Monotonicity_JEE_MAIN_27-01-2024_(s2) - Competishun – Live JEE & NEET Courses and Exam Prep

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JEE-Main 2024

27-01-24 S2

Question

Let $g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $f^{\prime \prime}(x)>0$ for all $\mathrm{x} \in(0,3)$. If g is decreasing in $(0, \alpha)$ and increasing in $(\alpha, 3)$, then $8 \alpha$ is

Select the correct option:

A

24

B

0.0

C

18

D

20

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QJEE MAIN 20242024

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Q JEE MAIN 20242024

Let $\vec{a}=\hat{\imath}+\hat{\jmath}+\hat{k}, \vec{b}=-\hat{\imath}-8 \hat{\jmath}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}=4 \hat{\imath}+\mathrm{c}_2 \hat{\jmath}+\mathrm{c}_3 \hat{\mathrm{k}}$ be three vectors such that $\vec{b} \times \vec{a}=\vec{c} \times \vec{a}$....

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QJEE Main 20242024

Let C be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the...

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If $\lambda>0$, let $\theta$ be the angle between the vectors $\vec{a}=\hat{\imath}+\lambda \hat{\jmath}-3 \hat{k}$ and $\vec{b}=3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$. If the vectors...

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If the function $f(x)=\left\{\begin{array}{ll}\frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}} & , x \neq 0 \\ \log _e 2 \log _e 3 & , x=0\end{array}\right.$...

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QJEE MAIN 20242024

If $y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x$, then $96 y^{\prime}\left(\frac{\pi}{6}\right)$ is equal to :

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QJEE Main 20242024

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QJEE MAIN 20242024

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Consider the following reaction, the rate expression of which is given below
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From 6.55 g of aniline, the maximum amount of acetanilide that can be prepared will be $\_\_\_\_$ $\times 10^{-1} \mathrm{~g}$.

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Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant pressure of 5...

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