Linear Inequations

Q.

Question 3 (ii)
Express $0.4\overline{7}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q. Question 1
Express $0.6+0.\overline{7}+0.4\overline{7}$ In the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q.

Question 3 (i)
Express $0.\overline{6}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Q. In how many ways can 5 boys and 4 girls be arranged on a bench if
(a) If boys and girls are in separate groups

1. $5760$
2. $5755$
3. $4329$
4. $4000$

Q.

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26, 000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

1. x ≥ 2, 000

2. x < 2, 000

3. x > 2, 000

4. x > 1, 000

Q. Solve the following inequation:$-\frac{1}{5}\le \frac{3x}{10}+1<\frac{2}{5}$
[4 MARKS]

Q.

Question 127(ii)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Where will the insect be after n hops?

Q. Express each of the following as a fraction in simplest form:

(i) $0.\overline{8}$
(ii) $2.\overline{4}$
(iii) $0.\overline{24}$
(iv) $0.\overline{12}$
(v) $0.2\overline{4}$
(vi) $0.3\overline{65}$

Q. What is the integer solution of the given linear inequation?
2 + 4x < 2x - 5 ≤ 3x, x ∈ Z

[2 marks]

1. {-6, -5, -4}
2. {-5, -4}
3. {-6, -5}
4. {-3, -4}

Q.

List the elements of the solution set of the inequation $-3<x-2\le 9-2x;x\in N$

1. { 0, 1, 2, 3 }
2. { 1, 2, 3 }
3. { -1, 0, 1, 2, 3 }
4. { -1, 0, 1, 2 }

Q.

By selling at Rs. 92, some 2.5% Rs. 100 shares and investing the proceeds in 5% Rs. 100 shares at Rs. 115, a person increased his annual income by Rs. 90. Find :
(i) the number of share sold.
(ii) the number of shares purchased.
(iii) the new income.
(iv) the rate per cent which he earns on his investment.

Q.

In a 2D plane, what does x > 2 represent?

1. 

2. 

3. 

4. 

Q.

If 15x > 17x then the set of values of x is

1. {$x<0:x\in N$}

2. {$x\in Z$}

3. {$x\in N$}

4. {$x<0:x\in Z$}

Q.

If there are $25$ toffees in a packet , how will you write the total number of toffees in terms of the number of packets ? ( Use for $\mathrm{P}$ the number of packets )

Q.

Question 127(iii)

An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop.
So, she will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Will the insect ever get to 1? Explain.

Q.

A mixture of $24$ litres contains $18$litres of pure milk. Find the quantity of pure milk in $32$ litres of the mixture.

Q.

Identify which of the following is linear inequation in one variable :

$10t+3\le 7s+10$

Q. what is the number of significant figures
in ( 3.50+450) * 10^5?

Q.

$f\left(x\right)$ is a function defined on the entire number line and is even and odd at the same time. Find the value of $f\left(10\right)\times f\left(5\right)$.

Q. $P=\{x:10<3x-2<34,x\in R\}Q=\{x:28\le 5X+3\le 68,x\in R\}$
The solution for $P\cap Q$ = .

1. $4\le x<13$
2. $4\le x\le 13$
3. $5\le x\le 12$
4. $5\le x<12$

Q.

Solve each of the following systems of eqautions by the method of cross-multiplication:

$ax+by=a^2$

$bx+ay=b^2$

Q.

Divide the following:

$500÷5$

Q. Given $A=\{x:-1\le x\le 4,xϵR\}$ and
$B=\{x:-4\le x<2,x\epsilon R\}$ Represent $A\cap B$ and $A^{\prime }\cap B$ on the number line.
[4 MARKS]

Q.

Amar helps his mother more than his sister does. Give the corresponding expression.

Q. If ${\log }_{0.5}\frac{3-x}{x+2}<0$, then the number of integral values of x is

1. 3
2. 4
3. 2
4. 1

Q.

If A = {1, 5, 6}, B = {4, 8, 9} and f : A$\to$B is a function defined by f(x) = x + 3, represent the function as a set of ordered pairs, table form and arrow diagram.

Q.

Solve the pair of equations using the method of substitution 3x-y = 8 , 5x+y = 0 [2 MARKS]

Q. If x is a natutal number, then for values of x the inequation 5x-23 < 0 is valid.

1. 2
2. 4
3. 5
4. 6

Q.

Given $A=\{x:-1<x\le 5,x\in R\}andB=\{x:-4\le x<3,x\in R\}$

Represent on different number lines :

(i) $A\cap B$ (ii) $A^{\prime }\cap B$ (iii) $A-B$

Q. $\frac{p^2+5}{3p^2}=-7$