If the function $f(x)=2x^{3}-9ax^{2}+12a^{2}x+1,;a>0$ has a local maximum at $x=\alpha$ and a local minimum at $x=\alpha^{2}$, then $\alpha$ and $\alpha^{2}$ are the roots of the equation:
Previous 10 Questions — JEE Main 2024 (8 April Evening Shift)
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The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets …
Topic: JEE Main 2024 (8 April Evening Shift)
The sum of all possible values of $\theta\in[-\pi,2\pi]$, for which $\dfrac{1+i\cos\theta}{1-2i\cos\theta}$ is purely i…
Topic: JEE Main 2024 (8 April Evening Shift)
Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}+3\hat{j}-5\hat{k}$ and $\vec{c}=3\hat{i}-\hat{j}+\lambda\hat…
Topic: JEE Main 2024 (8 April Evening Shift)
Let $A={2,3,6,8,9,11}$ and $B={1,4,5,10,15}$.
Let $R$ be a relation on $A\times B$ defined by
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Topic: JEE Main 2024 (8 April Evening Shift)
$\mathrm{a}, \mathrm{b}>0$, let $f(x)= \begin{cases}\frac{\tan ((\mathrm{a}+1) x)+\mathrm{b} \tan x}{x}, & x< 0 \\ 3, &…
Topic: JEE Main 2024 (8 April Evening Shift)
In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\dfrac{70}{3}$ and …
Topic: JEE Main 2024 (8 April Evening Shift)
Let $f(x)=\left\{\begin{array}{ccc}-\mathrm{a} & \text { if } & -\mathrm{a} \leq x \leq 0 \\ x+\mathrm{a} & \text { if …
Topic: JEE Main 2024 (8 April Evening Shift)
If the system of equations $x+4y-z=\lambda,; 7x+9y+\mu z=-3,; 5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\…
Topic: JEE Main 2024 (8 April Evening Shift)
Let $\int_\limits\alpha^{\log _e 4} \frac{\mathrm{d} x}{\sqrt{\mathrm{e}^x-1}}=\frac{\pi}{6}$. Then $\mathrm{e}^\alpha$…
Topic: JEE Main 2024 (8 April Evening Shift)
If $\alpha \neq \mathrm{a}, \beta \neq \mathrm{b}, \gamma \neq \mathrm{c}$ and $\left|\begin{array}{lll}\alpha & \mathr…
Topic: JEE Main 2024 (8 April Evening Shift)
Next 10 Questions — JEE Main 2024 (8 April Evening Shift)
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If the value of $\dfrac{5\cos36^{\circ}+5\sin18^{\circ}}{5\cos36^{\circ}-3\sin18^{\circ}}$ is $\dfrac{a\sqrt{5}-b}{c}$,…
Topic: JEE Main 2024 (8 April Evening Shift)
If the image of the point $(-4,5)$ in the line $x+2y=2$ lies on the circle $(x+4)^{2}+(y-3)^{2}=r^{2}$, then $r$ is equ…
Topic: JEE Main 2024 (8 April Evening Shift)
If the term independent of $x$ in the expansion of $\left(\sqrt{a},x^{2}+\dfrac{1}{2x^{3}}\right)^{10}$ is $105$, then …
Topic: JEE Main 2024 (8 April Evening Shift)
