Let $\vec{a} = \hat{i} - 2\hat{j} + 3\hat{k},; \vec{b} = 2\hat{i} + \hat{j} - \hat{k},; \vec{c} = \lambda\hat{i} + \hat{j} + \hat{k}$
and $\vec{v} = \vec{a} \times \vec{b}$. If $\vec{v} \cdot \vec{c} = 11$ and the length of the projection of $\vec{b}$ on $\vec{c}$ is $p$, then $9p^2$ is equal to:
Previous 10 Questions — JEE Main 2026 (23 January Morning Shift)
Nearest first
1
2
3
4
5
6
7
8
9
10
Let $\frac{\pi}{2} < \theta < \pi$ and $\cot\theta = -\frac{1}{2\sqrt{2}}$. Then the value of$\sin\left(\frac{150…
Topic: JEE Main 2026 (23 January Morning Shift)
If $f(x) = \begin{cases} \dfrac{a|x| + x^2 - 2(\sin x)(\cos x)}{x}, & x \ne 0 \ b, & x = 0 \end{cases}$
is cont…
Topic: JEE Main 2026 (23 January Morning Shift)
The number of $4$-letter words, with or without meaning, which can be formed using the letters $PQRPRSTUVP$, is ______.
Topic: JEE Main 2026 (23 January Morning Shift)
From the first $100$ natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If …
Topic: JEE Main 2026 (23 January Morning Shift)
Let $f$ be a twice differentiable non-negative function such that$(f(x))^2 = 25 + \int_0^x \big((f(t))^2 + (f'(t))^2\bi…
Topic: JEE Main 2026 (23 January Morning Shift)
Let the area of the region bounded by the curve
$y = \max{\sin x, \cos x}$, lines $x = 0,; x = \frac{3\pi}{2}$, and th…
Topic: JEE Main 2026 (23 January Morning Shift)
Let $|A| = 6$, where $A$ is a $3 \times 3$ matrix. If
$|\text{adj}(3\text{adj}(A^2 \cdot \text{adj}(2A)))| = 2^m \cdot…
Topic: JEE Main 2026 (23 January Morning Shift)
Let the direction cosines of two lines satisfy the equations:
$4\ell + m - n = 0$ and $2mn + 10n\ell + 3\ell m = 0$.
…
Topic: JEE Main 2026 (23 January Morning Shift)
Let the mean and variance of $8$ numbers
$-10,; -7,; -1,; x,; y,; 9,; 2,; 16$
be $\dfrac{7}{2}$ and $\dfrac{293}{4}$,…
Topic: JEE Main 2026 (23 January Morning Shift)
The value of $\dfrac{{}^{100}C_{50}}{51} + \dfrac{{}^{100}C_{51}}{52} + \cdots + \dfrac{{}^{100}C_{100}}{101}$ is:
Topic: JEE Main 2026 (23 January Morning Shift)
