JEE Main 2021 — Limits Questions with Solutions

lim n → ∞ 1 + 1 + 1 2 + … … + 1 n n 2 n is equal to

If lim x → 0 a e x - b cos x + c e - x x sin x = 2 , then a + b + c is equal to ________.

The value of lim n → ∞ r + 2 r + . . . + n r n 2 , where r is non-zero real number and r denotes the greate…

Let f x be a differentiable function at x = a with f ' a = 2 and f a = 4 . Then lim x → a x f a - a f x x - a equ…

lim x → 2 ∑ n = 1 9 x n ( n + 1 ) x 2 + 2 ( 2 n + 1 ) x + 4 is equal to :

If lim x → ∞ x 2 - x + 1 - a x = b , then the ordered pair ( a ,   b ) is:

The value of lim x → 0 x 1 - sin x 8 - 1 + sin x 8 is equal to :

If α ,   β are the distinct roots of x 2 + b x + c = 0 , then lim x → β e 2 x 2 + b x + c - 1…

Let f ( x ) = x 6 + 2 x 4 + x 3 + 2 x + 3 ,   x ∈ R . Then the natural number n for which lim x → 1 x…

If lim x → 0 sin - 1 x - tan - 1 x 3 x 3 is equal to L , then the value of ( 6 L + 1 ) is