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QJEE MAIN 2022
Let $f(x)=\left[2 x^2+1\right]$ and $g(x)=\left\{\begin{array}{ll}2 x-3, & x<0 \\ 2 x+3, & x \geq 0\end{array}\right.$, where $[t]$ is the greatest integer $\leq t$. Then, in...
JEE MainMathematicsMedium
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QJEE MAIN 2022
Let $c, k \in R$. If $f(x)=(c+1) x^2+\left(1-c^2\right) x+2 k$ and $f(x+y)=f(x)+f(y)-x y$, for all $x, y \in R$, then the value of $...
JEE MainMathematicsHard
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QJEE MAIN 2022
Let $f(x)=\min \{1,1+x \sin x\}, 0 \leq x \leq 2 \pi$. If m is the number of points, where f is not differentiable and n...
JEE MainMathematicsHard
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QJEE MAIN 2022
Let $f(x)=\left\{\begin{array}{ccc}\frac{\sin (x-[x])}{x-[x]}, & x \in(-2,-1) \\ \{\max 2 x, 3[|x|]\}, & |x|<1 \\ 1, & \text { other wise }\end{array}\right.$ where $[t]$ denotes greatest...
JEE MainMathematicsMedium
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QJEE MAIN 2022
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $$ f(x)=\left[\begin{array}{ll} {\left[e^x\right],} & x<0 \\ a e^x+[x-1], & 0 \leq x<1 \\ b+[\sin (\pi x)], &...
JEE MainMathematicsMedium
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QJEE MAIN 2023
Let $[x]$ denote the greatest integer function and $f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2$. Let $m$ be the number of points in...
JEE MainMathematicsMedium
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QJEE MAIN 2023
Let $[x]$ be the greatest integer $\leq x$. Then the number of points in the interval $(-2,1)$, where the function $f(x)=|[x]|+\sqrt{x-[x]}$ is discontinuous is $\_\_\_\_$...
JEE MainMathematicsMedium
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QJEE MAIN 2023
Let $f(x)=\left[x^2-x\right]+|-x+[x]|$, where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$. Then, f is
JEE MainMathematicsMedium
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QJEE-Main 2023
Let $a \in Z$ and [t] be the greatest integer $\leq$ t. Then the number of points, where the function f(x) = [a + 13...
JEE MainMathematicsMedium
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QJEE MAIN
Let f:(0,π)→R be a function given by Where a,b∈Z. If f is continuous at $\mathrm{x}=\frac{\pi}{2}$,...
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Where a,b∈Z. If f is continuous at $\mathrm{x}=\frac{\pi}{2}$,... 