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

Consider the system of linear equations $$x+y+z=4 \mu, x+2 y+2 \lambda z=10 \mu, x+3 y+4 \lambda^2 z=\mu^2+15$$ where $$\lambda, \mu \in \mathbf{R}$$. Which one of the following statements is NOT correct ?

A
The system has unique solution if $$\lambda \neq \frac{1}{2}$$ and $$\mu \neq 1,15$$
B
The system has infinite number of solutions if $$\lambda=\frac{1}{2}$$ and $$\mu=15$$
C
The system is consistent if $$\lambda \neq \frac{1}{2}$$
D
The system is inconsistent if $$\lambda=\frac{1}{2}$$ and $$\mu \neq 1$$
2
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$f:\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \rightarrow \mathbf{R}$$ be a differentiable function such that $$f(0)=\frac{1}{2}$$. If the $$\lim _\limits{x \rightarrow 0} \frac{x \int_0^x f(\mathrm{t}) \mathrm{dt}}{\mathrm{e}^{x^2}-1}=\alpha$$, then $$8 \alpha^2$$ is equal to :

A
4
B
2
C
1
D
16
3
JEE Main 2024 (Online) 30th January Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is :

A
$$\frac{1}{\sqrt{3}}$$
B
$$\frac{2}{\sqrt{5}}$$
C
$$\frac{\sqrt{3}}{2}$$
D
$$\frac{\sqrt{5}}{3}$$
4
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
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