1
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume that the balls are identical otherwise. Three balls are drawn randomly one after the other without replacement. For $i=1,2,3$, let $W_i, G_i$, and $B_i$ denote the events that the ball drawn in the $i^{\text {th }}$ draw is a white ball, green ball, and blue ball, respectively. If the probability $P\left(W_1 \cap G_2 \cap B_3\right)=\frac{2}{5 N}$ and the conditional probability $P\left(B_3 \mid W_1 \cap G_2\right)=\frac{2}{9}$, then $N$ equals ________.
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2
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by
$$ f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)} . $$
Then the number of solutions of $f(x)=0$ in $\mathbb{R}$ is _________.
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3
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
Let $\vec{p}=2 \hat{i}+\hat{j}+3 \hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha, \beta$, and $\gamma$, we have
$$ 15 \hat{i}+10 \hat{j}+6 \hat{k}=\alpha(2 \vec{p}+\vec{q})+\beta(\vec{p}-2 \vec{q})+\gamma(\vec{p} \times \vec{q}), $$
then the value of $\gamma$ is ________.
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4
JEE Advanced 2024 Paper 2 Online
Numerical
+4
-0
A normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0,-\alpha)$ to the parabola $x^2=-4 a y$, where $a>0$. Let $L$ be the line passing through $(0,-\alpha)$ and parallel to the directrix of the parabola. Suppose that $L$ intersects the parabola at two points $A$ and $B$. Let $r$ denote the length of the latus rectum and $s$ denote the square of the length of the line segment $A B$. If $r: s=1: 16$, then the value of $24 a$ is _______.
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Paper analysis
Total Questions
Chemistry
17
Mathematics
17
Physics
17
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