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 very carefully and strictly follow them:
- This question paper contains 38 questions. All questions are compulsory.
- This Question Paper is divided into FIVE Sections - Section A, B, C, D, and E.
- In Section - A question number 1 to 18 are Multiple Choice Questions (MCQs) and question number 19 & 20 are Assertion Reason based question of 1 mark each.
- In Section - B questions number 21 to 25 are Very Short-Answer (VSA) type questions of 2 marks each.
- In Section - C questions number 26 to 31 are Short Answer (SA) type questions carrying 3 marks each.
- In Section - D questions number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
- In Section - E questions number 36 to 38 are Case Study based integrated questions carrying 4 marks each. Internal choice is provided in 2 marks questions 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 diagrams wherever required. Take π = `22/7` wherever required if not stated.
- Use of a calculator is NOT allowed.
For a circle with centre O and radius 5 cm, which of the following statements is true?
P: Distance between every pair of parallel tangents is 5 cm.
Q: Distance between every pair of parallel tangents is 10 cm.
R: Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
S: There does not exist a point outside the circle from where length of tangent is 5 cm.
P
Q
R
S
Chapter:
In the adjoining figure, AP and AQ are tangents to the circle with centre O. If reflex ∠POQ = 210°, the value of 2x is:
30°
60°
120°
300°
Chapter:
If x = 2 sin 60° cos 60° and y = sin2 30° − cos2 30° and x2 = ky2, the value of k is ______.
`sqrt3`
`-sqrt3`
3
−3
Chapter:
A peacock sitting on the top of a tree of height 10 m observes a snake moving on the ground. If the snake is `10sqrt3` m away from the base of the tree, then angle of depression of the snake from the eye of the peacock is ______.
30°
45°
60°
90°
Chapter:
If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is ______.
1 : 1
1 : 3
2 : 1
3 : 1
Chapter:
If the mode of some observations is 10 and the sum of the mean and median is 25, then the mean and median, respectively, are ______.
12 and 13
13 and 12
10 and 15
15 and 10
Chapter:
If the maximum number of students has obtained 52 marks out of 80, then ______.
52 is the mean of the data.
52 is the median of the data.
52 is the mode of the data.
52 is the range of the data.
Chapter:
The system of equations y + a = 0 and 2x = b has ______.
No solution
`(-a, b/2)` as its solution
`(b/2, -a)` as its solution
Infinite solutions
Chapter:
In a right triangle ABC, right-angled at A, if sin B = `1/4`, then the value of sec B is ______.
4
`sqrt15/4`
`sqrt15`
`4/sqrt15`
Chapter:
`sqrt0.4` is a/an ______.
natural number
integer
rational number
irrational number
Chapter:
Which of the following cannot be the unit digit of 8n, where n is a natural number?
4
2
0
6
Chapter:
Which of the following equations does not have a real root?
x2 = 0
2x − 1 = 3
x2 + 1 = 0
x3 + x2 = 0
Chapter:
If the zeroes of the polynomial `ax^2+bx+(2a)/b` are reciprocal of each other, then the value of b is ______.
2
`1/2`
−2
`-1/2`
Chapter:
The distance of point P(3a, 4a) from the y-axis is ______.
3a
−3a
4a
−4a
Chapter:
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In the adjoining figure, PQ || XY || BC, AP = 2 cm, PX = 1.5 cm and BX = 4 cm. If QY = 0.75 cm, then AQ + CY is:
6 cm
4.5 cm
3 cm
5.25 cm
Chapter:
Given ΔABC ~ ΔPQR, ∠A = 30° and ∠Q = 90°. The value of (∠R + ∠B) is ______.
90°
120°
150°
180°
Chapter:
Two coins are tossed simultaneously. The probability of getting atleast one head is ______.
`1/4`
`1/2`
`3/4`
1
Chapter:
In the adjoining figure, PA and PB are tangents to a circle with centre O such that ∠P = 90°. If AB = `3sqrt2` cm, then the diameter of the circle is:
`3sqrt2` cm
`6sqrt2` cm
3 cm
6 cm
Chapter:
In an experiment of throwing a die,
Assertion (A):
Event E1: Getting a number less than 3.
Event E2: Getting a number greater than 3 are complementary events.
Reason (R): If two events E and F are complementary events, then P(E) + P(F) = 1
Both Assertion (A) and Reason (R) are true, and Reason (R) is a 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): For two odd prime numbers x and y, (x ≠ y), LCM (2x, 4y) = 4xy.
Reason (R): LCM (x, y) is a multiple of HCF (x, y).
Both Assertion (A) and Reason (R) are true, and Reason (R) is a correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Chapter:
If a sec θ + b tan θ = m and b sec θ + a tan θ = n, prove that a2 + n2 = b2 + m2.
Chapter:
Use the identity sin2 A + cos2 A = 1 to prove that tan2 A + 1 = sec2 A. Hence, find the value of tan A when sec A = `5/3`, where A is an acute angle.
Chapter:
Prove that the abscissa of a point P, which is equidistant from points with coordinates A(7, 1) and B(3, 5) is 2 more than its ordinate.
Chapter:
In the adjoining figure, AP = 1 cm, BP = 2 cm, AQ = 1.5 cm, and AC = 4.5 cm.
Prove that ΔАPQ ~ ΔАВС. Hence, find the length of PQ if BC = 3.6 cm.
