The distance of the point $Q(0,2,-2)$ from the line passing through the point $P(5,-4,3)$ and perpendicular to the lines $\ \vec r = (-3\hat i + 2\hat k) + \lambda(2\hat i + 3\hat j + 5\hat k),\ \lambda\in\mathbb R,$ and $\ \vec r = (\hat i - 2\hat j + \hat k) + \mu(-\hat i + 3\hat j + 2\hat k),\ \mu\in\mathbb R,$ is:
Previous 10 Questions — JEE Main 2024 (31 January Morning Shift)
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Two marbles are drawn in succession from a box containing $10$ red, $30$ white,
$20$ blue and $15$ orange marbles, with…
Topic: JEE Main 2024 (31 January Morning Shift)
The sum of the series
$\displaystyle \frac{1}{1-3\cdot1^{2}+1^{4}}+\frac{2}{1-3\cdot2^{2}+2^{4}}+\frac{3}{1-3\cdot3^{2}…
Topic: JEE Main 2024 (31 January Morning Shift)
Let $\vec a=3\hat i+\hat j-2\hat k,\ \vec b=4\hat i+\hat j+7\hat k$ and $\vec c=\hat i-3\hat j+4\hat k$ be three vector…
Topic: JEE Main 2024 (31 January Morning Shift)
Three rotten apples are accidentally mixed with fifteen good apples. Assuming the random
variable $x$ to be the number …
Topic: JEE Main 2024 (31 January Morning Shift)
Let $y=y(x)$ be the solution of the differential equation
$\displaystyle \frac{dy}{dx}=\frac{\tan x + y}{\sin x}$, $x\i…
Topic: JEE Main 2024 (31 January Morning Shift)
If $f(x)=\dfrac{4x+3}{6x-4}$, $x\ne\dfrac{2}{3}$, and $(f\circ f)(x)=g(x)$,
where $g:\mathbb{R}-\left\{\dfrac{2}{3}\rig…
Topic: JEE Main 2024 (31 January Morning Shift)
For $0 < c < b < a$, let
$(a+b-2c)x^{2} + (b+c-2a)x + (c+a-2b) = 0$
and let $\alpha \ne 1$ be one of its roots. Then, a…
Topic: JEE Main 2024 (31 January Morning Shift)
Let $\alpha,\beta,\gamma,\delta\in\mathbb{Z}$ and let
$A(\alpha,\beta),\ B(1,0),\ C(\gamma,\delta),\ D(1,2)$ be the ver…
Topic: JEE Main 2024 (31 January Morning Shift)
Let $S$ be the set of positive integral values of $a$ for which
$\frac{a x^{2}+2(a+1)x+9a+4}{x^{2}-8x+32}
Topic: JEE Main 2024 (31 January Morning Shift)
For $\alpha,\beta,\gamma\ne 0$, if
$\sin^{-1}\alpha+\sin^{-1}\beta+\sin^{-1}\gamma=\pi$
and
$(\alpha+\beta+\gamma)\,(\a…
Topic: JEE Main 2024 (31 January Morning Shift)
Next 10 Questions — JEE Main 2024 (31 January Morning Shift)
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Let $g(x)$ be a linear function and
$
f(x)=
\begin{cases}
g(x), & x\le 0,\\[2mm]
\left(\dfrac{1+x}{2+x}\right)^{\tfrac{…
Topic: JEE Main 2024 (31 January Morning Shift)
The area of the region
$\Big\{(x,y): y^{2}\le4x,\ x0,\ x\ne3\Big\}$
is:
Topic: JEE Main 2024 (31 January Morning Shift)
The solution curve of the differential equation
$y\dfrac{dx}{dy}=x(\log_e x-\log_e y+1),\ x>0,\ y>0,$
passing through…
Topic: JEE Main 2024 (31 January Morning Shift)
If the system of linear equations
$\begin{aligned}
& x-2 y+z=-4 \\
& 2 x+\alpha y+3 z=5 \\
& 3 x-y+\beta z=3
\end{align…
Topic: JEE Main 2024 (31 January Morning Shift)
Let $a$ be the sum of all coefficients in the expansion of
$\big(1-2x+2x^{2}\big)^{2023}\big(3-4x^{2}+2x^{3}\big)^{2024…
Topic: JEE Main 2024 (31 January Morning Shift)
If $f(x)=
\begin{vmatrix}
x^{3} & 2x^{2}+1 & 1+3x\\
3x^{2}+2 & 2x & x^{3}+6\\
x^{3}-x & 4 & x^{2}-2
\end{vmatrix}
\ \te…
Topic: JEE Main 2024 (31 January Morning Shift)
If one of the diameters of the circle $x^{2}+y^{2}-10x+4y+13=0$ is a chord of another
circle $C$, whose center is the p…
Topic: JEE Main 2024 (31 January Morning Shift)
If the foci of a hyperbola are the same as those of the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{25}=1$
and the eccentri…
Topic: JEE Main 2024 (31 January Morning Shift)
