1
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1
Change Language

Let $$\mathrm{S}$$ be the set of values of $$\lambda$$, for which the system of equations

$$6 \lambda x-3 y+3 z=4 \lambda^{2}$$,

$$2 x+6 \lambda y+4 z=1$$,

$$3 x+2 y+3 \lambda z=\lambda$$ has no solution. Then $$12 \sum_\limits{i \in S}|\lambda|$$ is equal to ___________.

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2
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1
Change Language

If the domain of the function $$f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)$$ is $$[\alpha, \beta) \mathrm{U}(\gamma, \delta]$$, then $$|3 \alpha+10(\beta+\gamma)+21 \delta|$$ is equal to _________.

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3
JEE Main 2023 (Online) 10th April Evening Shift
Numerical
+4
-1
Change Language

Let the equations of two adjacent sides of a parallelogram $$\mathrm{ABCD}$$ be $$2 x-3 y=-23$$ and $$5 x+4 y=23$$. If the equation of its one diagonal $$\mathrm{AC}$$ is $$3 x+7 y=23$$ and the distance of A from the other diagonal is $$\mathrm{d}$$, then $$50 \mathrm{~d}^{2}$$ is equal to ____________.

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4
JEE Main 2023 (Online) 10th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

A person travels $$x$$ distance with velocity $$v_{1}$$ and then $$x$$ distance with velocity $$v_{2}$$ in the same direction. The average velocity of the person is $$\mathrm{v}$$, then the relation between $$v, v_{1}$$ and $$v_{2}$$ will be.

A
$$\mathbf{V}=\mathbf{V}_{1}+\mathbf{V}_{2}$$
B
$$V=\frac{v_{1}+V_{2}}{2}$$
C
$$\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$$
D
$$\frac{2}{\mathrm{~V}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}$$
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