Let $\vec a=2\hat i+\lambda_{1}\hat j+3\hat k$, $\vec b=4\hat i+(3-\lambda_{2})\hat j+6\hat k$, and $\vec c=3\hat i+6\hat j+(\lambda_{3}-1)\hat k$ be three vectors such that $\vec b=2\vec a$ and $\vec a$ is perpendicular to $\vec c$. Then a possible value of $(\lambda_{1},\lambda_{2},\lambda_{3})$ is:
Previous 10 Questions — JEE Main 2019 (10 January Morning Shift)
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Let $n\ge 2$ be a natural number and $0
Topic: JEE Main 2019 (10 January Morning Shift)
The mean of five observations is $5$ and their variance is $9.20$. If three of the five observations are $1,\,3,$ and $…
Topic: JEE Main 2019 (10 January Morning Shift)
If the system of equations$x + y + z = 5$$x + 2y + 3z = 9$$x + 3y + az = \beta$has infinitely many solutions, then $\be…
Topic: JEE Main 2019 (10 January Morning Shift)
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In a class of $140$ students numbered $1$ to $140$, all even–numbered students opted Mathematics, those whose number is…
Topic: JEE Main 2019 (10 January Morning Shift)
If $5,\ 5r,\ 5r^{2}$ are the lengths of the sides of a triangle, then $r$ cannot be equal to:
Topic: JEE Main 2019 (10 January Morning Shift)
For each $t\in\mathbb{R}$, let $[t]$ be the greatest integer less than or equal to $t$.
Then
$\displaystyle \lim_{x\…
Topic: JEE Main 2019 (10 January Morning Shift)
Let $f\left( x \right) = \left\{ {\matrix{
{\max \left\{ {\left| x \right|,{x^2}} \right\}} & {\left|…
Topic: JEE Main 2019 (10 January Morning Shift)
If the third term in the binomial expansion of $(1+x^{\log_{8}x})^{5}$ equals $2560$, then a possible value of $x$ is:
Topic: JEE Main 2019 (10 January Morning Shift)
Let $d\in\mathbb{R}$, and
$A=\begin{bmatrix}
-2 & 4+d & \sin\theta-2\\
1 & \sin\theta+2 & d\\
5 & 2\sin\theta-d & -\sin…
Topic: JEE Main 2019 (10 January Morning Shift)
If the line $3x+4y-24=0$ intersects the $x$-axis at the point $A$ and the $y$-axis at the point $B$, then the incentre …
Topic: JEE Main 2019 (10 January Morning Shift)
The sum of all two–digit positive numbers which, when divided by $7$, yield $2$ or $5$ as remainder is:
Topic: JEE Main 2019 (10 January Morning Shift)
Consider the quadratic equation $(c - 5)x^2 - 2cx + (c - 4) = 0,\ c \ne 5.$
Let $S$ be the set of all integral values…
Topic: JEE Main 2019 (10 January Morning Shift)
If the area enclosed between the curves $y = kx^2$ and $x = ky^2$, $(k > 0)$, is $1$ square unit, then $k$ is:
Topic: JEE Main 2019 (10 January Morning Shift)
