Let $\vec a=\hat i+2\hat j+\hat k$, $\quad \vec b=3(\hat i-\hat j+\hat k)$. Let $\vec c$ be the vector such that $\vec a\times\vec c=\vec b$ and $\vec a\cdot\vec c=3$. Then $\vec a\cdot\big((\vec c\times\vec b)-\vec b-\vec c\big)$ is equal to:
Previous 10 Questions — JEE Main 2024 (27 January Morning Shift)
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Let $a_1,a_2,\ldots,a_{10}$ be $10$ observations such that
$\displaystyle \sum_{k=1}^{10} a_k = 50$
and
$\displaystyle …
Topic: JEE Main 2024 (27 January Morning Shift)
The number of common terms in the progressions
$4,\,9,\,14,\,19,\ldots,$ up to $25^{\text{th}}$ term and
$3,\,6,\,9,\,1…
Topic: JEE Main 2024 (27 January Morning Shift)
${}^{n-1}C_r \;=\; (k^2-8)\, {}^{n}C_{r+1}$ if and only if:
Topic: JEE Main 2024 (27 January Morning Shift)
The portion of the line $4x+5y=20$ in the first quadrant is trisected by the lines $L_1$ and $L_2$ passing through the …
Topic: JEE Main 2024 (27 January Morning Shift)
If the shortest distance between the lines
$\dfrac{x-4}{2}=\dfrac{y+1}{3}=\dfrac{z-\lambda}{2}$
and
$\dfrac{x-2}{…
Topic: JEE Main 2024 (27 January Morning Shift)
Four distinct points $(2k,3k)$, $(1,0)$, $(0,1)$ and $(0,0)$ lie on a circle for $k$ equal to:
Topic: JEE Main 2024 (27 January Morning Shift)
Consider the matrix
$f(x)=\begin{bmatrix}
\cos x & -\sin x & 0\\
\sin x & \cos x & 0\\
0 & 0 & 1
\end{bmatrix}$.
Give…
Topic: JEE Main 2024 (27 January Morning Shift)
If $a=\displaystyle\lim_{x\to 0}\dfrac{\sqrt{\,1+\sqrt{\,1+x^{2}\,}\,}-\sqrt{2}}{x^{2}}$
and $b=\displaystyle\lim_{x\to…
Topic: JEE Main 2024 (27 January Morning Shift)
Consider the function
$
f(x)=
\begin{cases}
\dfrac{a\,(7x-12-x^{2})}{\,b\,\lfloor x^{2}-7x+12\rfloor\,}, & x3,\\[6pt]
b…
Topic: JEE Main 2024 (27 January Morning Shift)
The length of the chord of the ellipse $\dfrac{x^2}{25}+\dfrac{y^2}{16}=1$,
whose midpoint is $\left(1,\dfrac{9}{5}\rig…
Topic: JEE Main 2024 (27 January Morning Shift)
Next 10 Questions — JEE Main 2024 (27 January Morning Shift)
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If $A$ denotes the sum of all the coefficients in the expansion of $(1-3x+10x^2)^n$
and $B$ denotes the sum of all the …
Topic: JEE Main 2024 (27 January Morning Shift)
The function $f:\,\mathbb{N}\setminus\{1\}\to\mathbb{N}$ defined by $f(n)=$ the highest prime factor of $n$, is:
Topic: JEE Main 2024 (27 January Morning Shift)
