Home · JEE PYQs · Mathematics · Trigonometry

JEE Trigonometry PYQs with Solutions

66 previous year questions from Trigonometry (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

66 questionsMathematicsAnswers + solutions

About Trigonometry PYQs

Trigonometry has 66 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 66 questions in this list come from Most Important Selected Qs for JEE Advanced (66). Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Trigonometry PYQs with Solutions

About Trigonometry PYQs

Trigonometry questions with solutions

The number of real root(s) of the equation x^2 x=1 lie(s) between 0 and 2 π is/are

If |x^2-(π)/(4)+ x-2|=|x^2-2|+| x|+(π)/(4) then

If 3 x+ (2 x-(7 π)/(6))=-2 , then x is equal to ( where m ∈ I)

What is the minimum value of ( ^4 α)/( ^2 β)+( ^4 β)/( ^2 α) for α, B ≠ (k π)/(2), k ∈ Z ?

If x+ y ≥ α x ∀ x ∈ R then y+ α is equal to

If A, B are the roots of the quadratic equation a b x^2-c^2 x+a b=0 where a, b, c are sides of the A B C then ^2 A+ ^2 B+ ^2 C is

If θ and - θ are the roots of the equation a x^2-b x-c=0 , where a, b, c are the sides of a triangle A B C , then B is equal to

If 2 ^2((π)/(2) ^2 x)=1- (π 2 x), x ≠(2 n+1) (π)/(2), n ∈ I , then

Consider the equation 1+ 3 2 x ^4 x+4 ^2 x + ^4 x+4 ^2 x = 2 ^ -1 ( 2 x) x ∈(-π, π)

Set of values of x of the equation 2 x= ( ^3 x- ^3 x) is -

If 4+ 8- 32+ 768 =a 2 \ left((11 π)/(b)), where a and b are natural numbers then (b)/(a) is divisible by

If a x+ x+1=cosec x then the possible values of x can be

For the equation 2( x- 2 x)- 2 x(1+2 x)+2 x=0, x ∈[0,2 π]-

Which of the following set of values of x satisfies the equation 2^ (2 ^2 x-3 x+1) +2^ (2-2 ^2 x+3 x) =9 ?

If α satisfies the equation 2 2 ^3 x-54 2 ^3 x=19 , then possible value of ( .2 ^2 α+ 2 α) can be equal to:

If f(x)=(3)/(1+ ^2 x)+(9)/(1+ ^2 x) , then :

Which of the following sets can be the subset of the general solution of the equation 1+ 3 x=2 2 x ?

If [ x ] represents the greatest integer less than or equal to x , then which of the following statement is true

If 2 ^2 θ+2 2 =3 cosec^2 θ , where θ ∈(0, π) , then:

For the equation 3 2 x= 2 x+2 (x)/(2)(1+ x) which of the following holds good?

Let f(θ)= (1+(4 θ)/( 6 θ)) (1+(4 2 θ)/( 5 θ)), then:

If α=(1)/(2) \ left(x+(1)/(x)) and \ beta=(1)/(2) left(y+(1)/(y)),( x y 0) x, y, α, β ∈ R then

If x+1=(1)/(2+(1)/(2+(1)/(2+… … ∞))) where x ∈(0,2 π) , then:

If (a+2) α+(2 a-1) α=2 a+1 , where 0 α (π)/(2) and a 1 , then α is equal to -

If ∑_ m=1 ^6 (α+(m-1) (π)/(4)) (α+(m π)/(4))=4 2 , where α ∈(0, π) then α can be:

Let y=( x · 2 x+ 3 x · 6 x+ 4 x · 13 x)/( x · 2 x+ 3 x · 6 x+ 4 x · 13 x) , then:

Let x= θ ^3 θ and y= ^3 θ θ , then:

Which of the following statement(s) is(are) correct?

If ( ^4 x)/(5)+( ^4 x)/(4)=(1)/(9) , then which of the following is/are TRUE?

The equation x^3-(3)/(4) x=- 3 8 is satisfied by

The values of ' t ' which satisfies (t-[| x|])!=3!5!7! is/are (where [.] denotes greatest integer function) -

If -(π)/(2) α_1 α_2 α_3 (π)/(2) , then number of values of θ ∈(-(π)/(2), (π)/(2)) satisfying ( θ- α_1)( θ- α_2)( θ- α_3)-(∑( θ- α_i)) is ______ .

Number of solution of the equation ^4 x- ^2 x x+2 ^2 x+ x=0 in 0 ≤ x ≤ 3 π is

If the largest possible value of x such that 0 < x < π satisfying the equation (2 2 x+1)/( x+ x)= 2 is (a π)/(b) . Find (a+b)

If sum of the roots of the equation 2 (x+(π)/(4))( ^2 x-(1+ 3 ) x+2+ 3 )= 9+18 x · x in [0,2 π] is (p)/(q) π where p, q ∈ N , then find the least value of |p-q| .

The number of integral values of a ; a ∈(6,100) for which the equation [ x]^2+ x-a=0 has real roots; where [.] denotes greatest integer function is __________ .

Let maximum value of the expression y=|k-3| 2 x+|t-4| 2 x+3 where 0 ≤ k ≤ 6 and 1 ≤ t ≤ 7 is equal to 6 then find the minimum value of (k^2+t^2) .

If (θ-α), 3 θ, (θ+α) are in A.P. and θ is not an integral multiple of (π)/(2) , then find the value of (2 ^2 θ)/( ^2 α) .

