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.
If HCF (x, 20) = 2 and LCM (x, 20) = 60, then the value of x is ______.
3
6
20
10
Chapter:
The distance between the points (–6, 9) and (2, 7) is ______.
`2sqrt(17)`
`4sqrt(17)`
`2sqrt(5)`
`2sqrt(15)`
Chapter:
If the nth term of an A.P. is 5n – 6, then its common difference is ______.
–6
5n
5
6
Chapter:
One of the zeroes of the polynomial p(x) = kx2 – 9x + 3 is `(-3/2)`. The value of k is ______.
`22/3`
`14/3`
`-14/3`
`-22/3`
Chapter:
Three coins are tossed together. The probability that only one coin shows tail, is ______.
`1/2`
`3/8`
`7/8`
1
Chapter:
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:
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:
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:
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:
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:
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:
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:
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:
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 sin A = `2/3`, then cos A is equal to ______.
`3/2`
`sqrt(5)/3`
`1/3`
`1/sqrt(3)`
Chapter:
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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:
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:
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:
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:
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:
Point P(x, 0) divides the line segment joining the points (2, 8) and (–3, –5) in a certain ratio. Find the ratio and hence find the value of x.
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:
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:
In the given figure, ∠ADE = ∠ACB and `(AD)/(DB) = (AE)/(EC)`. Prove that ΔABC is an isosceles triangle.
Chapter:
Find the zeroes of the polynomial p(x) = 6x2 + 13x – 5 and verify the relationship between its zeroes and the coefficients.
Chapter:
Find the sum of the A.P. 7, `10 1/2`, 14, ... 84.
Chapter:
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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:
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:
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 opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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 ‘mean’ and ‘mode’ of the following data:
| Class | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 | 40 – 45 |
| Frequency | 6 | 16 | 17 | 4 | 5 | 2 |
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:
From a point on the ground, the angle of elevation of the top of a pedestal is 30° and that of the top of the flagstaff fixed on the pedestal is 60°. If the length of the flagstaff is 5 m, then find the height of the pedestal and its distance from the point of observation on the ground. (Use `sqrt(3)` = 1.73)
Chapter:
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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:
|
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:
|
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:
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