Let $[x]$ denote the greatest integer function and $f(x)=\max\{\,1+x+[x],\ 2+x,\ x+2[x]\,\},\ 0\le x\le 2.$ Let $m$ be the number of points in $[0,2]$, where $f$ is not continuous and $n$ be the number of points in $(0,2)$, where $f$ is not differentiable. Then $(m+n)^2+2$ is equal to:
Previous 10 Questions — JEE Main 2023 (15 April Morning Shift)
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The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observ…
Topic: JEE Main 2023 (15 April Morning Shift)
If the domain of the function $f(x)=\log_e(4x^2+11x+6)+\sin^{-1}(4x+3)+\cos^{-1}\!\left(\dfrac{10x+6}{3}\right)$ is $(\…
Topic: JEE Main 2023 (15 April Morning Shift)
Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and
$\overrightarrow…
Topic: JEE Main 2023 (15 April Morning Shift)
The total number of three-digit numbers, divisible by 3, which can be formed using the digits , if repetition of d…
Topic: JEE Main 2023 (15 April Morning Shift)
If $\displaystyle \int_{0}^{1} \frac{1}{(5+2x-2x^2)\,(1+e^{\,2-4x})}\,dx=\frac{1}{\alpha}\log_e\!\left(\frac{\alpha+1}{…
Topic: JEE Main 2023 (15 April Morning Shift)
Let $x=x(y)$ be the solution of the differential equation
$2(y+2)\log_e(y+2)\,dx+\big(x+4-2\log_e(y+2)\big)\,dy=0,\quad…
Topic: JEE Main 2023 (15 April Morning Shift)
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Let $\left(a+bx+cx^2\right)^{10}=\displaystyle\sum_{i=0}^{20} p_i x^i,\ a,b,c\in\mathbb{N}.$
If $p_1=20$ and $p_2=210$…
Topic: JEE Main 2023 (15 April Morning Shift)
A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on …
Topic: JEE Main 2023 (15 April Morning Shift)
The number of real roots of the equation $x|x|-5|x+2|+6=0$ is:
Topic: JEE Main 2023 (15 April Morning Shift)
If $(\alpha,\beta)$ is the orthocenter of the triangle $ABC$ with vertices $A(3,-7)$, $B(-1,2)$ and $C(4,5)$, then $9\a…
Topic: JEE Main 2023 (15 April Morning Shift)
Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2, G_3$ be three geometric means of two distinct positive numbe…
Topic: JEE Main 2023 (15 April Morning Shift)
Let $S$ be the set of all values of $\lambda$ for which the shortest distance between the lines
$\dfrac{x-\lambda}{0}=…
Topic: JEE Main 2023 (15 April Morning Shift)
If the set $\left\{\operatorname{Re}\!\left(\dfrac{z-\overline{z}+z\overline{z}}{\,2-3z+5\overline{z}\,}\right): z\in\m…
Topic: JEE Main 2023 (15 April Morning Shift)
