Inverse Trigonometric Functions · Question 14

JEE Main 2025 (Online) 4th April Evening ShiftMCQMedium📈 Topic in 16% papers+4−1

The sum of the infinite series -1 ( 74 )+ -1 ( 194 )+ -1 ( 394 )+ -1 ( 674 )+ is :

Answer

(3) 2- -1 ( 12 )

Numerators 7, 19, 39, 67, have second differences constant (12, 20, 28): they are 4n2+3

Tn= -1 ( 4n2+34 )= -1 (n2+ 34 )= -1 11+ (n2- 14 )

Tn= -1 (n+ 12 )- (n- 12 )1+ (n+ 12 ) (n- 12 )

Tn= -1 (n+ 12 )- -1 (n- 12 )

Sn= r=1nTr= -1 (n+ 12 )- -1 ( 12 ) (telescoping)

As n , -1 (n+ 12 ) 2

S = 2- -1 ( 12 )

Answer: (3)

JEE Main 2025 (Online) 4th April Evening Shift

If y = ( 3 + -1 x2 ), then (x - y)2 + 3y2 is equal to .

JEE Main 2025 (Online) 2nd April Evening Shift

Let S = \x : -1x = + -1x + -1(2x + 1) \. Then x S(2x - 1)2 is equal to .

JEE Main 2025 (Online) 29th January Morning Shift

( -1 35 + -1 513 + -1 3365 ) is equal to:

JEE Main 2025 (Online) 28th January Morning Shift

Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = -1(2[x] + 1) is:

JEE Main 2025 (Online) 28th January Evening Shift

All JEE Main Mathematics chapters