A.P.
Chapter:
Find the sum of the first 20 terms of an A.P. whose nth term is given by an = 5 + 2n. Can 52 be a term of this A.P.?
Chapter:
Solve the following pair of linear equations by the graphical method:
2x + y = 9 and x – 2y = 2
Chapter:
Nidhi received a simple interest rate of 1,200 when she invested ₹ x at 6% p.a. and ₹ y at 5% p.a. for 1 year. Had she invested ₹ x at 3% p.a. and ₹ y at 8% p.a. for that year, she would have received simple interest of ₹ 1,260. Find the values of x and y.
Chapter:
The given figure shows a circle with centre O and radius 4 cm circumscribed by ΔABC. BС touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.
Chapter:
PA and PB are tangents drawn to a circle with centre O. If ∠AOB = 120° and OA = 10 cm, then
- Find ∠OPA. (1)
- Find the perimeter of ΔOAP. (3)
- Find the length of chord AB. (1)
Chapter:
The angles of depression of the top and the foot of a 9 m tall building from the top of a multistoreyed building are 30° and 60°, respectively. Find the height of the multi-storeyed building and the distance between the two buildings. (Use `sqrt(3)` = 1.73).
Chapter:
Find the ‘mean’ and ‘mode’ of the following data:
| Class | 15 − 20 | 20 − 25 | 25 − 30 | 30 − 35 | 35 − 40 | 40 − 45 |
| Frequency | 12 | 10 | 15 | 11 | 7 | 5 |
Chapter:
 A triangular window of a building is shown above. Its diagram represents a ΔABC with ∠A = 90° and AB = AC. Points P and R trisect AB and PQ || RS || AС. |
Based on the above, answer the following questions:
- Show that ΔBPQ ~ ΔBAC. (1)
- Prove that PQ = `1/3` AC. (1)
-
- If AB = 3 m, find the lengths of BQ and BS. Verify that BQ = `1/2` BS. (2)
OR - Prove that `BR^2 + RS^2 = 4/9 BC^2`. (2)
- If AB = 3 m, find the lengths of BQ and BS. Verify that BQ = `1/2` BS. (2)
Chapter:
|
|
Based on the above, answer the following questions:
- Find the dimensions of the cuboidal box. (1)
- Find the total outer surface area of the box. (1)
-
- Find the difference between the capacity of the bowl and the volume of the box. (Use π = 3.14). (2)
OR - The inner surface of the bowl and the thickness is to be painted. Find the area to be painted. (2)
- Find the difference between the capacity of the bowl and the volume of the box. (Use π = 3.14). (2)
Chapter:
|
Gurveer and Arushi built a robot that can paint a path as it moves on graph paper. Some coordinates of points are marked on it. It starts from (0, 0), moves to the points listed in order (in straight lines) and ends at (0, 0).
Arushi entered the points P(8, 6), Q(12, 2) and S(–6, 6) in order. The path drawn by the robot is shown in the figure. |
Based on the above, answer the following questions:
- Determine the distance OP. (1)
- QS is represented by the equation 2x + 9y = 42. Find the coordinates of the point where it intersects the y-axis. (1)
-
- Point R(48, y) divides the line segment OP in a certain ratio; find the ratio. Hence, find the value of y. (2)
OR - Using the distance formula, show that `(PQ)/(OS) = 2/3`. (2)
- Point R(48, y) divides the line segment OP in a certain ratio; find the ratio. Hence, find the value of y. (2)
Chapter:
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