Subject Experts Solutions for Chapter: Solved Paper 2018 (II), Exercise 1: PAPER I : Mathematics

Consider the following statements:
1. The angle between the planes: $2x-y+z=1$ and $x+y+2z=3$ is $\frac{\pi }{3}$.
2. The distance between the planes: $6x-3y+6z+2=0$ and $2x-y+2z+4=0$ is $\frac{10}{9}$.

Which of the above statements is/are correct?

Consider the following statements:

Statement $\mathrm{I}:$ If the line segment joining the points $P(m, n)$ and $Q(r, s)$ subtends an angle $\alpha$ at the origin, then $\cos \alpha =\frac{ms-nr}{\sqrt{\left(m^2+n^2\right)\left(r^2+s^2\right)}}$.

Statement $\mathrm{II}:$ In any triangle $ABC,$ it is true that $a^2=b^2+c^2-2bc\cos A.$ 

Which one of the following is correct in respect of the above two statements?

Two integers $x$ and $y$ are chosen with replacement from the set $[0,1,2,\dots ,10]$. The probability that $\left|x-y\right|>5$ is

An analysis of monthly wages paid to the workers in two firms $A$ and $B$ belonging to the same industry gives the following result:

The average of monthly wage and variance of distribution of wages of all the workers in the firms $A \& B$ taken together are

Three dice having digits $1, 2, 3, 4, 5$ and $6$ on their faces are marked $\mathrm{I}, \mathrm{II},$ and $\mathrm{III}$ and rolled. Let $x, y$ and $z$ represent the number on die-$\mathrm{I}$, die-$\mathrm{II}$ and die-$\mathrm{III}$, respectively. What is the number of possible outcomes such that $x>y>z$?

Which one of the following can be obtained from an ogive?

In any discrete series (when all values are not same), if $x$ represents mean deviation and $y$ represents standard deviation, then which one of the following is correct?

In which one of the following cases would you expect to get a negative correlation?