Let $P(\alpha,\beta,\gamma)$ be the image of the point $Q(3,-3,1)$ in the line $\dfrac{x-0}{1}=\dfrac{y-3}{1}=\dfrac{z-1}{-1}$ and let $R$ be the point $(2,5,-1)$. If the area of $\triangle PQR$ is $\lambda$ and $\lambda^{2}=14K$, then $K$ is:
Previous 10 Questions — JEE Main 2024 (6 April Evening Shift)
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Let $\vec a=6\hat i+\hat j-\hat k$ and $\vec b=\hat i+\hat j$. If $\vec c$ is a vector such that $|\vec c|\ge 6$, $\ \v…
Topic: JEE Main 2024 (6 April Evening Shift)
Let $\vec a=2\hat i+\hat j-\hat k,\quad \vec b=\big((\vec a\times(\hat i+\hat j))\times\hat i\big)\times\hat i.$
Then t…
Topic: JEE Main 2024 (6 April Evening Shift)
If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters a…
Topic: JEE Main 2024 (6 April Evening Shift)
If $A$ is a square matrix of order $3$ such that $\det(A) = 3$ and
$\det(\text{adj}(-4,\text{adj}(-3,\text{adj}(3,\text…
Topic: JEE Main 2024 (6 April Evening Shift)
Find the value of
$ \displaystyle \lim_{n \to \infty} \frac{(1^2 - 1)(n - 1) + (2^2 - 2)(n - 2) + \cdots + (n^2 - n)(n …
Topic: JEE Main 2024 (6 April Evening Shift)
Let $f(x)=\dfrac{1}{7-\sin5x}$ be a function defined on $\mathbb{R}$.
Then the range of the function $f(x)$ is equal to:
Topic: JEE Main 2024 (6 April Evening Shift)
Let $A={1,2,3,4,5}$. Let $R$ be a relation on $A$ defined by $xRy$ iff $4x \le 5y$.
Let $m$ be the number of elements i…
Topic: JEE Main 2024 (6 April Evening Shift)
If $z_1, z_2$ are two distinct complex number such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$, t…
Topic: JEE Main 2024 (6 April Evening Shift)
If the function $f(x)=\left(\dfrac1x\right)^{2x},; x>0$ attains its maximum at $x=\dfrac1e$, then:
Topic: JEE Main 2024 (6 April Evening Shift)
Next 10 Questions — JEE Main 2024 (6 April Evening Shift)
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Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the midpoints of all sides of $\triangle ABC$…
Topic: JEE Main 2024 (6 April Evening Shift)
If the area of the region $\left\{(x, y): \frac{\mathrm{a}}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2,0
Topic: JEE Main 2024 (6 April Evening Shift)
Suppose the solution of the differential equation
$ \displaystyle \frac{dy}{dx}=\frac{(2+\alpha)x-\beta y+2}{\beta x-2\…
Topic: JEE Main 2024 (6 April Evening Shift)
A software company sets up $n$ computer systems to finish an assignment in $17$ days. If $4$ systems crash at the start…
Topic: JEE Main 2024 (6 April Evening Shift)
If $P(6,1)$ is the orthocentre of the triangle whose vertices are $A(5,-2)$, $B(8,3)$ and $C(h,k)$, then the point $C$ …
Topic: JEE Main 2024 (6 April Evening Shift)
If all words (with or without meaning) formed using all the letters of the word NAGPUR are arranged in dictionary order…
Topic: JEE Main 2024 (6 April Evening Shift)
Suppose for a differentiable function $h$, $h(0)=0$, $h(1)=1$ and $h'(0)=h'(1)=2$.
If $g(x)=h(e^{x}),e^{h(x)}$, then $g…
Topic: JEE Main 2024 (6 April Evening Shift)
Let $0\le r\le n$. If ${}^{n+1}C_{r+1} : ^nC_{r} : ^{n-1}C_{r-1} = 55 : 35 : 21$, then $2n+5r$ is equal to:
Topic: JEE Main 2024 (6 April Evening Shift)
If $\displaystyle \int \frac{1}{a^{2}\sin^{2}x+b^{2}\cos^{2}x},dx=\frac{1}{12}\tan^{-1}(3\tan x)+\text{constant}$, then…
Topic: JEE Main 2024 (6 April Evening Shift)
If the locus of a point whose distances from $(2,1)$ and $(1,3)$ are in the ratio $5:4$ is
$ax^{2}+by^{2}+cxy+dx+ey+170…
Topic: JEE Main 2024 (6 April Evening Shift)
