Trigonometric Functions

JEE Main 2024 (Online) 30th January Morning ShiftMCQMedium📈 Topic in 36% papers+4−1

Ques. 1JEE 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 :

Answer

(4) (- , 0)

2x x=2 x 2x

2 x ( 2x+ 2x )+4 x-4=0 x= 23

Solutions: , - , 2 + , 3 - , where = -1 23< 2

exactly 3 of them lie in [0, n 2 ] only when 2 + n 2<3 - n=5

x2+5x+2=0 x= -5 172

17<5, both roots are negative roots (- , 0)

Answer: (4)

Ques. 2JEE 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

Ques. 3JEE Main 2024, 29 January (Morning Shift)

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

Ques. 4JEE 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

Ques. 5JEE 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. 6JEE 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:

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