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Trigonometry — JEE Main & Advanced Mathematics PYQs

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

66 questionsMathematicsSolutions on every page
1

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

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If |x^2- 4 + x-2 |= |x^2-2 |+| x|+ 4 then

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

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What is the minimum value of ^4 ^2 + ^4 ^2 for , B k 2 , k Z ?

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If x+ y x x R then y+ is equal to

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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

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If and - 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

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If 2 ^2 ( 2 ^2 x )=1- ( 2 x), x (2 n+1) 2 , n I , then

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

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

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

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

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

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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 ?

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

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

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

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

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

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

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

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If = 1 2 (x+ 1 x ) and = 1 2 (y+ 1 y ),(x y 0) x, y, , R then

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If x+1= 1 2+ 1 2+ 1 2+ where x (0,2 ) , then:

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

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

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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:

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Let x= ^3 and y= ^3 , then:

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

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

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

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

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If - 2 ₁ ₂ ₃ 2 , then number of values of (- 2 , 2 ) satisfying ( - ₁ ) ( - ₂ ) ( - ₃ )- ( ( - _i ) ) is ______ .

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

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

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

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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 __________ .

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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 ) .

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

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

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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- ( ^3(

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Let 0 < < 2 , such that ^2 2 +4 ^4 -4 ^2 ^2 4-4 ^2 - ^2 2 = 7-4 3 7+4 3 , then = n where n is:

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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) .

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

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

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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 co-prime

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

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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 .

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

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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

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

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Let = _ k=1 ²⁰ ( 3 k ) 4 ^2 ( k 9 )-1 and = _ k=1 ²⁰ ( 3 k ) 1-4 ^2 ( k 9 ) . If ^2- ^2=1+ ^ then find the value of .

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

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

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

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

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

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

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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 , k R . Find k.

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

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

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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 equations o

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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 equations o

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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 equations o

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

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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 t

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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 t

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