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.
The 20th term of the A.P.: `10sqrt(2), 6sqrt(2), 2sqrt(2),...` is:
`-76 + 10sqrt(2)`
`-62sqrt(2)`
`-66sqrt(2)`
`86sqrt(2)`
Chapter:
If sec θ – tan θ = 2, then sec θ + tan θ is equal to ______.
`1/2`
`sqrt(2)`
`1/sqrt(2)`
2
Chapter:
PQ and PR are tangents to the circle of radius 3 cm and centre O. If the length of each tangent is 4 cm, then the perimeter of ΔOQP is:
5 cm
12 cm
9 cm
8 cm
Chapter:
The value of m for which the lines 14x + my = 20 and –3x + 2y = 16 are parallel is ______.
`-3/14`
`-7/3`
`-28/3`
`-3/28`
Chapter:
If the nth term of an A.P. is 5n – 6, then its common difference is ______.
–6
5n
5
6
Chapter:
The distance between the points (2, –7) and (–2, –1) is ______.
10
`2sqrt(13)`
8
`4sqrt(13)`
Chapter:
The length of the arc subtending an angle of 210° at the centre of the circle is `44/3` cm. The radius of the circle is ______.
`2sqrt(2)` cm
4 cm
8 cm
`1/4` cm
Chapter:
A card is drawn at random from a well shuffled deck of 52 playing cards. The probability that drawn card shows number ‘9’ is ______.
`1/26`
`4/13`
`1/52`
`1/13`
Chapter:
In ΔABC, PQ || BC. It is given that AP = 2.4 cm, PB = 3.6 cm and BC = 5.4 cm. PQ is equal to:
2.7 cm
1.8 cm
3.6 cm
2.16 cm
Chapter:
PA and PB are tangents to a circle with centre O. If ∠AOB = 105°, then ∠OAP + ∠APB is equal to:
75°
175°
180°
165°
Chapter:
Two dice are rolled together. The probability that at least one of them shows a six is ______.
`12/36`
`5/36`
`11/36`
`6/36`
Chapter:
The curved surface area of a cone with base radius 7 cm is 550 cm2. The slant height of the cone is ______.
25 cm
14 cm
20 cm
24 cm
Chapter:
If tan A = `1/2`, then sin A is equal to ______.
`2/sqrt(5)`
`1/sqrt(3)`
`1/sqrt(5)`
1
Chapter:
If `sqrt(2) sin θ = 1`, then cot θ × cosec θ is equal to ______.
`1/sqrt(2)`
`1/(2sqrt(2))`
`sqrt(2)`
`1/2`
Chapter:
Three coins are tossed together. The probability that only one coin shows tail, is ______.
`1/2`
`3/8`
`7/8`
1
Chapter:
In the given figure, the graph of p(x) is shown. Number of distinct zeroes of p(x) is:
0
1
2
many
Chapter:
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Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. The ratio of their radii is ______.
`sqrt(2) : 1`
1 : 2
1 : 4
`1 : sqrt(2)`
Chapter:
α, β are zeroes of the polynomial 2x2 + 5x + 1. The value of `(1/α + 1/β)` is ______.
`-5/4`
5
`5/4`
–5
Chapter:
Assertion (A): If E is an event such that P(E) = `1/999`, then `P(barE)` = 0.001.
Reason (R): `P(E) + P(barE) = 1`
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Assertion (A): Median marks of students in a class test is 16. It means half of the class got marks less than 16.
Reason (R): Median divides the distribution in two equal parts.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
Two chords BA and CD intersect at point P outside the circle. Prove that ΔPDA ~ ΔPBC.
Chapter:
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact to the centre.
Chapter:
Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Chapter:
Find the ratio in which point P(–1, m) divides the line segment joining the points A(2, 5) and В(–5, –2). Hence, find the value of m.
Chapter:
Show that 45n can not end with the digit 0, n being a natural number. Write the prime number ‘a’ which on multiplying with 45n makes the product end with the digit 0.
Chapter:
A coin is dropped at random on the rectangular region shown in the figure. What is the probability that it will land inside the circle with radius 0.7 m?
Chapter:
A die is thrown twice. What is the probability that (i) the difference between two numbers obtained is 3? (ii) the sum of the numbers obtained is 8?
