There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC. Similarly, there are 6 points P6, P7,..., P11 on the side BC and 7 points P12, P13,..., P18 on the side CA. The number of triangles that can be formed using the points P1, P2,..., P18 as vertices is:
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Let
$f(x)=
\begin{cases}
-2, & -2 \le x \le 0,\\[4pt]
x-2, & 0 < x \le 2,
\end{cases}$
and $h(x)=f(|x|)+|f(x)|.$
The…
Topic: JEE Main 2024 (4 April Morning Shift)
One of the points of intersection of the curves
$y=1+3x-2x^2$ and $y=\dfrac{1}{x}$
is $\left(\dfrac{1}{2},\,2\right)$…
Topic: JEE Main 2024 (4 April Morning Shift)
A square is inscribed in the circle $x^2 + y^2 - 10x - 6y + 30 = 0$.
One side of this square is parallel to $y = x + …
Topic: JEE Main 2024 (4 April Morning Shift)
Let $\alpha, \beta \in \mathbb{R}$.
Let the mean and the variance of 6 observations $-3,\, 4,\, 7,\,-6,\, \alpha,\, \…
Topic: JEE Main 2024 (4 April Morning Shift)
Let $f(x)=x^5+2e^{x/4}$ for all $x\in\mathbb R$.
Consider a function $g(x)$ such that $(g\circ f)(x)=x$ for all $x\in…
Topic: JEE Main 2024 (4 April Morning Shift)
Let a unit vector which makes an angle of $60^\circ$ with $\,2\hat i+2\hat j-\hat k\,$ and an angle of $45^\circ$ with …
Topic: JEE Main 2024 (4 April Morning Shift)
If the domain of the function
$\sin^{-1}\!\left(\dfrac{3x-22}{2x-19}\right)+\log_e\!\left(\dfrac{3x^2-8x+5}{x^2-3x-10}…
Topic: JEE Main 2024 (4 April Morning Shift)
Let the point, on the line passing through the points $P(1,-2,3)$ and $Q(5,-4,7)$,
farther from the origin and at a di…
Topic: JEE Main 2024 (4 April Morning Shift)
The vertices of a triangle are $A(-1,3)$, $B(-2,2)$ and $C(3,-1)$.
A new triangle is formed by shifting the sides of …
Topic: JEE Main 2024 (4 April Morning Shift)
Three urns $A$, $B$ and $C$ contain $(7\text{ red}, 5\text{ black})$, $(5\text{ red}, 7\text{ black})$ and $(6\text{ re…
Topic: JEE Main 2024 (4 April Morning Shift)
