1
JEE Main 2024 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the value of $$\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}$$ is $$\frac{a \sqrt{5}-b}{c}$$, where $$a, b, c$$ are natural numbers and $$\operatorname{gcd}(a, c)=1$$, then $$a+b+c$$ is equal to :

A
54
B
52
C
50
D
40
2
JEE Main 2024 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the image of the point $$(-4,5)$$ in the line $$x+2 y=2$$ lies on the circle $$(x+4)^2+(y-3)^2=r^2$$, then $$r$$ is equal to:

A
2
B
3
C
4
D
1
3
JEE Main 2024 (Online) 8th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the term independent of $$x$$ in the expansion of $$\left(\sqrt{\mathrm{a}} x^2+\frac{1}{2 x^3}\right)^{10}$$ is 105 , then $$\mathrm{a}^2$$ is equal to :

A
6
B
4
C
2
D
9
4
JEE Main 2024 (Online) 8th April Evening Shift
Numerical
+4
-1
Change Language

Let $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}$$ and $$\mathrm{a}< \mathrm{b}< \mathrm{c}$$. Let the mean, the mean deviation about the mean and the variance of the 5 observations $$9,25, a, b, c$$ be 18, 4 and $$\frac{136}{5}$$, respectively. Then $$2 a+b-c$$ is equal to ________

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