1
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A coin is biased so that the head is 3 times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $$\mathrm{X}$$ denotes the number of tosses of the coin, then the mean of $$\mathrm{X}$$ is :

A
$$\frac{81}{64}$$
B
$$\frac{37}{16}$$
C
$$\frac{21}{16}$$
D
$$\frac{15}{16}$$
2
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The set of all $$a \in \mathbb{R}$$ for which the equation $$x|x-1|+|x+2|+a=0$$ has exactly one real root, is :

A
$$(-\infty, \infty)$$
B
$$(-6, \infty)$$
C
$$(-\infty,-3)$$
D
$$(-6,-3)$$
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\int_\limits{0}^{\infty} \frac{6}{e^{3 x}+6 e^{2 x}+11 e^{x}+6} d x=$$

A
$$\log _{e}\left(\frac{256}{81}\right)$$
B
$$\log _{e}\left(\frac{64}{27}\right)$$
C
$$\log _{e}\left(\frac{32}{27}\right)$$
D
$$\log _{e}\left(\frac{512}{81}\right)$$
4
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$s_{1}, s_{2}, s_{3}, \ldots, s_{10}$$ respectively be the sum to 12 terms of 10 A.P. s whose first terms are $$1,2,3, \ldots .10$$ and the common differences are $$1,3,5, \ldots \ldots, 19$$ respectively. Then $$\sum_\limits{i=1}^{10} s_{i}$$ is equal to :

A
7360
B
7220
C
7260
D
7380
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