1
WB JEE 2023
+1
-0.25

Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then

A
f is discontinuous everywhere.
B
f is continuous everywhere.
C
f is continuous at only those points which are perfect squares.
D
f is continuous at only those points which are not perfect squares.
2
WB JEE 2023
+2
-0.5

The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \right) + \left( {{1 \over {{2^2}\,.\,{3^2}}} + {1 \over {{2^3}\,.\,{3^2}}}} \right)\, + \,...\, + \,\left( {{2 \over {{2^n}\,.\,{3^n}}} + {1 \over {{2^{n + 1}}\,.\,3n}}} \right)} \right]$$ is

A
$${3 \over 8}$$
B
$${3 \over {10}}$$
C
$${3 \over {14}}$$
D
$${3 \over {16}}$$
3
WB JEE 2022
+1
-0.25

The values of a, b, c for which the function $$f(x) = \left\{ \matrix{ {{\sin (a + 1)x + \sin x} \over x},x < 0 \hfill \cr c,x = 0 \hfill \cr {{{{(x + b{x^2})}^{{1 \over 2}}} - {x^{{1 \over 2}}}} \over {b{x^{{1 \over 2}}}}},x > 0 \hfill \cr} \right.$$ is continuous at x = 0, are

A
$$a = {3 \over 2},b = - {3 \over 2},c = {1 \over 2}$$
B
$$a = - {3 \over 2},c = {3 \over 2},b$$ is arbitrary non-zero real number.
C
$$a = - {5 \over 2},b = - {3 \over 2},c = {3 \over 2}$$
D
$$a = - 2,b \in R - \{ 0\} ,c = 0$$
4
WB JEE 2022
+1
-0.25

Let $$f(x) = {a_0} + {a_1}|x| + {a_2}|x{|^2} + {a_3}|x{|^3}$$, where $${a_0},{a_1},{a_2},{a_3}$$ are real constants. Then f(x) is differentiable at x = 0

A
whatever be $${a_0},{a_1},{a_2},{a_3}$$.
B
for no values of $${a_0},{a_1},{a_2},{a_3}$$.
C
only if $${a_1} = 0$$
D
only if $${a_1} = 0,{a_3} = 0$$
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