Nishit K Sinha Solutions for Chapter: X+2 Maths, Exercise 9: Benchmarking Test 3

In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

Let $p$ and $q$ be roots of the equation $x^2-2x+A=0$ and let $r$ and $s$ be the roots of the equation $x^2-18x+B=0.$ If $p<q<r<s$ are in arithmetic progression, then the values of $A$ and $B$ are

Let $a_1,a_2,\dots ,a_{10}$ be in $\mathrm{AP}$ and $h_1,h_2,\dots ,h_{10}$ be in $\mathrm{HP}$. If $a_1=h_1=2$ and $a_{10}=h_{10}=3$, then $a_4{h}_7$ is

If the integers $m$ and $n$are chosen at random between $1$ and $100$, then the probability that a number of the form $7^m+7^n$ is divisible by $5$ equals

Let $S_1,S_2,\dots .$ be squares such that for each $n\ge 1,$ the length of a side of $S_{\mathit{n}}$ equals the length of a diagonal of $S_{n+1}$. If the length of a side of $S_1$ is $10 \mathrm{cm},$ then for which of the following values of $n$ is the area of $S_{\mathit{n}}$ less than $1 \mathrm{sq}. \mathrm{cm}$

If $a, b, c, d$ are positive real numbers such that $a+b+c+d=2,$ then$M=(a+b)(c+d)$ satisfies the relation

How many different nine-digit numbers can be formed from the number $223355888$ by rearranging its digits so that the odd digits occupy even positions?

The area bounded by the curves $y=\left|x\right|-1$ and $y=-\left|x\right|+1$ is