JEE MAIN Increasing Decreasing Function Previous Year Question Paper and Solution with PDF

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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN Increasing Decreasing Function PYQ

Qus : 1 JEE MAIN PYQ

$f:R \to R$ be defined as$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$ Let A = {x $ \in $ R : f is increasing}. Then A is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (24 February Evening Shift) PYQ

Solution

Qus : 2 JEE MAIN PYQ

For $f(x)=\sin x+3x-\dfrac{2}{\pi}(x^{2}+x)$, where $x\in\left[0,\tfrac{\pi}{2}\right]$, consider: (I) $f$ is increasing in $\left(0,\tfrac{\pi}{2}\right)$. (II) $f'$ is decreasing in $\left(0,\tfrac{\pi}{2}\right)$.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (5 April Morning Shift) PYQ

Solution

Qus : 3 JEE MAIN PYQ

Let $(2,3)$ be the largest open interval in which the function $f(x)=2\log_e(x-2)-x^2+ax+1$ is strictly increasing and $(b,c)$ be the largest open interval in which the function $g(x)=(x-1)^3(x+2-a)^2$ is strictly decreasing. Then $100(a+b-c)$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (24 January Evening Shift) PYQ

Solution

Qus : 4 JEE MAIN PYQ

Let $\lambda^*$ be the largest value of $\lambda$ for which the function $f_\lambda(x) = 4\lambda x^3 - 36\lambda x^2 + 36x + 48$ is increasing for all $x \in \mathbb{R}$. Then $f_{\lambda^*}(1) + f_{\lambda^*}(-1)$ is equal to:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (24 June Evening Shift) PYQ

Solution

Qus : 5 JEE MAIN PYQ

The function $f(x) = x e^{\,x(1-x)}, \, x \in \mathbb{R}$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 July Evening Shift) PYQ

Solution

Qus : 6 JEE MAIN PYQ

The interval in which the function $f(x)=x^{x}$, $x>0$, is strictly increasing is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (6 April Morning Shift) PYQ

Solution

Qus : 7 JEE MAIN PYQ

If the function $f$ given by $f(x)=x^3-3(a-2)x^2+3ax+7$, for some $a\in\mathbb{R}$, is increasing in $(0,1]$ and decreasing in $[1,5)$, then a root of the equation $\dfrac{f(x)-14}{(x-1)^2}=0\ (x\ne1)$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 January Evening Shift) PYQ

Solution

Qus : 8 JEE MAIN PYQ

Let f be a real valued function, defined on R $-$ {$-$1, 1} and given by f(x) = 3 log_e $\left| {{{x - 1} \over {x + 1}}} \right| - {2 \over {x - 1}}$. Then in which of the following intervals, function f(x) is increasing?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (16 March Evening Shift) PYQ

Solution

Qus : 9 JEE MAIN PYQ

For the function $f(x)=\cos x - x + 1,; x\in\mathbb{R}$, consider the statements (S1) $f(x)=0$ for only one value of $x$ in $[0,\pi]$. (S2) $f(x)$ is decreasing in $\left[0,\tfrac{\pi}{2}\right]$ and increasing in $\left[\tfrac{\pi}{2},\pi\right]$. Which is/are correct?

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (8 April Morning Shift) PYQ

Solution

Qus : 10 JEE MAIN PYQ

Let the function $f(x)=\dfrac{x}{3}+\dfrac{3}{x}+3,\ x\ne0$ be strictly increasing in $(-\infty,\alpha_1)\cup(\alpha_2,\infty)$ and strictly decreasing in $(\alpha_3,\alpha_4)\cup(\alpha_4,\alpha_5)$. Then $\displaystyle \sum_{i=1}^{5}\alpha_i^{2}$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (8 April Evening Shift) PYQ

Solution

Qus : 11 JEE MAIN PYQ

Let $f:[0,2]\to\mathbb{R}$ be a twice differentiable function such that $f''(x)>0$ for all $x\in(0,2)$. If $\phi(x)=f(x)+f(2-x)$, then $\phi$ is:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (8 April Morning Shift) PYQ

Solution

Qus : 12 JEE MAIN PYQ

Consider the function $f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}$ defined by $f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1$. Consider the statements

(I) The curve $y=f(x)$ intersects the $x$-axis exactly at one point.

(II) The curve $y=f(x)$ intersects the $x$-axis at $x=\cos \frac{\pi}{12}$

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Morning Shift) PYQ

Solution

Qus : 13 JEE MAIN PYQ

The function, f(x) = (3x – 7)x^2/3, x $ \in $ R, isincreasing for all x lying in

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 3 September 2020 (Morning) PYQ

Solution

Qus : 14 JEE MAIN PYQ

Let $f:(0,1)\to \mathbb{R}$ be a function defined by $f(x)=\dfrac{1}{1-e^{-x}}$, and $g(x)=\bigl(f(-x)-f(x)\bigr)$.

Consider two statements:

(I) $g$ is an increasing function in $(0,1)$

(II) $g$ is one-one in $(0,1)$

Then,

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2023 (25 January Morning Shift) PYQ

Solution

Qus : 15 JEE MAIN PYQ

The function $f(x)=2x+3x^{\frac{1}{3}},; x\in\mathbb{R}$ has:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2025 (29 January Evening Shift) PYQ

Solution

Qus : 16 JEE MAIN PYQ

The number of real solutions of :- ${x^7} + 5{x^3} + 3x + 1 = 0$ is equal to ____________.

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2022 (28 June Morning Shift) PYQ

Solution

Qus : 17 JEE MAIN PYQ

The function $f(x) = {x^3} - 6{x^2} + ax + b$ is such that $f(2) = f(4) = 0$. Consider two statements : Statement 1 : there exists x₁, x₂ $\in$(2, 4), x₁ < x₂, such that f'(x₁) = $-$1 and f'(x₂) = 0. Statement 2 : there exists x₃, x₄ $\in$ (2, 4), x₃ < x₄, such that f is decreasing in (2, x₄), increasing in (x₄, 4) and $2f'({x_3}) = \sqrt 3 f({x_4})$.Then

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2021 (1 September Evening Shift) PYQ

Solution

Qus : 18 JEE MAIN PYQ

If $5f(x)+4f\!\left(\frac{1}{x}\right)=x^{2}-2,\ \forall x\ne 0$ and $y=9x^{2}f(x)$, then $y$ is strictly increasing in:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2024 (1 February Morning Shift) PYQ

Solution

Qus : 19 JEE MAIN PYQ

Let $f(x)=\sin^{4}x+\cos^{4}x$. Then $f$ is an increasing function in the interval :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

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