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Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - JEE MCQ


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16 Questions MCQ Test Chapter-wise Tests for JEE Main & Advanced - Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations for JEE 2024 is part of Chapter-wise Tests for JEE Main & Advanced preparation. The Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations questions and answers have been prepared according to the JEE exam syllabus.The Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations below.
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Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 1

 The period of sin2θ is [2002]  

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 1

 ;  Period

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 2

The number of solution of tan x + sec x = 2cos x in [0, 2π) is [2002]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 2

The given equation is tanx + secx = 2 cos x;
⇒ sin x + 1 = 2cos2 x ⇒ sin x + 1 = 2(1 – sin2 x);
⇒ 2sin2x + sin x – 1= 0;
⇒ (2sin x – 1)(sin x + 1) = 0 ⇒ sin x =   , –1.;
⇒ x = 30°, 150°, 270°

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 3

Which one is not periodic [2002]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 3

∵ cos is non periodic

∴ cos + cos 2x can not be periodic.

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 4

Let a, b be such that p < a - b < 3p. If and then the value of [2004]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 4

.....(1)

.....(2)

Square and add (1) and (2)

 

 

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 5

If   then the difference between the maximum and minimum values of u2 is given by [2004]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 5

u2 = a2 + b

Now (a 4 + b4 ) cos2θ sin 2θ + a 2b 2 (cos 4θ+ sin4θ)

= (a4 + b4 ) cos 2θ sin2θ + a 2 b 2 (1 - 2 cos 2θ sin2θ)

= (a4 + b4 - 2a b2) cos2θ sin 2θ+ a 2  b2

…(2)

∴ from (1) , (2) and (3)

Minimum value of u2 = a 2 + b2

Maximum value of u2

= a 2 + b2

= a 2 + b2 = 2(a 2+b2)

∴ Max value - Min value

= 2(a2 + b2 ) - (a +b2 ) = (a-b)2

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 6

A line makes the same angle θ, with each of the x and z axis.
If the angle β, which it makes with y-axis, is such that sin 2β = 3 sin 2θ, then cos2θ equals [2004]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 6

The direction cosines of the line are cosθ, cosβ, cosθ

∴ cos 2θ + cos 2β + cos 2θ = 1

⇒ 2 cos 2θ = sin 2β = 3 sin 2θ (given)

⇒ 2 cos 2θ = 3 - 3 cos 2θ

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 7

The number of values of x in the interval [0, 3π] satisfying the equation 2 sin 2 x + 5 sinx - 3 =0 is [2006]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 7

2 sin 2 x + 5 sinx - 3=0

⇒ (sin x + 3)(2 sinx - 1) = 0            

⇒ sin x =   and sin x ≠-3

∴ In [0, 3π] , x has 4 values.

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 8

If 0 < x < π and cosx + sin x = , then tan x is [2006]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 8

⇒ 3 tan 2 x + 8 tanx + 3= 0

⇒ 3 tan 2 x + 8 tanx + 3= 0

as  tan x <0  

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 9

Let A and B denote the statements A : cosα + cosβ + cosγ = 0 B : sinα + sinβ + sinγ = 0

If cos (β – γ) + cos (γ – α) + cos (α – β) =       then : [2009]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 9

We have

cos (β – γ) + cos (γ – α) + cos (α – β) =

⇒ 2 [cos (β – γ) + cos (γ – α) + cos (α – β)] + 3 = 0

⇒ 2 [cos (β – γ) + cos (γ – α) + cos (α – β)]

+ sin2α + cos2α + sin2β + cos2β + sin2γ + cos2γ = 0

⇒ [sin2α + sin2β + sin2γ + 2 sinα  sinβ + 2 sinβ sinγ

+ 2 sinγ sinα ] + [cos2α + cos2β + cos2γ + 2cosα cosβ

+ 2 cosβ cosγ + 2cosγ cosα] = 0

⇒ [sinα + sinβ + sinγ]2 + (cos2α + cosβ + cos2γ )2= 0

⇒ sinα + sinβ + sinγ = 0 and cosα + cosβ + cosγ =0

∴ A and B both are true.

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 10

Let and   sin  where  Then tan 2α  = [2010]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 10

 

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 11

If A = sin2 x + cos4x, then for all real x : [2011]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 11

A = sin 2 x+ cos4x = sin 2 x + cos 2 x(1- sin2x)

 

Now 

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 12

In a ΔPQR, If 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then  the angle R is equal to : [2012]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 12

Given 3 sin P + 4cos Q = 6 ...(i)

4 sin Q + 3cos P = 1 ...(ii)

Squaring and adding (i) & (ii) we get

9 sin2 P + 16cos2Q + 24 sin P cos Q

+ 16 sin2Q + 9cos2 P + 24 sin Q cos P = 36 + 1 = 37

⇒ 9 (sin2P + cos2P) + 16 (sin2 Q + cos2 Q) + 24 (sinP cosQ + cosP sinQ) = 37

⇒ 9 + 16 + 24 sin ( P + Q) = 37

[∵ sin2θ + cos2θ = 1 and sinα cos B + cos2α sinβ = sin (A + B)]

 

(∵P + Q + R = p)

If  R =then 0 < P,Q <

⇒ cos Q <1 and sin P < 

⇒ 3 sin P + 4 cos Q < which is not true.

So R  = 

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 13

A B C D is a trapezium such that A B and CD are parallel and BC ⊥ CD. If ΔADB = θ, BC = p and CD = q, then AB is equal to : [JEE M 2013]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 13

From Sine Rule

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 14

The expression           can be written as :[JEE M 2013]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 14

Given expression can be written as

=  1 + sec A cosec AA

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 15

Let   where x ∈ R and k ≥ 1.Then f4 (x) - f6 (x) equals [JEE M 2014]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 15

Let  Consider

 

 

Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 16

If 0 ≤ x < 2p, then the number of real values of x, which satisfy the equation cos x + cos 2x + cos 3x + cos 4x = 0 is: [JEE M 2016]

Detailed Solution for Test: JEE Main 35 Year PYQs- Trigonometric Functions & Equations - Question 16

cos x + cos 2x + cos 3x + cos 4x = 0

⇒ 2 cos 2x cos x + 2 cos 3x cos x = 0

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