$[3, 7]$
$R$
$[2, 6]$
$[1, 4]$
Leela and Madan pooled their music $CD's$ and sold them. They got as many rupees for each $CD$ as the total number of $CD's$ they sold. They share the money as follows: Leela first takes $10$ rupees, then Madan takes $10$ rupees and they continue taking $10$ rupees alternately till Madan is left out with less than $10$ rupees to take. Find the amount that is left out for Madan at the end, with justification.
The number of roots of the equation $|x{|^2} - 7|x| + 12 = 0$ is
If $x$ is real, then the maximum and minimum values of the expression $\frac{{{x^2} - 3x + 4}}{{{x^2} + 3x + 4}}$ will be
Number of integral values of '$m$' for which $\{x\}^2 + 5m\{x\} - 3m + 1 < 0 $ $\forall x \in R$, is (where $\{.\}$ denotes fractional part function)
Let $\alpha, \beta ; \alpha>\beta$, be the roots of the equation $x^2-\sqrt{2} x-\sqrt{3}=0$. Let $P_n=\alpha^n-\beta^n, n \in N$. Then $(11 \sqrt{3}-10 \sqrt{2}) \mathrm{P}_{10}+(11 \sqrt{2}+10) \mathrm{P}_{11}-11 \mathrm{P}_{12}$ is equal to :