1
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
$$\left( {{4 \over 3},3} \right)$$
2
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
$$\infty $$
3
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let f : [a, b] $$ \to $$ R be differentiable on [a, b] and k $$ \in $$ R. Let f(a) = 0 = f(b). Also let J(x) = f'(x) + kf(x). Then
A
J(x) > 0 for all x $$ \in $$ [a, b]
B
J(x) < 0 for all x $$ \in $$ [a, b]
C
J(x) = 0 has at least one root in (a, b)
D
J(x) = 0 through (a, b)
4
WB JEE 2018
MCQ (Single Correct Answer)
+1
-0.25
Change Language
Let $$f(x) = 3{x^{10}} - 7{x^8} + 5{x^6} - 21{x^3} + 3{x^2} - 7$$.

Then $$\mathop {\lim }\limits_{h \to 0} {{f(1 - h) - f(1)} \over {{h^3} + 3h}}$$
A
does not exist
B
is $${{50} \over 3}$$
C
is $${{53} \over 3}$$
D
is $${{22} \over 3}$$
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