1
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\mathrm{A}(-1,1)$$ and $$\mathrm{B}(2,3)$$ be two points and $$\mathrm{P}$$ be a variable point above the line $$\mathrm{AB}$$ such that the area of $$\triangle \mathrm{PAB}$$ is 10. If the locus of $$\mathrm{P}$$ is $$\mathrm{a} x+\mathrm{by}=15$$, then $$5 \mathrm{a}+2 \mathrm{~b}$$ is :

A
$$-\frac{12}{5}$$
B
$$-\frac{6}{5}$$
C
6
D
4
2
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The values of $$m, n$$, for which the system of equations

$$\begin{aligned} & x+y+z=4, \\ & 2 x+5 y+5 z=17, \\ & x+2 y+\mathrm{m} z=\mathrm{n} \end{aligned}$$

has infinitely many solutions, satisfy the equation :

A
$$\mathrm{m}^2+\mathrm{n}^2-\mathrm{m}-\mathrm{n}=46$$
B
$$\mathrm{m}^2+\mathrm{n}^2+\mathrm{mn}=68$$
C
$$\mathrm{m}^2+\mathrm{n}^2-\mathrm{mn}=39$$
D
$$\mathrm{m}^2+\mathrm{n}^2+\mathrm{m}+\mathrm{n}=64$$
3
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}$$, then at $$\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+y$$ is equal to :

A
$$\frac{1}{2}$$
B
1
C
$$\frac{3}{2}$$
D
2
4
JEE Main 2024 (Online) 5th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\beta(\mathrm{m}, \mathrm{n})=\int_\limits0^1 x^{\mathrm{m}-1}(1-x)^{\mathrm{n}-1} \mathrm{~d} x, \mathrm{~m}, \mathrm{n}>0$$. If $$\int_\limits0^1\left(1-x^{10}\right)^{20} \mathrm{~d} x=\mathrm{a} \times \beta(\mathrm{b}, \mathrm{c})$$, then $$100(\mathrm{a}+\mathrm{b}+\mathrm{c})$$ equals _________.

A
2012
B
1021
C
1120
D
2120
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