Properties of inequalities

Q. If $\left[x\right]$ represents the greatest integer less than or equal to $x$, then $\sum _{k=1}^{4020}[\frac{1}{2}+\frac{k-1}{4020}]$ is equal to

Q.

Find the value of [2 - h] + [2 + h], where h is really small. $(h\to 0orhtendstozero)$ and [x] is the greatest integer function

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Q. The contrapositive of the converse of the statement ''If Sam scores less than $30$ marks, then he will not pass the paper.'' is

1. If Sam scores less than $30$ marks, then he will pass the paper.
2. If Sam does not score less than $30$ marks, then he will pass the paper.
3. If Sam will pass the paper, then he does not score less than $30$ marks.
4. If Sam will pass the paper, then he scores less than $30$ marks.

Q. If $a>b$ and k is a non-zero integer, which of the following is always true?

1. $\frac{k}{a}>\frac{k}{b}$
2. $a+k>b+k$
3. $a^k>b^k$
4. $ka>kb$

Q. If 2 more than $m$ is a negative integer and if 5 more than $m$ is a positive integer, which of the following could be the value of $m$?

1. $-7$
2. $-5$
3. $-3$
4. 4

Q. If $8<15mx-7<24$, where m is a positive constant, what is the possible range of values of -5mx.

1. Any value greater than -5 or less than $-\frac{31}{5}$
2. Any value greater than $-\frac{31}{5}$ and less than -5
3. Any value greater than $-\frac{7}{3m}$ or less than $-\frac{31}{15m}$
4. Any value greater than $-\frac{31}{15m}$ or less than $-\frac{7}{3m}$

Q. If $3<p<7$ and $-9<q<-4$, then what is the range of p - q?

1. (-16, -7)
2. (16, 7)
3. (7, 16)
4. (-7, -16)

Q. If P, Q, R, S are the points (4, 5, 3) (6, 3, 4), (2, 4, -1), (0, 5, 1) the length of projection RS and PQ is

1. $\frac{2}{3}$
2. $4$
3. $6$
4. $\frac{4}{3}$

Q. If $-5<p<-2$ and $7<q<9$, then what is the range of p + q?

1. (-2, -7)
2. (2, 7)
3. (7, 2)
4. (-7, -2)

Q. If n is a positive integer, which of the following is always odd?

1. $19n+6$
2. $18n+4$
3. $19n^2+5$
4. $19n+5$
5. $18n+5$

Q. If $A=\{a,b,c,d\},B=\{p,q,r,s\}$, then which of the following are relations from $A$ to $B$?

1. $R_1=\{(a,p),(b,r),(c,s)\}$
2. $R_4=\{(a,p),(q,a),(b,s),(s,b)\}$
3. $R_2=\{(q,b),(c,s),(d,r)\}$
4. $R_3=\{(a,p),(a,q),(d,p),(c,r),(b,r)\}$