1
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

Suppose $$\mathrm{AB}$$ is a focal chord of the parabola $$y^2=12 x$$ of length $$l$$ and slope $$\mathrm{m}<\sqrt{3}$$. If the distance of the chord $$\mathrm{AB}$$ from the origin is $$\mathrm{d}$$, then $$l \mathrm{~d}^2$$ is equal to _________.

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2
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

The number of ways of getting a sum 16 on throwing a dice four times is ________.

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3
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

Let $$f$$ be a differentiable function in the interval $$(0, \infty)$$ such that $$f(1)=1$$ and $$\lim _\limits{t \rightarrow x} \frac{t^2 f(x)-x^2 f(t)}{t-x}=1$$ for each $$x>0$$. Then $$2 f(2)+3 f(3)$$ is equal to _________.

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4
JEE Main 2024 (Online) 5th April Morning Shift
Numerical
+4
-1
Change Language

If $$S=\{a \in \mathbf{R}:|2 a-1|=3[a]+2\{a \}\}$$, where $$[t]$$ denotes the greatest integer less than or equal to $$t$$ and $$\{t\}$$ represents the fractional part of $$t$$, then $$72 \sum_\limits{a \in S} a$$ is equal to _________.

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