Let $\vec a=2\hat i+\alpha\hat j+\hat k,\ \vec b=-\hat i+\hat k,\ \vec c=\beta\hat j-\hat k$, where $\alpha,\beta$ are integers and $\alpha\beta=-6$. Let the values of the ordered pair $(\alpha,\beta)$ for which the area of the parallelogram whose diagonals are $\vec a+\vec b$ and $\vec b+\vec c$ is $\dfrac{\sqrt{21}}{2}$ be $(\alpha_1,\beta_1)$ and $(\alpha_2,\beta_2)$. Then $\alpha_1^{,2}+\beta_1^{,2}-\alpha_2\beta_2$ is equal to:
Previous 10 Questions — JEE Main 2024 (9 April Evening Shift)
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The sum of the coefficients of $x^{2/3}$ and $x^{-2/5}$ in the binomial expansion of
$\big(x^{2/3}+\tfrac{1}{2}x^{-2/5}…
Topic: JEE Main 2024 (9 April Evening Shift)
Let $a,ar,ar^{2},\ldots$ be an infinite G.P. If $\displaystyle \sum_{n=0}^{\infty} a r^{n}=57$ and $\displaystyle \sum_…
Topic: JEE Main 2024 (9 April Evening Shift)
The area (in square units) of the region enclosed by the ellipse $x^{2}+3y^{2}=18$ in the first quadrant below the line…
Topic: JEE Main 2024 (9 April Evening Shift)
Consider the line $L$ passing through the points $(1,2,3)$ and $(2,3,5)$.
The distance of the point $\left(\dfrac{11}{3…
Topic: JEE Main 2024 (9 April Evening Shift)
$\displaystyle \lim_{x\to 0}\ \frac{e^{-(1+2x)^{\tfrac{1}{2x}}}}{x}$ is equal to:
Topic: JEE Main 2024 (9 April Evening Shift)
Let $B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$ and $A$ be a $2 \times 2$ matrix such that $A B^{-1}=A^…
Topic: JEE Main 2024 (9 April Evening Shift)
If the variance of the frequency distributionis $160$, then the value of $c\in\mathbb{N}$ is:
Topic: JEE Main 2024 (9 April Evening Shift)
Between the following two statements:
Statement I:
Let $\vec{a} = \hat{i} + 2\hat{j} - 3\hat{k}$ and $\vec{b} = 2\hat{…
Topic: JEE Main 2024 (9 April Evening Shift)
The value of the integral
$\displaystyle \int_{-1}^{2} \log_e \big(x + \sqrt{x^2 + 1}\big),dx$ is
Topic: JEE Main 2024 (9 April Evening Shift)
$\lim _\limits{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos…
Topic: JEE Main 2024 (9 April Evening Shift)
