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Trigonometric Functions

JEE Main 2024 (Online) 5th April Morning ShiftMCQMedium📈 Topic in 36% papers+4−1
Ques. 1JEE Main 2024, 5 April (Morning Shift)

Suppose [0, 4 ] is a solution of 4 - 3 = 1. Then is equal to :

  1. 6 - 6(3 6 - 2)
  2. 4(3 6 + 2)
  3. 6 + 6(3 6 + 2)
  4. 4(3 6 - 2)

Answer

(4) 4(3 6 - 2)

Solution

Put t = 2, so = 1 - t21 + t2 and = 2t1 + t2:

4(1 - t2) - 6t = 1 + t2 5t2 + 6t - 3 = 0

t = -3 2 65

Since [0, 4 ], t 0, so t = 2 6 - 35 and t2 = 33 - 12 625

= 1 - t21 + t2 = 12 6 - 858 - 12 6 = 6 6 - 429 - 6 6

Because (6 6 - 4)(3 6 - 2) = 116 - 24 6 = 4(29 - 6 6), this is 43 6 - 2

Answer: (4)

Keep practising — Trigonometric Functions

Ques. 2JEE Main 2024, 5 April (Evening Shift)

The number of solutions of 2 x + (2 + 2x - x2 ) x - 3(x - 1)2 = 0, where - x , is .

Ques. 3JEE Main 2024, 1 February (Morning Shift)

If = 1 x(x2+x+1), = x x2+x+1 and = (x-3+x-2+x-1 )1/2, 0<A, B, C< 2, then A+B is equal to :

  1. C
  2. -C
  3. 2 -C
  4. 2-C
Ques. 4JEE Main 2024, 1 February (Evening Shift)

The number of solutions of the equation 4 2 x-4 3 x+9-4 x=0 ; x [-2 , 2 ] is :

  1. 0
  2. 3
  3. 1
  4. 2
Ques. 5JEE Main 2024, 31 January (Evening Shift)

The number of solutions, of the equation e x-2e- x=2, is :

  1. 0
  2. 1
  3. 2
  4. more than 2
Ques. 6JEE Main 2024, 30 January (Morning Shift)

If 2 3 x+ 2x x+4 x-4=0 has exactly 3 solutions in the interval [0, n 2 ], n N, then the roots of the equation x2+nx+(n-3)=0 belong to :

  1. (0, )
  2. Z
  3. (- 172, 172 )
  4. (- , 0)
Ques. 7JEE Main 2024, 30 January (Evening Shift)

For , (0, /2), let 3 ( + )=2 ( - ) and a real number k be such that =k . Then, the value of k is equal to

  1. 5
  2. -2/3
  3. -5
  4. 2/3
Ques. 8JEE Main 2024, 29 January (Morning Shift)

If ,- 2< < 2 is the solution of 4 +5 =1, then the value of is

  1. 10- 1012
  2. 10-106
  3. 10-1012
  4. 10- 106
Ques. 9JEE Main 2024, 29 January (Evening Shift)

The sum of the solutions x R of the equation 3 2x+ 3 2x 6 x- 6 x=x3-x2+6 is

  1. 3
  2. 1
  3. 0
  4. -1
Ques. 10JEE Main 2024, 27 January (Morning Shift)

Let the set of all a such that the equation 2x+a x=2a-7 has a solution be [p, q] and r= 9 - 27 - 1 63 + 81 , then pqr is equal to .

Ques. 11JEE 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 )

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