1
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The number of symmetric matrices of order 3, with all the entries from the set $$\{0,1,2,3,4,5,6,7,8,9\}$$ is :

A
$$10^{9}$$
B
$$9^{10}$$
C
$$10^{6}$$
D
$$6^{10}$$
2
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Out of Syllabus
Change Language

Let $$m_{1}$$ and $$m_{2}$$ be the slopes of the tangents drawn from the point $$\mathrm{P}(4,1)$$ to the hyperbola $$H: \frac{y^{2}}{25}-\frac{x^{2}}{16}=1$$. If $$\mathrm{Q}$$ is the point from which the tangents drawn to $$\mathrm{H}$$ have slopes $$\left|m_{1}\right|$$ and $$\left|m_{2}\right|$$ and they make positive intercepts $$\alpha$$ and $$\beta$$ on the $$x$$-axis, then $$\frac{(P Q)^{2}}{\alpha \beta}$$ is equal to __________.

Your input ____
3
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Change Language

Let the mean of the data

$$x$$ 1 3 5 7 9
Frequency ($$f$$) 4 24 28 $$\alpha$$ 8

be 5. If $$m$$ and $$\sigma^{2}$$ are respectively the mean deviation about the mean and the variance of the data, then $$\frac{3 \alpha}{m+\sigma^{2}}$$ is equal to __________

Your input ____
4
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1
Change Language

Let $$w=z \bar{z}+k_{1} z+k_{2} i z+\lambda(1+i), k_{1}, k_{2} \in \mathbb{R}$$. Let $$\operatorname{Re}(w)=0$$ be the circle $$\mathrm{C}$$ of radius 1 in the first quadrant touching the line $$y=1$$ and the $$y$$-axis. If the curve $$\operatorname{Im}(w)=0$$ intersects $$\mathrm{C}$$ at $$\mathrm{A}$$ and $$\mathrm{B}$$, then $$30(A B)^{2}$$ is equal to __________

Your input ____
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