Chapter:
A bag contains balls numbered 2 to 91 such that each ball bears a different number. A ball is drawn at random from the bag. Find the probability that:
- It bears a 2-digit number.
- It bears as a multiple of 1.
Chapter:
Solve the following pair of equations algebraically:
101x + 102y = 304
102x + 101y = 305
Chapter:
In a pair of supplementary angles, the greater angle exceeds the smaller by 50°. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.
Chapter:
Check whether the given system of equations is consistent or not. If consistent, solve graphically.
x − 2y = 0
2x + y = 0
Chapter:
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If the points A(6, 1), B(p, 2), C(9, 4) and D(7, q) are the vertices of a parallelogram ABCD, then find the values of p and q. Hence, check whether ABCD is a rectangle or not.
Chapter:
Prove that `(cos θ - 2 cos^3 θ)/(sin θ - 2 sin^3 θ) + cot θ = 0`.
Chapter:
Given that sin θ + cos θ = x, prove that sin4 θ + cos4 θ = `(2-(x^2-1)^2)/2`.
Chapter:
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If ∠OPQ = 15° and ∠PTQ = θ, then find the value of sin 2θ.
Chapter:
Let p, q and r be three distinct prime numbers.
Check whether p × q × r + q is a composite number or not.
Further, give an example for 3 distinct primes p, q, r such that
- p × q × r + 1 is a composite number.
- p × q × r + 1 is a prime number.
Chapter:
Find the zeroes of the polynomial r(x) = 4x2 + 3x − 1. Hence, write a polynomial whose zeroes are the reciprocals of the zeroes of polynomial r(x).
Chapter:
If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side.
State and prove the converse of the above statement.
Chapter:
In the adjoining figure, ΔCAB is a right triangle, right angled at A and AD ⊥ BC. Prove that ΔADB ~ ΔCDA. Further, if BC = 10 cm and CD = 2 cm, find the length of AD.
Chapter:
Fermentation tanks are designed in the form of a cylinder mounted on a cone, as shown below:
The total height of the tank is 3.3 m, and the height of the conical part is 1.2 m. The diameter of the cylindrical as well as conical part is 1 m. Find the capacity of the tank. If the level of liquid in the tank is 0.7 m from the top, find the surface area of the tank in contact with liquid.
Chapter:
The population of lions was noted in different regions across the world in the following table:
| Number of lions | Number of regions |
| 0 − 100 | 2 |
| 100 − 200 | 5 |
| 200 − 300 | 9 |
| 300 − 400 | 12 |
| 400 − 500 | x |
| 500 − 600 | 20 |
| 600 − 700 | 15 |
| 700 − 800 | 9 |
| 800 − 900 | y |
| 900 − 1000 | 2 |
| 100 |
If the median of the given data is 525, find the values of x and y.
Chapter:
There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter.
An entry gate is to be constructed at the point P on the boundary of the park such that the distance of P from A is 35 m more than the distance of P from B. Find the distance of point P from A and B, respectively.
Chapter:
Find the smallest value of p for which the quadratic equation x2 − 2(p + 1)x + p2 = 0 has real roots. Hence, find the roots of the equation so obtained.
Chapter:
|
The Statue of Unity, situated in Gujarat, is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of the Statue of Unity using it. He noted the following observations from two places: Situation I: The angle of elevation of the top of Statue from Place A, which is `80sqrt3` m away from the base of the Statue is found to be 60°. Situation II: The angle of elevation of the top of Statue from Place B, which is 40 m above the ground, is found to be 30° and entire height of the statue, including the base, is found to be 240 m.
|
Based on the given information, answer the following questions:
- Represent Situation I with the help of a diagram. (1)
- Represent Situation II with the help of a diagram. (1)
-
- Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation I. (2)
OR - Find the horizontal distance of point B (Situation II) from the Statue and the value of tan α, where α is the angle of elevation of the top of the base of the Statue from point B. (2)
- Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation I. (2)
Chapter:
|
Anurag purchased a farmhouse which is in the form of a semicircle of diameter 70 m. He divides it into three parts by taking a point P on the semicircle in such a way that ∠PAB = 30° as shown in the following figure, where O is the centre of the semicircle.
In part I, he planted saplings of the Mango tree, in part II, he grew tomatoes, and in part III, he grew oranges. |
Based on the given information, answer the following questions.
- What is the measure of ∠POA? (1)
- Find the length of wire needed to fence the entire piece of land. (1)
-
- Find the area of the region in which saplings of the Mango tree are planted. (2)
OR - Find the length of wire needed to fence the region III. (2)
- Find the area of the region in which saplings of the Mango tree are planted. (2)
Chapter:
|
In order to organise, Annual sports Day, a school prepared an eight-lane running track with an integrated football field inside the track area as shown below:
The length of the innermost lane of the track is 400 m and each subsequent lane is 7.6 m longer than the preceding lane. |
Based on the given information, answer the following questions, using the concept of arithmetic progression.
- What is the length of the 6th lane? (1)
- How long is the 8th lane than that of 4th lane? (1)
-
- While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student. (2)
OR - A student took one round each in lane 4 to lane 8. Find the total distance covered by the student. (2)
- While practicing for a race, a student took one round each in first six lanes. Find the total distance covered by the student. (2)
Chapter:
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