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CAT Exam  >  CAT Test  >  Level-wise Tests  >  Test Level 2: Trigonometry - 1 - CAT MCQ

Test Level 2: Trigonometry - 1 Solved MCQs CAT


MCQ Practice Test & Solutions: Test Level 2: Trigonometry - 1 (10 Questions)

You can prepare effectively for CAT Level-wise Tests for CAT with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test Level 2: Trigonometry - 1". These 10 questions have been designed by the experts with the latest curriculum of CAT 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Test Level 2: Trigonometry - 1 - Question 1
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Find the value of (cosθ cos(90 - θ) secθ) ÷ (tanθ sin (90 - θ)).

Detailed Solution: Question 1

(cosθ cos(90 - θ) secθ) ÷ (tanθ sin (90 - θ))
= cosθ sinθ secθ ÷ tanθ cosθ
= cosθ sinθ secθ ÷ cosθ sinθ secθ
= 1 

Test Level 2: Trigonometry - 1 - Question 2
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If a = x sinθ + y cosθ and b = y sinθ - x cosθ, then y2 - a2 is equal to

Detailed Solution: Question 2

a = x sinθ+ y cosθ
b = y sinθ- x cosθ
y2 - a2 = y2 - (x sinθ+ y cosθ)2
= y2 - x2 sin2θ - y2 cos2θ - 2xy sinθ cosθ
= y2 sin2θ - x2 sin2θ - 2xy sinθ cosθ
= y2 sin2θ + x2 cos2θ - x2 - 2xy sinθ cosθ
= (y sinθ - x cosθ)2 - x2
= b2 - x2

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Test Level 2: Trigonometry - 1 - Question 3
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If sin (π cos x) = cos (π sin x), then x equals

Detailed Solution: Question 3

Given: sin (π cos x) = cos (π sin x)

Test Level 2: Trigonometry - 1 - Question 4
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In the given figure, AB is the height of a tree. C and D are the two points in a straight line on the ground at b units and a units respectively away from the tree. What is the height of the tree (AB)?

Detailed Solution: Question 4

In ΔABC
AB/BC = tan 60°
AB = √3b units
In Δ ABD
AB/BD = tan 30°
AB = a/√3 units
Now AB × AB = √3b × a/√3 units2 
AB2 = ab units2
AB = √ab units

Test Level 2: Trigonometry - 1 - Question 5
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A man on the top of a tower observes a car moving towards the base of the tower at an angle of depression α. Ten minutes later, the angle of depression of the car is found to be β. If the tangent of angle α. is equal to 1/√5, co-tangent of angle β is equal to 1/√5 and the car is moving with a uniform speed, find the total time taken by the car to reach the base of the tower.

Detailed Solution: Question 5


Distance travelled in 10 minutes = CD = x metres

Solving (i) and (ii), we get

CB + x = 5CB
x = 4CB
or, CB = x/4 metres
Total time taken to cover a distance of x/4 metres 

Test Level 2: Trigonometry - 1 - Question 6
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Detailed Solution: Question 6



Multiply and divide by 2,

Test Level 2: Trigonometry - 1 - Question 7
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If  then the value of sin is

Detailed Solution: Question 7



The componendo - dividendo method state that
Using above theorem in equation (1) we get

Test Level 2: Trigonometry - 1 - Question 8
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The angles of elevation of the top of the tower, as observed from each of the points A, B and C on the ground, form a triangle at the same angle α. If R is the circum-radius of the triangle ABC, then the height of the tower is

Detailed Solution: Question 8

The tower makes equal angles at the vertices of the triangle.
Therefore, foot of the tower is at the circumcentre.
From ΔOAP, we have tanα = OP/OA
⇒ OP = OA tan α
⇒ OP = R tan α

Test Level 2: Trigonometry - 1 - Question 9
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If sin x + cos y = a and cos x + sin y = b, then what will be the value of tan (x - y)/2 ?

Detailed Solution: Question 9


Test Level 2: Trigonometry - 1 - Question 10
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A vertical building and a tower are on the same ground level. From the top of the building, the angle of elevation of the top of the tower is 45° and the angle of depression of the foot of the tower is 60°. Find the height of the tower, if the height of the building is 30 m.

Detailed Solution: Question 10

In the diagram, BC = 30 m = DE, ∠ABD = 45° and ∠EBD = 60°.

Let AD = x m and AE = (x + 30) m.
In right-angled ΔABD,
tan 45° = AD/BD
⇒ 1 = x/BD ⇒ BD = x m … (1)
In right-angled ΔEBD,
tan 60° = DE/BD

From equations (1) and (2), we get

∴ Height of the tower = AE = (x + 30) m
= (10√ + 30) m
= (10 × 1.732 + 30) m = 47.32 m

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About this CAT Practice Test

This test contains 10 MCQs on Test Level 2: Trigonometry - 1 with detailed solutions for each question. It is part of the Level-wise Tests for CAT course on EduRev, designed to align with the current CAT syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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