If the coefficient of $x^{15}$ in the expansion of $\left(a x^{3}+\dfrac{1}{b x^{1/3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{1/3}-\dfrac{1}{b x^{3}}\right)^{15}$, where $a$ and $b$ are positive real numbers, then for each such ordered pair $(a,b)$:
Previous 10 Questions — JEE Main 2023 (30 January Morning Shift)
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If $\tan 15^\circ + \dfrac{1}{\tan 75^\circ} + \dfrac{1}{\tan 105^\circ} + \tan 195^\circ = 2a$, then the value of $(a+…
Topic: JEE Main 2023 (30 January Morning Shift)
If the solution of the equation $\log_{\cos x}\!\big(\cot x\big) + 4\log_{\sin x}\!\big(\tan x\big) = 1,\ x\in\left(0,\…
Topic: JEE Main 2023 (30 January Morning Shift)
$ \text{Suppose } f:\mathbb{R}\to(0,\infty) \text{ be a differentiable function such that } 5f(x+y)=f(x)\cdot f(y),\ \f…
Topic: JEE Main 2023 (30 January Morning Shift)
$ \text{If [t] denotes the greatest integer } \le t, \text{ then the value of } \frac{3(e-1)}{e} \int_{1}^{2} x^2 e^{\l…
Topic: JEE Main 2023 (30 January Morning Shift)
Let the system of linear equations
\[
\begin{cases}
x + y + kz = 2,\\
2x + 3y - z = 1,\\
3x + 4y + 2z = k
\end{cases}
\…
Topic: JEE Main 2023 (30 January Morning Shift)
The minimum number of elements that must be added to the relation $R=\{(a,b),(b,c)\}$ on the set $\{a,b,c\}$ so that it…
Topic: JEE Main 2023 (30 January Morning Shift)
Let the solution curve $y=y(x)$ of the differential equation
\[
\frac{dy}{dx}=\frac{3x^5\tan^{-1}(x^3)}{(1+x^6)^{3/2}}\…
Topic: JEE Main 2023 (30 January Morning Shift)
Next 10 Questions — JEE Main 2023 (30 January Morning Shift)
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Let a unit vector $\overrightarrow{OP}$ make angles $\alpha,\beta,\gamma$ with the positive directions of the coordinat…
Topic: JEE Main 2023 (30 January Morning Shift)
If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the produ…
Topic: JEE Main 2023 (30 January Morning Shift)
