Trigonometric Functions

JEE Main 2024 (Online) 29th January Evening ShiftMCQMedium📈 Topic in 9% papers+4−1

Ques. 1JEE 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

Answer

(4) -1

6x- 6x=( 2x- 2x)(1- 2x 2x)

= 2x (1- 22x4 )= 2x (3+ 22x)4

LHS = 2x (3+ 22x) 2x (3+ 22x)/4=4 ( 2x 0)

x3-x2+2=0 (x+1)(x2-2x+2)=0

x2-2x+2=(x-1)2+1>0, only real root x=-1 (and (-2) 0)

Sum =-1

Answer: (4)

Ques. 2JEE 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. 3JEE 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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