1
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The function $$f(x)=\frac{x}{x^2-6 x-16}, x \in \mathbb{R}-\{-2,8\}$$

A
decreases in $$(-\infty,-2) \cup(-2,8) \cup(8, \infty)$$
B
increases in $$(-\infty,-2) \cup(-2,8) \cup(8, \infty)$$
C
decreases in $$(-2,8)$$ and increases in $$(-\infty,-2) \cup(8, \infty)$$
D
decreases in $$(-\infty,-2)$$ and increases in $$(8, \infty)$$
2
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If R is the smallest equivalence relation on the set $$\{1,2,3,4\}$$ such that $$\{(1,2),(1,3)\} \subset \mathrm{R}$$, then the number of elements in $$\mathrm{R}$$ is __________.

A
15
B
10
C
12
D
8
3
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the mean and variance of five observations are $$\frac{24}{5}$$ and $$\frac{194}{25}$$ respectively and the mean of the first four observations is $$\frac{7}{2}$$, then the variance of the first four observations in equal to

A
$$\frac{5}{4}$$
B
$$\frac{4}{5}$$
C
$$\frac{105}{4}$$
D
$$\frac{77}{12}$$
4
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{P}(3,2,3), \mathrm{Q}(4,6,2)$$ and $$\mathrm{R}(7,3,2)$$ be the vertices of $$\triangle \mathrm{PQR}$$. Then, the angle $$\angle \mathrm{QPR}$$ is

A
$$\cos ^{-1}\left(\frac{7}{18}\right)$$
B
$$\frac{\pi}{6}$$
C
$$\cos ^{-1}\left(\frac{1}{18}\right)$$
D
$$\frac{\pi}{3}$$
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