Sample QuestionsInequalities questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the solution set of inequation : $4-2 x<3 x+19<42-5 x, x \in Z$
View full solution →If $x \in Z^{-}$, find the solution set of inequation :
$\frac{1}{3}>\frac{6}{7} x+4$
Represent solution set on the number line.
View full solution →If $x \in Z^{-}$, find the solution set of inequation :
$10-2(1+4 x)<26$
Represent solution set on the number line.
View full solution →If $x \in Z^{-}$, find the solution set of inequation :
$5+6 x>x-10$
Represent solution set on the number line.
View full solution →If $x \in Z^{-}$, find the solution set of inequation :
$-4(x+5)<9$
Represent solution set on the number line.
View full solution →If $x \in Z^{-}$, find the solution set of inequation :
$-29<9 x-2$
Represent solution set on the number line.
View full solution →Madan Singh runs a rental car company. He charges ₹ 250 per day plus ₹ 15 for every kilometre the car is driven. Professor Dayal rents a car for 1 day, while his own car is being repaired. He assures Madan Singh that he will pay him more than ₹ 500 as rent for the day.
Q.1. The inequality for the rent paid by Dayal for 1 day is :
(a) $3 x<100$$\quad$$\quad$ (b) $x>25$ $\quad$$\quad$(c) $3 x>50$ $\quad$$\quad$(d) $x<75$
Q.2. The solution set for the inequality obtained above is given by :
(a) $\{16,17,18, \ldots\}$ $\quad$(b) $\{17,18,19, \ldots\}$$\quad$ (c) $\{19,20,21, \ldots\}$ $\quad$(d) $\{20,21,22, \ldots\}$
Q.3. Dayal estimated that the rent for 1 day would be less than $₹ 600$ as he calculated the distance he has to drive the car. The inequality for the rent in this case would be :
(a) $y>30$ $\quad$$\quad$(b) $2 y<35$ $\quad$$\quad$(c) $3 y<70$ $\quad$$\quad$(d) $4 y>45$
Q.4. The solution set for the above inequality is given by :
(a) $\{\ldots ., 20,21,22,23\}$ $\quad$$\quad$(b) $\{\ldots ., 17,18,19,20\}$
(c) $\{\ldots ., 18,19,20,21\}$ $\quad$$\quad$(d) $\{\ldots ., 15,16,17,18\}$
View full solution →Find the solution set of inequation : $9-\frac{2}{3} x<5 x-11<17-\frac{x}{4}, x \in Z$
View full solution →Find the solution set of inequation : $-5<\frac{x}{2}-3<\frac{5}{2}, x \in Z$
View full solution →Find the solution set of inequation : $2-x<4 x-7<11-2 x, x \in Z$
View full solution →Find the solution set of inequation : $10<4 x-5<21, x \in N$
View full solution →If $a > b$ and $m > 0$, then $\frac{a}{m}<\frac{b}{m}$.
View full solution →If $a> b$ and $m< 0$, then $a m< b m$.
View full solution →If $a < b, m< 0$, then $a-m >b-m$.
View full solution →If $a< b$ and $m< 0$, then $\frac{a}{m}>\frac{b}{m}$.
View full solution →$\frac{2}{3} x-\frac{4}{5} \geq 8$ is an inequation.
View full solution →If $a \neq 0, b \neq 0$ and $a < b$, then $\frac{1}{a}$ _________ $\frac{1}{b}$.
View full solution →Multiplying each side of an inequality by a negative number, ________the inequality.
Subset of the replacement set, consisting of all those values of the variable which satisfy the given inequation is called the __________.
The set from which the values of the variable satisfying a given inequality are chosen, is called the ________.
A statement of inequality between two expressions is called an _________.
Which one of the following statements is incorrect?
- A
If a < b then a - m < b - m
- B
If a > b and m > 0 then am > bm
- ✓
If $a < b$ and $m >0$, then $\frac{a}{m}>\frac{b}{m}$.
- D
If $a \neq 0$ and $b \neq 0$, then $a>b \Rightarrow \frac{1}{a}<\frac{1}{b}$.
Answer: C.
View full solution →Which one of the following is not a solution to the inequality 2x > 18 - 5 * x'
Answer: D.
View full solution →The solution set of the inequality $17-4 x<7, x \in Z$ is
- A
$\{1,2,3, \ldots\}$
- B
$\{2,3,4, \ldots\}$
- ✓
$\{3,4,5, \ldots\}$
- D
$\{4,5,6, \ldots\}$
Answer: C.
View full solution →Which one of the following is a solution to the inequality 3x - 5 < 6 ?
Answer: A.
View full solution →If a > b and m < 0 then which of the following is correct :
- ✓
- B
- C
- D
am and bm cannot be compared
Answer: A.
View full solution →