Let $\mathbb{N}$ be the set of natural numbers and two functions $f$ and $g$ be defined as $f,g:\mathbb{N}\to\mathbb{N}$ such that $$ f(n)= \begin{cases} \dfrac{n+1}{2}, & \text{if $n$ is odd},\\[4pt] \dfrac{n}{2}, & \text{if $n$ is even}, \end{cases} \qquad g(n)=n-(-1)^n. $$ Then $f\circ g$ is –
Previous 10 Questions — JEE Main 2019 (10 January Evening Shift)
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The length of the chord of the parabola $x^2=4y$ having equation $x-\sqrt{2}\,y+4\sqrt{2}=0$ is –
Topic: JEE Main 2019 (10 January Evening Shift)
If the area of an equilateral triangle inscribed in the circle $x^{2}+y^{2}+10x+12y+c=0$ is $27\sqrt{3}$ sq units, then…
Topic: JEE Main 2019 (10 January Evening Shift)
If $\displaystyle \int x^{5}\,e^{-4x^{3}}\,dx=\dfrac{1}{48}\,e^{-4x^{3}}\,f(x)+C$, where $C$ is a constant of integrati…
Topic: JEE Main 2019 (10 January Evening Shift)
A helicopter is flying along the curve given by $y - x^{3/2} = 7,\ (x \ge 0)$. A soldier positioned at the point $\left…
Topic: JEE Main 2019 (10 January Evening Shift)
Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at $(2,4)$, then on…
Topic: JEE Main 2019 (10 January Evening Shift)
The value of $\cot\!\left(\displaystyle\sum_{n=1}^{19}\cot^{-1}\!\left(1+\sum_{p=1}^{n}2p\right)\right)$ is :
Topic: JEE Main 2019 (10 January Evening Shift)
If mean and standard deviation of 5 observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$ respectively, then the variance…
Topic: JEE Main 2019 (10 January Evening Shift)
The value of $\cos \dfrac{\pi}{22}\cdot \cos \dfrac{\pi}{23}\cdot \ldots \cdot \cos \dfrac{\pi}{210}\cdot \sin \dfrac{\…
Topic: JEE Main 2019 (10 January Evening Shift)
If $\displaystyle \sum_{r=0}^{25} \left\{ {^{50}C_{r}} \cdot {^{\,50-r}C_{\,25-r}} \right\} = K \binom{50}{25}$, then $…
Topic: JEE Main 2019 (10 January Evening Shift)
Let $a_1,a_2,\dots,a_{10}$ be in G.P. with $a_i>0$ for $i=1,2,\dots,10$ and $S$ be the set of pairs $(r,k)$, $r,k\in\ma…
Topic: JEE Main 2019 (10 January Evening Shift)
