Solving Inequalities

Q. The H.C.F. and L.C.M. of two numbers are 11 and 385 respectively. If one number lies between 75 and 125, then that number is ____.

1. 77
2. 88
3. 110
4. 99
5. 55

Q.

In a two – digit number, the digit in the unit's place exceeds twice the digit in the ten's place by 1. If the digit in the unit’s place and the ten’s place are interchanged, then the difference between the newly formed number and the original number is less than the original number by 1. What is the original number?

1. 25

2. 37

3. 49

4. 52

5. 67

Q.

Sneha's age is ${\frac{1}{6}}^{th}$ of her father's age. Sneha's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, then what is Sneha's present age?

1. 

2. 30 years

3. 32 years

4. None of these

5. 24 years

Q.

An elevator has a weight limit of 630 kg. It is carrying group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?___

Q.

Walking $\frac{7}{8}$${}^{th}$ of his usual speed, a man is 24 minutes late. What is the usual time taken by him to cover that distance?

1. 2hr 12 min

2. 2hr 21 min

3. 2hr27 min

4. 2hr24 min

5. 2hr 30 min

Q. $5$ pencils and $7$ pens together cost Rs. $50$ whereas $7$ pencils and $5$ pens together cost Rs. $46$. Find the cost of one pen and one pencil in Rs. respectively.

1. $5,3$
2. $6,2$
3. $4,4$
4. $7,1$

Q. The set of all real numbers x for which $x^2-[x+2]+x>0,$ is

1. $(\sqrt{2},\infty )$
2. $(-\infty ,-2)\cup (2,\infty )$
3. $(-\infty ,-1)\cup (1,\infty )$
4. $(-\infty ,-\sqrt{2})\cup (\sqrt{2},\infty )$

Q. The cost of 8 pens and 4 pencils is Rs. 176 and the cost of 2 pens and 2 pencils is Rs 48. What is the cost of 1 pen?

1. Rs. 14
2. Rs. 12
3. Rs 23
4. None of the above
5. Rs. 16

Q.

The sum of two numbers is 9. The sum of squares of the numbers is 41. Find the smaller of the two numbers.

1. 1

2. 4

3. 3

4. 2

5. None of these

Q.

Pencils, pens and exercise books in a shop are in the ratio 10:2:3. If there are 120 pencils, the number of exercise books in the shop is?

1. 27

2. 36

3. 45

4. 54

5. None

Q. If a and b are negative, and c is positive, which of the following statements is/are true?
I. a - b < a - c
II. if $a<b,then\frac{a}{c}<\frac{b}{c}$
III. $\frac{1}{b}<\frac{1}{c}$

1. II and III only
2. I only
3. III only
4. II only

Q. $16\times 12-672÷21=?-211$

1. 381
2. 347
3. 372
4. 311
5. None of these

Q.

(17)${}^{3.5}$ x (17)${}^{?}$ = 17${}^8$

1. 2.29

2. 2.75

3. 4.25

4. 4.5

5. None of these

Q. If n is such that $36\le n\le 72,$ then $X=\frac{n^2+2\sqrt{n}(n+4)+16}{n+4\sqrt{n}+4}$ satisfies?

1. 20 < x < 54
2. 23 < x < 58
3. 25 < x < 64
4. 28 < x < 59

Q.

$\text{If the length is increased by 3 cm and the breadth is increased by 2 cm, the area of a rectangle increases by 67}c{m}^2.\text{But, if the length is reduced by 5 cm and the breadth is increased by 3 cm, the area reduces by 9}c{m}^2.\text{Find the area of the rectangle}\left(inc{m}^2\right).$

1. 176

2. 153

3. 150

4. 149

Q. What is the solution set of the equation $x^3-x^2+x-1>0$?

1. x > 0
2. x > 1
3. x < -1
4. -1 < x < 1

Q. The total amount of money spent on the purchase of pencils, rubbers and pens is Rs. 45. The cost of one pencil, one rubber and two pens is Rs. 2, Rs. 3 and Rs. 8 respectively. The total number of pencils bought is greater and less than the number of pens and the number of rubbers bought respectively. How many different combinations of the number of pencils, rubbers and pens bought are possible?

1. 1

2. 2

3. 3

4. 4

Q. Given that $-1\le v\le 1,-2\le u\le -0.5and-2\le z\le -0.5$ and $w=\frac{vz}{u}$, then which of the following is necessarily true?

1. $-0.5\le w\le 2$
2. $-4\le w\le 4$
3. $-4\le w\le 2$
4. $-2\le w-\le -0.5$

Q. $1\frac{1}{4}+1\frac{5}{9}\times 1\frac{5}{8}÷6\frac{1}{2}=?$

1. 17
2. 27
3. 42
4. 18
5. None of these

Q. $4003\times 77-21015=?\times 116$

1. 2477
2. 2478
3. 2467
4. 2476
5. None of these

Q. Which of the following values of x do not satisfy the inequality $x^2-3x+2>0$ at all?

1. $-5\le x\le -1$
2. $1\le x\le 2$
3. $2<x<4$
4. $5<x\le 10$

Q.

What will come in place of the question mark (?) in each of the following series?

28, 25, 5, 21, 18, 5, 14, ?

1. 12

2. 11

3. 5

4. 19

5. None of these

Q.

Solve the inequality. Graph the solution.

$-3x\ge 18$

Q. If x is real and $x^2-3x+2>0,x^2-3x-4\le 0,$ then which one of the following is correct ?

1. $-1\le x\le 4$
2. $-1\le x<1or2<x\le 4$
3. $-1<x\le 1$
4. $2\le x\le 4$

Q. What approximate value should come in place of the question mark (?) in the given question? (You are not expected to calculate the exact value).
${\left(\frac{24}{9}\right)}^2\times \frac{399}{39}÷\frac{41}{899}=?$

1. 1550
2. 1750
3. 1700
4. 1600
5. 1650

Q.

The root(s) of the equation (2x - 3) = $\sqrt{2x^2-2x+21}$are:

1. 4, -2

2. 6, -1

3. 6

4. -1

Q. $I.\sqrt{500x}+\sqrt{402}=0$
$II.\sqrt{360y}+(200{)}^{\frac{1}{2}}=0$

1. $x\ge y$
2. $x<y$
3. $x>y$
4. $x\le y$
5. $x=y$or the relationship cannot be established

Q. x and y are real numbers satisfying the conditions 2 < x < 3 and -8 < y < - 7. Which of the following expressions will have the least value ?

1. $x^{2}y$
2. $x{y}^2$
3. $5xy$
4. $x^2{y}^2$

Q. $\frac{5^2\times 14+1450}{5}=1998÷?$

1. 5.05
2. 5.55
3. 55.5
4. 50.5
5. 50.05

Q. What values of x satisfy $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2\le 0$?

1. $-1\le x\le 8$
2. $-8\le x\le 1$
3. $1<x<8$
4. $1\ge x\ge 8$