SILVER OAKS SCHOOL
CLASS TEST PAPER (2026–27)
SUBJECT: MATHEMATICS
CLASS: X CODE: 041
(STANDARD)
CHAPTER 9: SOME APPLICATIONS OF
MAX MARKS: 16 TIME: 45 MINS
TRIGONOMETRY
Student's Name:
Roll No: Date:
GENERAL INSTRUCTIONS:
1. All questions are compulsory.
2. The question paper consists of 5 questions divided into three sections: A, B, and C.
3. Section A comprises 3 short answer questions (Q1 to Q3).
4. Section B comprises 1 Case-Study based question (Q4) with 4 sub-parts of 1 mark each.
5. Section C comprises 1 long proof question (Q5) carrying 5 marks.
6. Use of calculators is strictly prohibited. Draw neat diagrams wherever required.
SECTION A (7 MARKS)
(Short Answer Type Questions)
Q1. [2 Marks]
A vertical pole of length 6 m casts a shadow 2√3 m long on the ground. Find the angle of elevation of the sun.
Q2. [2 Marks]
From the top of a 75 m high tower, the angle of depression of a car standing on the ground is observed to be 30°.
Find the distance of the car from the base of the tower.
Q3. [3 Marks]
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her
eyes is 45°. What is the height of the chimney?
SECTION B (4 MARKS)
(Case-Study Based Question)
Q4. Read the following text and answer the sub-questions that follow: [4 Marks]
Mr. and Mrs. Chawla visited the historical Qutub Minar in Delhi with their family. Standing at a point on the
ground 30 m away from the foot of the tower, Mr. Chawla observed that the angle of elevation to the top of the
tower was 60°. Meanwhile, Mrs. Chawla, standing on the balcony of a nearby building at a vertical height of 15
m above the ground, looked up at the top of the tower and noted the angle of elevation to be 45°.
(i) What is the height of the Qutub Minar? [1 Mark]
(ii) Find the distance between Mr. Chawla and the top of the Qutub Minar. [1 Mark]
(iii) Calculate the horizontal distance between Mrs. Chawla's building and the Qutub Minar. [1 Mark]
(iv) Find the direct distance (straight-line distance) between Mrs. Chawla on the balcony and the top of the Qutub
Minar. [1 Mark]
SECTION C (5 MARKS)
(Long Answer / Proof Question)
Page 1 of 2
CLASS TEST PAPER (2026–27)
SUBJECT: MATHEMATICS
CLASS: X CODE: 041
(STANDARD)
CHAPTER 9: SOME APPLICATIONS OF
MAX MARKS: 16 TIME: 45 MINS
TRIGONOMETRY
Student's Name:
Roll No: Date:
GENERAL INSTRUCTIONS:
1. All questions are compulsory.
2. The question paper consists of 5 questions divided into three sections: A, B, and C.
3. Section A comprises 3 short answer questions (Q1 to Q3).
4. Section B comprises 1 Case-Study based question (Q4) with 4 sub-parts of 1 mark each.
5. Section C comprises 1 long proof question (Q5) carrying 5 marks.
6. Use of calculators is strictly prohibited. Draw neat diagrams wherever required.
SECTION A (7 MARKS)
(Short Answer Type Questions)
Q1. [2 Marks]
A vertical pole of length 6 m casts a shadow 2√3 m long on the ground. Find the angle of elevation of the sun.
Q2. [2 Marks]
From the top of a 75 m high tower, the angle of depression of a car standing on the ground is observed to be 30°.
Find the distance of the car from the base of the tower.
Q3. [3 Marks]
An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her
eyes is 45°. What is the height of the chimney?
SECTION B (4 MARKS)
(Case-Study Based Question)
Q4. Read the following text and answer the sub-questions that follow: [4 Marks]
Mr. and Mrs. Chawla visited the historical Qutub Minar in Delhi with their family. Standing at a point on the
ground 30 m away from the foot of the tower, Mr. Chawla observed that the angle of elevation to the top of the
tower was 60°. Meanwhile, Mrs. Chawla, standing on the balcony of a nearby building at a vertical height of 15
m above the ground, looked up at the top of the tower and noted the angle of elevation to be 45°.
(i) What is the height of the Qutub Minar? [1 Mark]
(ii) Find the distance between Mr. Chawla and the top of the Qutub Minar. [1 Mark]
(iii) Calculate the horizontal distance between Mrs. Chawla's building and the Qutub Minar. [1 Mark]
(iv) Find the direct distance (straight-line distance) between Mrs. Chawla on the balcony and the top of the Qutub
Minar. [1 Mark]
SECTION C (5 MARKS)
(Long Answer / Proof Question)
Page 1 of 2
