JEE MAIN Function Previous Year Questions (PYQs) – Page 13 of 15

Let f(x) = log_e(sin x), (0 < x < $\pi $) and g(x) = sin^–1 (e^–x ), (x $ \ge $ 0). If $\alpha $ is a positive real number such that a = (fog)'($\alpha $) and b = (fog)($\alpha $), then :

The function $f(x) = \left\{ {\matrix{ {{\pi \over 4} + {{\tan }^{ - 1}}x,} & {\left| x \right| \le 1} {{1 \over 2}\left( {\left| x \right| - 1} \right),} & {\left| x \right| > 1} } } \right.$is :

Let $x=(8\sqrt{3}+13)^{13}$ and $y=(7\sqrt{2}+9)^{9}$. If $[t]$ denotes the greatest integer $\le t$, then:

If the domain of the function $f(x)=\sqrt{\dfrac{x^{2}-25}{4-x^{2}}}+\log_{10}(x^{2}+2x-15)$ is $(-\infty,\alpha)\cup[\beta,\infty)$, then $\alpha^{2}+\beta^{3}$ is equal to:

The number of real roots of the equation $5+\lvert 2^{x}-1\rvert=2^{x},(2^{x}-2)$ is:

Let [x] denote the greatest integer less than or equal to x. Then, the values of x$\in$R satisfying the equation ${[{e^x}]^2} + [{e^x} + 1] - 3 = 0$ lie in the interval :

For any real number $x$, let $[x]$ denote the largest integer less than equal to $x$. Let $f$ be a real valued function defined on the interval $[-10,10]$ by $f(x)=\left\{\begin{array}{l}x-[x], \text { if }[x] \text { is odd } \\ 1+[x]-x, \text { if }[x] \text { is even } .\end{array}\right.$Then the value of $\frac{\pi^{2}}{10} \int_{-10}^{10} f(x) \cos \pi x \,d x$ is :

$ \text{If the domain of } f(x)=\dfrac{\lfloor x\rfloor}{1+x^{2}},\ \text{where } \lfloor x\rfloor \text{ is greatest integer } \le x,\ \text{is } [2,6),\ \text{then its range is:} $

Let $f$ be a function such that $f(x)+3f\left(\dfrac{24}{x}\right)=4x,; x\ne0$. Then $f(3)+f(8)$ is equal to

Let $A=\{x\in\mathbb{R}:\ x\ \text{is not a positive integer}\}$. Define a function $f:A\to\mathbb{R}$ as $f(x)=\dfrac{2x}{x-1}$. Then $f$ is: