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

The coefficients $$a, b, c$$ in the quadratic equation $$a x^2+b x+c=0$$ are chosen from the set $$\{1,2,3,4,5,6,7,8\}$$. The probability of this equation having repeated roots is :

A
$$\frac{1}{128}$$
B
$$\frac{1}{64}$$
C
$$\frac{3}{256}$$
D
$$\frac{3}{128}$$
2
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the system of equations

$$\begin{array}{r} 11 x+y+\lambda z=-5 \\ 2 x+3 y+5 z=3 \\ 8 x-19 y-39 z=\mu \end{array}$$

has infinitely many solutions, then $$\lambda^4-\mu$$ is equal to :

A
51
B
45
C
47
D
49
3
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The integral $$\int_\limits0^{\pi / 4} \frac{136 \sin x}{3 \sin x+5 \cos x} \mathrm{~d} x$$ is equal to :

A
$$3 \pi-50 \log _e 2+20 \log _e 5$$
B
$$3 \pi-25 \log _e 2+10 \log _e 5$$
C
$$3 \pi-10 \log _{\mathrm{e}}(2 \sqrt{2})+10 \log _{\mathrm{e}} 5$$
D
$$3 \pi-30 \log _e 2+20 \log _e 5$$
4
JEE Main 2024 (Online) 5th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If $$\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots+\frac{1}{\sqrt{99}+\sqrt{100}}=m$$ and $$\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\ldots+\frac{1}{99 \cdot 100}=\mathrm{n}$$, then the point $$(\mathrm{m}, \mathrm{n})$$ lies on the line

A
$$11(x-1)-100 y=0$$
B
$$11 x-100 y=0$$
C
$$11(x-1)-100(y-2)=0$$
D
$$11(x-2)-100(y-1)=0$$
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