Solving Inequalities by Multiplication and Division by a Positive Number

Q.

The converse of the contrapositive of the conditional $p\to ~q$is

1. $p\to q$

2. $~p\to ~q$

3. $~q\to p$

4. $~p\to q$

Q.

Find the related number from $26:5::65:?$

Q.

If $R$ is a relation on the set of integers given by $aRb$ such that $a=2^k\cdot b$ for some integer $k$. Then, $R$ is

1. an equivalence relation

2. reflexive but not symmetric

3. reflexive and transitive but not symmetric

4. reflexive and symmetric but not transitive

5. symmetric and transitive but not reflexive

Q.

The next two numbers in the number pattern $1,4,9,16,25\dots$ are

1. $35$

2. $36,49$

3. $36,48$

4. $35,49$

Q. Select all inequalities that include 0 in the solution set.

1. $x>4.24$
2. $x>5.13$
3. $x<\frac{2}{5}$
4. $x>\frac{7}{2}$

Q.

If $5=5,6=12,7=21,8=32$, then $9$ is equal to

Q. Solve for $q$ : $2q<12$

$q<$

Q.

If $AB+7C=102$, where $B\ne 0$, $C\ne 0$, then$A+B+C=14$. State, whether the statement given, is true or false .

1. True
2. False

Q. Find the minimum value of $x,$ if $5x+8\ge 3x.$

Q. Which option represents the inequality $1\le 2x+5<15$ on the number line?

Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

1. 
2. 
3. 
4. 

Q. Which of the following option(s) satisfies inequality $\frac{x}{5}\ge -7$?

1. $x=-35$
2. $x=-30$
3. $x=-40$
4. $x=-45$

Q. Complete the following statement:
Multiplying each side of an inequality by a positive number

1. changes the direction of the inequality
2. does not change the direction of the inequality