1
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
2
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
$$\frac{77}{12}$$
3
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
$$\frac{\pi}{3}$$
4
JEE Main 2024 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$\text { Let } y=\log _e\left(\frac{1-x^2}{1+x^2}\right),-1 < x<1 \text {. Then at } x=\frac{1}{2} \text {, the value of } 225\left(y^{\prime}-y^{\prime \prime}\right) \text { is equal to }$$

A
732
B
736
C
742
D
746
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