Let f(x) = 15 – |x – 10|; x $\in$ R. Then the set of all values of x, at which the function, g(x) =...

If the function f defined on $\left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ by $f(x)=\left\{\begin{array}{cc}\frac{\sqrt{2} \cos x-1}{\cot x-1}, & x \neq \frac{\pi}{4} \\ k, & x=\frac{\pi}{4}\end{array}\right.$ is continuous, then k...

If the line $\frac{x-2}{3}=\frac{y+1}{2}=\frac{z-1}{-1}$ intersects the plane $2 x+3 y-z+13=0$ at a point $P$ and the plane $3 x+y+4 z=16$ at a point $Q$, then...

Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function which satisfies $f(\mathrm{x}+\mathrm{y})=f(\mathrm{x})+f(\mathrm{y}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R}$. If $f(1)=2$ and $\mathrm{g}(\mathrm{n})=\sum_{\mathrm{k}=1}^{(\mathrm{n})} \mathrm{f}(\mathrm{k}), \mathrm{n} \in \mathrm{N}$ then...

Let $S$ be the set of all points in $(-\pi, \pi)$ at which the function, $f(x)=\min \{\sin x, \cos x\}$ is not differentiable. Then $S$...

If a function f(x) defined by

be continuous for some $a, b, c \in R$...

If $...

Let $f(x)=x \cdot\left[\frac{x}{2}\right]$ for $-10

JEE Main Mathematics Easy

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