Given A= ^2 θ( ^2 θ+1)+2 ^2 θ . Then for all θ,[A] can assume values whose sum is ______ (Where [.] denotes the greatest integer function).

If x, y and z are real numbers that satisfy the three equations \ array l (x)+ (y)+ (z)=6-( (x)+ (y)+ (z)) ^2(x)+ ^2(y)+ ^2(z)=6-( ^2(x)+ ^2(y)+ ^2(z)) ^3(x)+ ^3(y)+ ^3(z)=6-(

Let 0 < θ < (π)/(2) , such that ( ^2 2 θ+4 ^4 θ-4 ^2 θ ^2 θ)/(4-4 ^2 θ- ^2 2 θ)= 7-4 3 7+4 3 , then θ=(π)/(n) where n is:

If ((1)/(4) 36^ ∘ 54^ ∘ )^2-( 12^ ∘ 36^ ∘ 48^ ∘ 72^ ∘ )^2= a -b c where a, c are relatively prime numbers, then find the value of (a+b+c) .

Let 0 ≤ θ ≤ 2 π and x=| θ+1|+| θ-1|+| θ-2|+| θ-3| , then product of the maximum and minimum values of x is:

The number of real solutions of the equation 1+ 2 x = 2 ^ -1 ( x) where -π ≤ x ≤ π .

a^2 9^ ∘ +b^2 27^ ∘ +c^2 63^ ∘ +d^2 81^ ∘ Let a, b, c and d be real numbers satisfying a+b+c+d=5 . If the minimum value of the expression above is equal to x y , where x and y are

Given that x ∈ R , find the minimum value of (3 5-4 x + 13-12 x )^2 .

Let f(x)=( a^ ^4 x a^ 2 ^2 x )^3 ·(a^ 5 ^3 x · a^ 5 x ) and b=( 5 )^ 2 _5 3 (a 0, a ≠ 1) . If the minimum value of (f(x) · a^b)^ cosec^2 x + _a x is equal to a^k, k ∈ N , find k .

If the sum of the roots of the equation 4 x+6=7 2 x in the interval [0,314] is k π, k ∈ R . Find k .

Given that for a, b, c, d ∈ R , if a (200^ ∘ )-c (200^ ∘ )=d and b (200^ ∘ )+d (200^ ∘ )=c then (a^2+b^2+c^2+d^2)/(a c-b d)=p cosec(200^ ∘ ) find the value of p

Find the number of solution of the equation 2^ ^2 x +5 · 2^ ^2 x =7 in the interval [0,315] .

Let α=∑_ k=1 ^ 20 ( ((π)/(3) k))/(4 ^2((k π)/(9))-1) and β=∑_ k=1 ^ 20 ( ((π)/(3) k))/(1-4 ^2((k π)/(9))) . If β^2-α^2=1+ λ^ ∘ then find the value of λ .

Find the value of 16( ^2 18^ ∘ + ^2 36^ ∘ + ^2 54^ ∘ + ^2 72^ ∘ ) .

Let x= 4 80^ ∘ 65^ ∘ 55^ ∘ 20^ ∘ + 50^ ∘ + 70^ ∘ , then x is:

If ( 25^ ∘ + 3 85^ ∘ + 85^ ∘ )^2=a+b 50^ ∘ , then (a+b)=

Let λ=( 65^ ∘ + 3 85^ ∘ + 85^ ∘ 65^ ∘ )^2 , then λ=

If 0 < α < 30^ ∘ , then find the value of _2( 8 (30^ ∘ -2 α)- 8 α+ (30^ ∘ -α) 3 ) .

Let L be the least value of the expression ( 2 x- 2 x)/(1+ ((5 π)/(2)-8 x)) if x ∈(0, (π)/(8)) and M denotes the value of 4( ^3 10^ ∘ + ^3 20^ ∘ ) ( 10^ ∘ + 20^ ∘ ) . Find the

Find the value of 32 90^ ∘ 17 180^ ∘ 17 360^ ∘ 17 720^ ∘ 17 . If the sum of the roots of the equation 4 x+6=7 2 x in the interval [0,314] is k π, k ∈ R . Find k.

If the equation |2 x+ ^2 a|+|2 x+3+2 a|=0 has exactly one solution x=λ (where ' a ' is a constant) then find the value of 4 λ^2 .

Paragraph: In reducing a given equation to the standard forms ( x= α etc ) we apply several trigonometric or algebraic transformations. As a result of which the canonical form

Paragraph: Let a, b, c, d ∈ R . Then the cubic equation of the type a x^3+b x^2+c x+d=0 has either one root real or all three roots are real. But in case of trigonometric

Paragraph: Let a, b, c, d ∈ R . Then the cubic equation of the type a x^3+b x^2+c x+d=0 has either one root real or all three roots are real. But in case of trigonometric

Paragraph: Let a, b, c, d ∈ R . Then the cubic equation of the type a x^3+b x^2+c x+d=0 has either one root real or all three roots are real. But in case of trigonometric

Paragraph: In reducing a given equation to the standard forms ( x= α etc ) we apply several trigonometric or algebraic transformations. As a result of which the canonical form

Paragraph: While finding the sine of a contain angle x , an absent minded professor failed to notice that his calculator was not in the correct angular mode. However he was lucky

Paragraph: While finding the sine of a contain angle x , an absent minded professor failed to notice that his calculator was not in the correct angular mode. However he was lucky

Related JEE Mathematics chapters