Chapter:
If points A(–5, y), В(2, –2), C(8, 4) and D(x, 5) taken in order, form a parallelogram ABCD, then find the values of x and y. Hence, find the lengths of the sides of the parallelogram.
Chapter:
A(6, –3), В(0, 5) and C(–2, 1) are vertices of ΔАВС. Points P(3, 1) and Q(2, –1) lie on sides AB and AC respectively. Check whether `(AP)/(PB) = (AQ)/(QC)`.
Chapter:
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A chord of a circle of radius 10 cm subtends an angle of 60° at the centre O. Find the area of the shaded region. `("Use" sqrt(3) = 1.73, sqrt(2) = 1.41 and π = 3.14)`
Chapter:
Prove that a parallelogram circumscribing a circle is a rhombus.
Chapter:
Find the sum of the A.P. 7, `10 1/2`, 14, ... 84.
Chapter:
If the sum of first n terms of an A.P. is given by `S_n = n/2 (2n + 8)`. Then, find its first term and common difference. Hence, find its 15th term.
Chapter:
Find the zeroes of the polynomial p(x) = 4x2 – 4x – 3 and verify the relationship between zeroes and its coefficients.
Chapter:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.
Chapter:
In a ΔABC, P and Q are points on AB and AC respectively such that PQ || BC. Prove that the median AD, drawn from A to BC, bisects PQ.
Chapter:
As observed from the top of a 70 m high lighthouse from the sea level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. (Use `sqrt(3)` = 1.73)
Chapter:
It is given that p2x2 + (p2 – q2)x – q2 = 0; (p ≠ 0).
- Show that the discriminant (D) of the above equation is a perfect square.
- Find the roots of the equation.
Chapter:
Three consecutive positive integers are such that the sum of the square of the smallest and the product of the other two is 67. Find the numbers, using the quadratic equation.
Chapter:
Find the ‘median’ and ‘mode’ of the following data:
| Class | 100 – 105 | 105 – 110 | 110 – 115 | 115 – 120 | 120 – 125 | 125 – 130 |
| Frequency | 6 | 8 | 10 | 4 | 9 | 3 |
Chapter:
|
Rahim and Nadeem are two friends whose plots are adjacent to each other. Rahim’s son made a drawing of the plots with necessary details. It is decided that Rahim will fence the triangular plot ABC and Nadeem will fence along the sides AF, FE and BE.
|
Observe the diagram carefully and answer the following questions:
(Use `sqrt(2)` = 1.41 and `sqrt(3)` = 1.73)
- Find the length of BC. (1)
- Find the length of AG. (1)
-
- Calculate perimeter of ΔАВС. (2)
OR - Calculate the length of (AF + FE + EB). (2)
- Calculate perimeter of ΔАВС. (2)
Chapter:
|
Playing in a ball pool is good entertainment for kids. Suhana bought 600 new balls of diameter 7 cm to fill in the pool for her kids. The cuboidal box containing 600 balls has dimensions 42 cm × 91 cm × 50 cm (l × b × h).
|
Based on the above information, answer the following questions.
- Find the volume of one ball. (1)
- 10 balls are painted with neon colours. Determine the area of painted surface. (1)
-
- Find the volume of empty space in the box. (2)
OR - The lowermost layer of the balls covers the base of the box, edge to edge, when the balls are placed evenly adjacent to each other. (2)
- How much area is covered by one ball?
- How many balls are there in the lowermost layer?
- Find the volume of empty space in the box. (2)
Chapter:
|
A telecommunication company came up with two plans- plan A and plan B for its customers. The plans are represented by linear equations where ‘t’ represents the time (in minutes) bought and ‘C’ represents the cost. The equations are:
Plant B : 3C = 10t + 300 |
Based on the above information, answer the following questions:
- If you purchase plan B, how much initial amount you have to pay? (1)
- Charu purchased plan A. How many minutes she bought for ₹250? (1)
-
- At how many minutes, do both the plans charge the same amount? What is that amount? (2)
OR - Which plan is better if you want to buy 60 minutes? Give reason for your answer. (2)
- At how many minutes, do both the plans charge the same amount? What is that amount? (2)
Chapter:
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