$\text{Consider the lines } L_{1}: , x-1=y-2=z \quad \text{and} \quad L_{2}: , x-2=y=z-1.$ $\text{Let the feet of the perpendiculars from the point } P(5,1,-3) \text{ on } L_{1} \text{ and } L_{2} \text{ be } Q \text{ and } R \text{ respectively.}$ $\text{If the area of the triangle } PQR \text{ is } A, \text{ then } 4A^{2}\text{ is equal to:}$
Previous 10 Questions — JEE Main 2025 (7 April Evening Shift)
Nearest first
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The number of solutions of the equation
$ \cos 2\theta \cos \frac{\theta}{2} + \cos \frac{5\theta}{2} = 2\cos^3 \frac{…
Topic: JEE Main 2025 (7 April Evening Shift)
If the area of the region ${(x,y):, 1+x^2 \le y \le \min{x+7,; 11-3x}}$ is $A$, then $3A$ is equal to:
Topic: JEE Main 2025 (7 April Evening Shift)
If the sum of the second, fourth and sixth terms of a G.P. of positive terms is $21$ and the sum of its eighth, tenth a…
Topic: JEE Main 2025 (7 April Evening Shift)
If the equation of the line passing through the point $ \left( 0, -\frac{1}{2}, 0 \right) $ and perpendicular to the li…
Topic: JEE Main 2025 (7 April Evening Shift)
Let $e_1$ and $e_2$ be the eccentricities of the ellipse $\dfrac{x^2}{b^2}+\dfrac{y^2}{25}=1$ and the hyperbola $\dfrac…
Topic: JEE Main 2025 (7 April Evening Shift)
Let the length of a latus rectum of an ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$ be $10$. If its eccentrici…
Topic: JEE Main 2025 (7 April Evening Shift)
The number of real roots of the equation $x|x-2|+3|x-3|+1=0$ is:
Topic: JEE Main 2025 (7 April Evening Shift)
If the range of the function $f(x)=\dfrac{5-x}{x^2-3x+2}$, $x\ne1,2$, is $(-\infty,\alpha]\cup[\beta,\infty)$, then $\a…
Topic: JEE Main 2025 (7 April Evening Shift)
A bag contains $19$ unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and a head …
Topic: JEE Main 2025 (7 April Evening Shift)
Let $a_n$ be the $n^{\text{th}}$ term of an A.P. If $S_n=a_1+a_2+\cdots+a_n=700$, $a_6=7$ and $S_7=7$, then $a_n$ is eq…
Topic: JEE Main 2025 (7 April Evening Shift)
Next 10 Questions — JEE Main 2025 (7 April Evening Shift)
Ascending by ID
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$A={(\alpha,\beta)\in\mathbb{R}\times\mathbb{R}:\ |\alpha-1|\le 4\ \text{and}\ |\beta-5|\le 6}$
$B={(\alpha,\beta)\in\m…
Topic: JEE Main 2025 (7 April Evening Shift)
Let $\vec a$ and $\vec b$ be vectors of the same magnitude such that
$\displaystyle \frac{\lvert\vec a+\vec b\rvert+\lv…
Topic: JEE Main 2025 (7 April Evening Shift)
Let the system of equations
x + 5y - z = 1
4x + 3y - 3z = 7
24x + y + λz = μ
λ, μ ∈ ℝ, have infinitely many solutions. …
Topic: JEE Main 2025 (7 April Evening Shift)
Let $p$ be the number of all triangles that can be formed by joining the vertices of a regular $n$-gon $P$, and $q$ be …
Topic: JEE Main 2025 (7 April Evening Shift)
Let a random variable $X$ take values $0,1,2,3$ with $P(X=0)=P(X=1)=p$, $P(X=2)=P(X=3)$ and $E(X^2)=2E(X)$. Then the va…
Topic: JEE Main 2025 (7 April Evening Shift)
If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + c is at (3, -1), then m - c i…
Topic: JEE Main 2025 (7 April Evening Shift)
