1
MHT CET 2021 20th September Evening Shift
+2
-0

If $$a=\lim _\limits{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$$ and $$b=\lim _\limits{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$$, then

A
a = b
B
2a = 3b
C
a = 2b
D
3a = 2b
2
MHT CET 2021 20th September Evening Shift
+2
-0

If $$f(x) = {{{4^{x - \pi }} + {4^{x - \pi }} - 2} \over {{{(x - \pi )}^2}}}$$, for $$x \ne \pi$$, is continuous at $$x=\pi$$, then k =

A
$$2\log2$$
B
$$(\log2)^2$$
C
$$-(\log2)^2$$
D
$$8(\log2)^2$$
3
MHT CET 2021 20th September Morning Shift
+2
-0

$$\mathop {\lim }\limits_{x \to \infty } \left( {\sqrt {{x^2} + 5x - 7} - x} \right) =$$

A
$${7 \over 2}$$
B
5
C
$${5 \over 2}$$
D
6
4
MHT CET 2021 20th September Morning Shift
+2
-0

If f(x) = |x|, for x $$\in$$ ($$-1,2$$), then f is discontinuous at (where [x] represents floor function)

A
x = $$-1,0,1,2$$
B
x = $$-1,0,1$$
C
x = 0, 1
D
x = 2
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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