Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \in \mathcal{N}$, then $3(\mathrm{~b}+\mathrm{c})$ is equal to
Previous 10 Questions — JEE Main 2025 (23 January Morning Shift)
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Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, z \in C$, be the equation of a circle with center at $C$. …
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)
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)
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)
$
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)
The value of $(\sin 70^\circ)\,\big(\cot 10^\circ \cot 70^\circ - 1\big)$ 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)
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)
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)
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)
Next 10 Questions — JEE Main 2025 (23 January Morning Shift)
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If the line $3x - 2y + 12 = 0$ intersects the parabola $4y = 3x^2$ at the points $A$ and $B$, then at the vertex of the…
Topic: JEE Main 2025 (23 January Morning Shift)
If the first term of an A.P. is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next fo…
Topic: JEE Main 2025 (23 January Morning Shift)
Let the arc $AC$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $AC$ divides the arc …
Topic: JEE Main 2025 (23 January Morning Shift)
Let the area of $\triangle PQR$ with vertices $P(5,4),\ Q(-2,4)$ and $R(a,b)$ be $35$ square units. If its orthocenter …
Topic: JEE Main 2025 (23 January Morning Shift)
If $A,B$ and $\big(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1})\big)$ are non-singular matrices of the same or…
Topic: JEE Main 2025 (23 January Morning Shift)
Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation on the set $\{1,2,3,4\}$. The minimum number of ordered pairs that must be …
Topic: JEE Main 2025 (23 January Morning Shift)
