1
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let M denote the median of the following frequency distribution

Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20
Frequency 3 9 10 8 6

Then 20M is equal to :

A
104
B
52
C
208
D
416
2
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Two integers $$x$$ and $$y$$ are chosen with replacement from the set $$\{0,1,2,3, \ldots, 10\}$$. Then the probability that $$|x-y|>5$$, is :

A
$$\frac{31}{121}$$
B
$$\frac{60}{121}$$
C
$$\frac{62}{121}$$
D
$$\frac{30}{121}$$
3
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$A(2,3,5)$$ and $$C(-3,4,-2)$$ be opposite vertices of a parallelogram $$A B C D$$. If the diagonal $$\overrightarrow{\mathrm{BD}}=\hat{i}+2 \hat{j}+3 \hat{k}$$, then the area of the parallelogram is equal to :

A
$$\frac{1}{2} \sqrt{410}$$
B
$$\frac{1}{2} \sqrt{306}$$
C
$$\frac{1}{2} \sqrt{586}$$
D
$$\frac{1}{2} \sqrt{474}$$
4
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$y=y(x)$$ be the solution of the differential equation $$\sec x \mathrm{~d} y+\{2(1-x) \tan x+x(2-x)\} \mathrm{d} x=0$$ such that $$y(0)=2$$. Then $$y(2)$$ is equal to:

A
$$2\{\sin (2)+1\}$$
B
2
C
1
D
$$2\{1-\sin (2)\}$$
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