Sine Rule MCQ Quiz in मल्याळम - Objective Question with Answer for Sine Rule - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Mar 16, 2025
Latest Sine Rule MCQ Objective Questions
Top Sine Rule MCQ Objective Questions
Sine Rule Question 1:
is equal to
Answer (Detailed Solution Below)
Sine Rule Question 1 Detailed Solution
Concept:
Sine Rule:
In a triangle Δ ABC,
Where,
∠A + ∠B + ∠C = π
Formula used:
- cos(π - θ) = -cos θ
- 1 - sin2θ = cos2θ
- cos(A + B) cos(A − B) = cos2A - sin2Bcos(A+B)cos(A−B)=cos2A−sin2B
Calculation:
We have
From the sine rule,
⇒ sin A = ka, sin B = kb, sin C = kc
Hence, required value
Sine Rule Question 2:
In a triangle ABC, ∠A = 30°, ∠B = 45°, AC = 3√2 cm then find the length BC -
Answer (Detailed Solution Below)
Sine Rule Question 2 Detailed Solution
Formula used -
In a triangle ABC, Sine rule,
(sinA/a) = (sinB/b) = (sinC/c)
Given -
∠A = 30°, ∠B = 45°, AC = 3√2 cm
Solution -
⇒ (sin45°/3√2) = (sin30°/BC)
⇒ (1/6) = {1/(2 BC)}
⇒ BC = 3cm
∴ side BC = 3 cm
Sine Rule Question 3:
If α =
Answer (Detailed Solution Below)
Sine Rule Question 3 Detailed Solution
Concept:
3 sin α - 4 sin3 α = sin 3α
Explanation:
We know,
3 sin α - 4 sin3 α = sin 3α
Since, α =
⇒ 3 sin
⇒ 3 sin α
Sine Rule Question 4:
Comprehension:
Consider the following for the two (02) items that follow:
In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3: 1.
Consider the following statements:
I. The triangle is right-angled.
II. One of the sides of the triangle is 3 times the other.
III. The angles A, C and B of the triangle are in AP.
Which of the statements given above is/are correct?
Answer (Detailed Solution Below)
Sine Rule Question 4 Detailed Solution
Explanation:
We are given the triangle with angles:
Step 1: Check if the sum of the angles is 180°:
This confirms that the angles satisfy the angle sum property of a triangle.
Statement I. The triangle is right-angled.
Since
Statement III: III. The angles A, C and B of the triangle are in AP.
The angles
This confirms that the angles are in AP.
Statement II is not correct because there is no mention of a side being 3 times the other.
∴ The correct answer is Option (I) and (III) are correct.
Hence, the correct answer is Option 3.
Sine Rule Question 5:
Comprehension:
Consider the following for the two (02) items that follow:
In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3: 1.
One of the angles of the triangle is
Answer (Detailed Solution Below)
Sine Rule Question 5 Detailed Solution
Calculation:
We are given the equation for the ratio of sides using the Sine Rule:
Step 3: Use the identity for sin(3x), which is
We have two possible solutions for this equation:
∴ The correct answer is Option (2)
Sine Rule Question 6:
If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of length of the sides of this triangle is:
Answer (Detailed Solution Below)
Sine Rule Question 6 Detailed Solution
Put
Sine Rule Question 7:
In
Answer (Detailed Solution Below)
Sine Rule Question 7 Detailed Solution
We know that
Thus,
Using above relation we can claim that
Sine Rule Question 8:
In
Answer (Detailed Solution Below)
Sine Rule Question 8 Detailed Solution
Calculation
From sine rule
Using equation
But maximum value of
OR
Hence option 3 is correct
Sine Rule Question 9:
If one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is
Answer (Detailed Solution Below)
Sine Rule Question 9 Detailed Solution
Answer : 2
Solution :
In ΔABC, by sine rule,
According to the given condition,
In ΔABC, a = 2 b and
A - B = 60° A = 60° + B
⇒
⇒
⇒ 2 sin B = sin B cos 60° + cos B sin 60°
⇒
⇒
⇒
∴ A = 30° + 60° = 90°
∴ ΔABC is right angled.
Sine Rule Question 10:
In a triangle ABC, with usual notations, if c = 4, then value of
Answer (Detailed Solution Below)
Sine Rule Question 10 Detailed Solution
Concept Used:
1. Cosine Rule:
2. Half-angle formulas:
Calculation:
Given:
In triangle ABC, c = 4
Expression:
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒
⇒ 16
∴ The value of the expression is 16.
Hence option 2 is correct