Let $P$ be the foot of the perpendicular from the point $Q(10,-3,-1)$ on the line $\dfrac{x-3}{7}=\dfrac{y-2}{-1}=\dfrac{z+1}{-2}$. Then the area of the right-angled triangle $PQR$, where $R$ is the point $(3,-2,1)$, is:
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The number of words that can be formed using all the letters of the word "DAUGHTER" such that all the vowels never come…
Topic: JEE Main 2025 (23 January Morning Shift)
Let $f(x)=\log_e x$ and $g(x)=\dfrac{x^{4}-2x^{3}+3x^{2}-2x+2}{2x^{2}-2x+1}$. Then the domain of $f\circ g$ is:
Topic: JEE Main 2025 (23 January Morning Shift)
Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be $\hat{i}+2\hat{j}+\hat{k}$, $\hat{i}+3\hat…
Topic: JEE Main 2025 (23 January Morning Shift)
If $\dfrac{\pi}{2}\le x\le \dfrac{3\pi}{4}$, then $\cos^{-1}\!\left(\dfrac{12}{13}\cos x+\dfrac{5}{13}\sin x\right)$ is…
Topic: JEE Main 2025 (23 January Morning Shift)
One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face m…
Topic: JEE Main 2025 (23 January Morning Shift)
The value of $(\sin 70^\circ)\,\big(\cot 10^\circ \cot 70^\circ - 1\big)$ is:
Topic: JEE Main 2025 (23 January Morning Shift)
$
f(x)=\left\{\begin{array}{l}
\frac{2}{x}\left\{\sin \left(k_1+1\right) x+\sin \left(k_2-1\right) x\right\}, \quad x0
…
Topic: JEE Main 2025 (23 January Morning Shift)
If the system of equations
$(\lambda-1)x+(\lambda-4)y+\lambda z=5$
$\lambda x+(\lambda-1)y+(\lambda-4)z=7$
$(\lambd…
Topic: JEE Main 2025 (23 January Morning Shift)
The value of $\int_{e^2}^{e^4} \frac{1}{x}\left(\frac{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}}{e^{\left(\left(…
Topic: JEE Main 2025 (23 January Morning Shift)
Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. T…
Topic: JEE Main 2025 (23 January Morning Shift)
