Relations and Functions

JEE Main 2024 (Online) 4th April Morning ShiftMCQMedium📈 Topic in 31% papers+4−1

Ques. 1JEE Main 2024, 4 April (Morning Shift)

Let the sum of the maximum and the minimum values of the function f(x)= 2x2-3x+82x2+3x+8 be mn, where (m, n)=1. Then m+n is equal to :

Answer

(3) 201

Let y= 2x2-3x+82x2+3x+8

(denominator >0 for all real x, D=9-64<0)

(2y-2)x2+(3y+3)x+(8y-8)=0

x is real D 0:

(3y+3)2-4(2y-2)(8y-8) 0

9(y+1)2-64(y-1)2 0

(11y-5)(11-5y) 0 511 y 115

(y= 511 at x=2, y= 115 at x=-2)

mn= 511+ 115= 14655 m+n=146+55=201

Answer: (3)

Ques. 2JEE Main 2024, 1 February (Evening Shift)

If the domain of the function f(x)= x2-25 (4-x2 )+ 10 (x2+2x-15 ) is (- , ) [ , ), then 2+ 3 is equal to :

Ques. 3JEE Main 2024, 30 January (Morning Shift)

If the domain of the function f(x)= -1 ( 2-|x|4 )+ \ e(3-x) \-1 is [- , )-\ \, then + + is equal to :

Ques. 4JEE Main 2024, 30 January (Evening Shift)

If the domain of the function f(x)= e ( 2 x+34 x2+x-3 )+ -1 ( 2 x-1x+2 ) is ( , ], then the value of 5 -4 is equal to

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