1
JEE Main 2023 (Online) 25th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f:(0,1)\to\mathbb{R}$$ be a function defined $$f(x) = {1 \over {1 - {e^{ - x}}}}$$, and $$g(x) = \left( {f( - x) - f(x)} \right)$$. Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0, 1)

Then,

A
Both (I) and (II) are true
B
Neither (I) nor (II) is true
C
Only (II) is true
D
Only (I) is true
2
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

The constant term in the expansion of $${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$$ is ___________.

Your input ____
3
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

Your input ____
4
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1
Change Language

Let $$x$$ and $$y$$ be distinct integers where $$1 \le x \le 25$$ and $$1 \le y \le 25$$. Then, the number of ways of choosing $$x$$ and $$y$$, such that $$x+y$$ is divisible by 5, is ____________.

Your input ____
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