Direct Ratio MCQ Quiz in मल्याळम - Objective Question with Answer for Direct Ratio - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Given: 

2cotθ = 3 

Formula used: 

Sinθ = P/H 

Cosθ = B/H 

Tanθ = P/B 

Cotθ = B/P 

H2 = P2 + B2

where P = Perpendicular 

B = Base 

H = Height 

Calculation: 

2cotθ = 3 

⇒ cotθ = 3/2 

on comparing with (Cotθ = B/P), we get 

⇒ B = 3

⇒ P = 2 

According to Pythagorean theorem

⇒ H² = P² + B²

⇒ H2 = 22 + 32

⇒ H = √13 

⇒ Sinθ = 2/√13  

⇒ Cosθ = 3/√13  

⇒ Tanθ = 2/3 

Putting all the values in the given equation:

= (√13 * 2/√13  - 3 *  2/3 )/ (3 *  2/3 + √13 * 3/√13)

⇒ (2 - 2)/(2 + 3)

⇒ 0

The value of the expression is 0.

Given:

Concept used:

TanA = SinA / CosA

Calculation:

Dividing by CosA we get,

3 TanA + 2 / 3 TanA - 2

Now putting the value of Tan A we get,

⇒ 

⇒ 

∴ The  correct option is 2

Given

tan x = 7/5

Formula used

tan x = P/B

sin x = P/H

cos x = B/H

Calculation

tan x = 7/5 = P/B

H² = P² + B²

H2 = 7² + 5²

H2 = 49 + 25 = 74

h = √74.

⇒ (9 × 7/√74 - 42/5 × 5/√74)/(15 × 7/√74 + 21 × 5/√74)

⇒ (21/√74)/(210/√74)

⇒ 21/210

⇒ 0.1

The value is 0.1

Given

a cot θ = b

Calculation

Dividing the whole equation by cosθ, we get:

⇒ (b - asinθ/cosθ)/(b + asinθ/cosθ)

⇒ (b - atanθ)/(b + atanθ)

⇒ (b - a × a/b)/(b + a × a/b) 

⇒ (b² - a²)/(b² + a²) 

The value of the expression is  (b2 - a2)/(b2 + a2) .

Given:

Cos A = 9/41 

Formula used:

 cot A = cos A/sin A

Cos² A + sin² A = 1

Calculation:

Cos2 A + sin2 A = 1

⇒ ( 9/41)² + sin2 A = 1

⇒  sin2 A = 1 - 81/1681

 ⇒ sin2 A = 1600/1681

⇒  sin A = 40/41

⇒ cot A = cos A/sin A

 ⇒ cot A = 9/40

∴ Option 1 is the correct answer.

Given:

sin θ = 

Concept used:

Calculation:

sin θ = 

⇒ sinθ = sin 30°

So, θ = 30°

3cos θ - 4 cos3 θ

⇒ 3 ×  - 4 × 

⇒ 

⇒ 0

∴ The required answer is 0.

Given:

The expression to evaluate is:

Formula used:

The cosecant function is defined as:

Properties used:

is the cosine of angle x.

Step 1: Substitute the value of cosecant using the identity into the expression:

We now have:

Step 2: The expression becomes:

Step 2: Apply the identity to both terms:

Step 3: Simplify the expression using the identity:

Step 4: Simplify the terms:

∴ The value of the expression is 

Given:

7tan θ = 3

Calculation:

Divide by 'cos θ' in both numerator and denominator,

⇒ 

⇒ 

⇒ [5 × 3/7 - 1] / [5 × 3/7 + 2]

⇒ [15/7 - 1] / [15/7 + 2]

⇒ [(15 - 7)/7] / [(15 + 14)/7]

⇒ [8/7] / [29/7]

⇒ 8/29

∴ The correct answer is option (1).

Given:

Tan α = 6

Concept used:

Tan θ = P/B

Sec θ = H/B

Where, P = perpendicular; B = base; H = hypotenuse

Formula used:

Pythagorean theorem:

H² = P² + B²

Where, P = perpendicular; B = base; H = hypotenuse

Calculation:

Tan α = 6/1 = P/B

Using Pythagorean theorem:

⇒ H2 = P2 + B2

⇒ H² = (6)² + (1)²

⇒ H = √37

Sec α = H/B = √37

∴ The correct answer is √37. 

Given:

If 7 cosA = 6

Formula Used:

cosec A = 1/sin A

cot A = cos A/sin A

Calculation:

(cosec A + cot A) / (cosec A - cot A)

⇒ ( + ) / ( - )

⇒  / 

⇒ (1 + cos A) / (1 - cos A)

⇒ (1 + 6/7) / (1 - 6/7)

⇒ (13/7) / (1/7)

⇒ 13 / 1 = 13

∴ The correct answer is option (3).