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Trigonometric Functions

JEE Main 2024 (Online) 27th January Morning ShiftNumericalMedium📈 Topic in 36% papers+4
Ques. 1JEE 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 .

Answer

48

Solution

1-2 2x+a x=2a-7 ⇒ 2( 2x-4)-a( x-2)=0

⇒ ( x-2)(2 x+4-a)=0

∵ x 2 ⇒ a=2 x+4 [2, 6] ⇒ p=2, q=6

1 63 = 27 , 81 = 9

⇒ r=( 9 + 9 )-( 27 + 27 )

∵ + = 2 2

⇒ r= 2 18 - 2 54 = 8 5-1- 8 5+1= 164=4

∴ pqr=2 6 4=48

Answer: 48

Keep practising — Trigonometric Functions

Ques. 2JEE 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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