Nishit K Sinha Solutions for Chapter: X+2 Maths, Exercise 1: Practice Exercises

The smallest integer n for which $4^{\mathrm{n}}>{17}^{19}$ holds, is closest to:

If a, b, c, and d are integers such that $\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}=30$, then the minimum possible value of $(\mathrm{a}-\mathrm{b}{)}^2+(\mathrm{a}-\mathrm{c}{)}^2+(\mathrm{a}-\mathrm{d}{)}^2$ is _____.

The simplest value of the expression ${\left\{\frac{4^{\mathrm{p}+\frac{1}{4}}\times \sqrt{2\times 2^{\mathrm{p}}}}{2\times \sqrt{2^{-\mathrm{p}}}}\right\}}^{1/\mathrm{p}}$ is:

The price of Darjeeling tea (in rupees per kilogram) is $100+0.10\mathrm{n}$, on the ${\mathrm{n}}^{\mathrm{th}}$ day of $2007(\mathrm{n}=1,2,\dots 100$) and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is $89+0.15 \mathrm{n}$, on the ${\mathrm{n}}^{\mathrm{th}}$ day of $2007$ $(\mathrm{n}=1,2,\dots ,365)$. On which date in $2007$will the prices of these two varieties of tea be equal?

If $\frac{\mathrm{a}}{\mathrm{b}+\mathrm{c}}=\frac{\mathrm{b}}{\mathrm{c}+\mathrm{a}}=\frac{\mathrm{c}}{\mathrm{a}+\mathrm{b}}=\mathrm{r}$ then r cannot take any value except.

A man had to do multiplication, instead of taking $35$ as one of the multipliers, he took $53$. As a result, the product went up by $540$. What is the new product?

If a, b, c and d are four positive real numbers such that $\mathrm{abcd}=1$, what is the minimum value of $(1+\mathrm{a})(1+\mathrm{b})(1+\mathrm{c})(1+\mathrm{d})$ ?

Each of the numbers ${\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{\mathrm{n}},\mathrm{n}\ge 4$, is equal to $1$ or $-1$. Suppose

${\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3{\mathrm{x}}_4+{\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3{\mathrm{x}}_4{\mathrm{x}}_5+{\mathrm{x}}_3{\mathrm{x}}_4{\mathrm{x}}_5{\mathrm{x}}_6+\dots +{\mathrm{x}}_{\mathrm{n}-3}{\mathrm{x}}_{\mathrm{n}-2}{\mathrm{x}}_{\mathrm{n}-1}{\mathrm{x}}_{\mathrm{n}}{\mathrm{x}}_1+{\mathrm{x}}_{\mathrm{n}-1}{\mathrm{x}}_{\mathrm{n}}{\mathrm{x}}_1{\mathrm{x}}_2+{\mathrm{x}}_{\mathrm{n}}{\mathrm{x}}_1{\mathrm{x}}_2{\mathrm{x}}_3=0$, then: