1
WB JEE 2019
MCQ (Single Correct Answer)
+1
-0.25
Change Language
$$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$
A
Does not exist finitely
B
is 1
C
is e2
D
is 2
2
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over {{\theta ^2}}}$$. Then $$\sum\limits_{r = 0}^n {{a^r}{b^{n - r}}} $$ is
A
$${{{2^{n + 1}} - 1} \over {3\,.\,{2^n}}}$$
B
$${{{2^{n + 1}} + 1} \over {3\,.\,{2^n}}}$$
C
$${{{4^{n + 1}} - 1} \over {3\,.\,{2^n}}}$$
D
$${1 \over 2}({2^n} - 1)$$
3
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves $${1 \over 2}$$ unit vertically up and reaches P2, then it moves $${1 \over 4}$$ unit horizontally to right and reaches P3, then it moves $${1 \over 8}$$ unit vertically down and reaches P4, then it moves $${1 \over 16}$$ unit horizontally to right and reaches P5 and so on. Let Pn = (xn, yn) and $$\mathop {\lim }\limits_{n \to \infty } {x_n} = \alpha $$ and $$\mathop {\lim }\limits_{n \to \infty } {y_n} = \beta $$. Then, ($$\alpha$$, $$\beta$$) is
A
(2, 3)
B
$$\left( {{4 \over 3},{2 \over 5}} \right)$$
C
$$\left( {{2 \over 5},1} \right)$$
D
$$\left( {{4 \over 3},3} \right)$$
4
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The value of $$\mathop {\lim }\limits_{x \to {0^ + }} {x \over p}\left[ {{q \over x}} \right]$$ is
A
$${{[q]} \over p}$$
B
0
C
1
D
$$\infty $$
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