Concept of Inequality

Q.

Find the value: $\left(\frac{3}{7}\right)+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)$

Q. Question 6
The equation x = 7, in two variables, can be written as:


A) 1.x + 1.y = 7
B) 1.x + 0.y = 7
C) 0.x + 1.y = 7
D) 1.x - 1.y = 7

Q. What is linear combination?

Q. If $\frac{2}{x}+\frac{3}{y}=\frac{9}{xy}\mathrm{and}\frac{4}{x}+\frac{9}{y}=\frac{21}{xy}$, find the values of x and y.

Q.

Which of the following pairs of equations represent inconsistent system?

1. 3x - y = -8 3x - y = 24

2. 3x - 2y = 8 2x + 3y = 1

3. 5x - y = 10 10x - 2y = 20

4. lx - y = m x + my = l

Q.

$8(2x-5)-6(3x-7)=1$

Q.

State, Whether the following statements are true of false.

(i) If $a<b,thena-c<b-c$

(ii) If $a>b,thena+c>b+c$

(iii) If $a<b,thenac>bc$

(iv) If $a>b,then\frac{a}{c}<\frac{b}{c}$

(v) If $a-c>b-d;thena+d>b+c$

(vi) If $a<b,andc>0,thena-c>b-c\text{where a, b, c and are real numbers and}c\ne 0.$

Q. ax + b = c is the general form of a linear where a, b and c are numbers.

1. natural
2. whole
3. real
4. integral

Q.

In a mathematical statement , if one quantity is not equal to another then it is called as ___

1. Equation

2. Always greater

3. Inequation

4. Always smaller

Q.

Dylan is organizing a curling tournament. The sports complex charges ₹ 116/ h for the ice rental. Dylan has booked it for 7h. He will charge each of the 14 teams in the tournament an entrance fee which is more than per hour charges . How much should he charge from each team in order to make a profit?

1. x < Rs. 23

2. x > Rs. 43

3. x ≥ Rs. 50

4. x < Rs. 120

Q. A relation R is defined from a set A={2, 3, 4, 5} to set B={3, 6, 7, 10} as follows (x, y) belongs to R if and only if x divides y. Express R as a set of ordered pairs and determine the domain and range of R, also find the inverse of R.

Q.

x = −5 can be written as equation in two variable in which of the following ways

1. 1x+1y=5

2. 1x+0y= -5

3. 1x+0y+5=0

4. both B and C

Q. If $\frac{x}{4}+\frac{y}{3}=\frac{5}{12}\mathrm{and}\frac{x}{2}+y=1$, then find the value of (x + y).

Q. Who is the scientist behind linear equation in two variable?

Q.

Which of the following mathematical statement represents inequation

1. x + y = 6

2. 2x > 8

3. 2x = y + 3

4. m + 2 = 5

Q.

Q.

Simplify :

$3-\frac{11}{12}+\frac{5}{8}$

Q. $$\begin{gathered} \frac{x}{a}+\frac{y}{b}=(a+b), \\ \frac{x}{a^2}+\frac{y}{b^2}=2. \end{gathered}$$

Q.

In elimination method _____________ is an important condition

1. Equating either of the coefficients

2. Equating only the y coefficient

3. Equating both the coefficients

4. Equating only the x co-efficient

Q. 13. Let a and b be positive integer show that root 2 always lies between a÷b and a+2b÷a+b

Q. $\mathrm{If}∆=\left|\begin{array}{ccc}1& x& x^2\\ 1& y& y^2\\ 1& z& z^2\end{array}\right|,{∆}_1=\left|\begin{array}{ccc}1& 1& 1\\ yz& zx& xy\\ x& y& z\end{array}\right|,\mathrm{then}\mathrm{prove}\mathrm{that}∆+{∆}_1=0.$

Q.

A garage worker goes to a nearby store to buy nuts and bolts. He has ₹ 40 and he is going to buy nuts for 40 paisa and bolts for ₹ 1.5 each. Write an inequality to describe the possible number of nuts and bolts that he can buy (Take the cost price of each bolt and nut as ₹ x and ₹ y respectively).

1. None of these

2. 1.5 x + 0.4 y < 40

3. 1.5 x + 0.4 y > 40

4. 1.5 x + 0.4 y ≤ 40

Q.

Raju wants to see Avengers Infinity war on the 1st day of release i.e., after 20 days. The money required is Rs. 500 and at the end of 20 days he was unable to make 500. Money he saved per day is (Assume he saved the same amount every day)

1. more than 50

2. less than 50

3. less than Rs.25

4. more than Rs.25

Q. $\frac{44}{x+y}+\frac{30}{x-y}=10,\frac{55}{x+y}+\frac{40}{x-y}=13.$

Q.

If x and y are two quantities such that they are not equal to each other , then x will be always greater than y.

1. False

2. True

Q. Simplify the following:

(i)

(ii)

(iii)

(iv)

Q.

The H.C.F. and L.C.M of two expression are (a − 7) and (a³ − 10a² + 11a + 70) respectively. If one of the expressions is (a² − 12a + 35) find the other.

Q. prove that (root3 + 1)(3 - cot30degrees) = tancube60degrees - 2sin60dgrees

Q.

Subtraction of $-7$ from $-4$.

Q.

If 2x, x+10, 3x+2 are in AP find the value of x

With explaination please