Let a curve $y=f(x)$ pass through the points $(0,5)$ and $(\log_e 2,\,k)$. If the curve satisfies the differential equation $2(3+y)e^{2x}\,dx-(7+e^{2x})\,dy=0$, then $k$ is equal to:
Next 10 Questions — JEE Main 2025 (23 January Morning Shift)
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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}=\dfra…
Topic: JEE Main 2025 (23 January Morning Shift)
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)
