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Trigonometric Functions

JEE Main 2024 (Online) 27th January Evening ShiftMCQHard📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2024, 27 January (Evening Shift)

If 2 2 -5 =1 has exactly 7 solutions in the interval [0, n 2 ], for the least value of n , then k=1n k2k is equal to:

  1. 1214 (215-15 )
  2. 1- 15213
  3. 1215 (214-14 )
  4. 1213 (214-15 )

Answer

(4) 1213 (214-15 )

Solution

2 ( 2 -1 )-5 -1=0 (2 +1)( -3)=0

∵ | | 1: =3, i.e. = 13

[figure]

7th solution is 6 + -1 13 (between 6 and 13 2) least n=13

S= k=113 k2k: S- S2= ( 12+ 122+ + 1213 )- 13214

S2=1- 1213- 13214

S=2- 15213= 1213 (214-15 )

Answer: (4)

Keep practising — Trigonometric Functions

Ques. 2JEE Main 2026, 6 April (Morning Shift)

Let S= \ (-2 , 2 ) : +1= 3 \. Then S is equal to :

  1. - 2 3
  2. - 4 3
  3. 2 3
  4. 4 3
Ques. 3JEE Main 2026, 5 April (Morning Shift)

Let A, B, where A, B (- 2, 2 ), be the roots of the quadratic equation x2-2x-5=0. Then 20 2 ( A+B2 ) is equal to :

  1. 10+ 10
  2. 10-2 10
  3. 10-3 10
  4. 10- 10
Ques. 4JEE Main 2026, 5 April (Morning Shift)

The sum of all the integral values of p such that the equation 3 2 x+12 x-3=p, x R, has at least one solution, is:

  1. -54
  2. -60
  3. -75
  4. -84
Ques. 5JEE Main 2026, 5 April (Evening Shift)

If S= \ [- , ] : . . 5 2= 7 7 2 \, then n(S) is equal to .

Ques. 6JEE Main 2026, 4 April (Morning Shift)

If A= 3 9 + 9 27 + 27 81 and B= 81 - 3 , then BA is equal to .

Ques. 7JEE Main 2026, 2 April (Morning Shift)

If ( 18 ) ( 5 18 ) ( 7 18 )=K, then the value of ( 10K 3 ) is :

  1. 3+12 2
  2. 3-1 2
  3. 32
  4. 12
Ques. 8JEE Main 2026, 2 April (Morning Shift)

Let S=\x [- , ] : x( x+ x)=a, a Z\. Then n(S) is equal to :

  1. 3
  2. 6
  3. 7
  4. 9
Ques. 9JEE Main 2026, 2 April (Evening Shift)

Let P=\ [0, 4 ] : 2 1\ and S=\a Z : 2( 8 - 8 ) 2 =a2, P\. Then n(S) is:

  1. 0
  2. 1
  3. 2
  4. 3
Ques. 10JEE Main 2026, 28 January (Morning Shift)

If (A - B) A + 2 C 2 A = 1, A, B, C (0, 2 ), then

  1. A, C, B are in A.P.
  2. A, C, B are in G.P.
  3. A, B, C are in G.P.
  4. A, B, C are in A.P.
Ques. 11JEE Main 2026, 28 January (Evening Shift)

The sum of all the elements in the range of f(x) = Sgn( x) + Sgn( x) + Sgn( x) + Sgn( x), x n 2, n Z, where Sgn(t) = cases 1, & if t > 0 \ -1, & if t < 0 cases is :

  1. 4
  2. 0
  3. 2
  4. -2

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