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A manufacturer has employed $5$ skilled men and $10$ semi-skilled men and makes two models $A$ and $B$ of an article. The making of one item of model $A$ requires $2$ hours work by a skilled men and $2$ hours work by a semi-skilled man. One item of model $B$ requires $1$ hour by a skilled man and $3$ hours by a semi-skilled man. No man is expected to work more than $8$ hours per day. The manufacturer's profit on an item of model $A$ is Rs.$15$ and on an item of model $B$ is Rs.$10,$ then the total number of items of each model should be made per day in order to maximize daily profit.

$[$where, $n\left(A\right)=$ number of items of artical $A$ and $n\left(B\right)=$ number of items of artical $A]$

Find the value of $(\frac{-2}{5}{)}^7÷(\frac{-2}{5}{)}^6$.

Find the ratio of 5 km to 500 m.

Shina and Bhuwan started a business of utensils by investing their money in the ratio of $4:3$ respectively. After seven months, Preeti joined them by investing her money equal to Shina’s investment. After $2$ years of starting the business, they get $25\%$ profit which is equal to the amount $\text{Rs.}14750.$ Then the investment of Preeti is

Which of the following will have 1 in its unit's place?

Which of
the following figures have rotational symmetry of order more than 1:

Which of the following identity can be used to solve $1001\times 999$?

If $3\frac{p}{q}=\frac{11}{3}$, where $3\frac{p}{q}$ is a mixed fraction, then the value of $\frac{p}{q}$ is:

Statements:

All radios are stations.

Some tracks are trains.

Some radios are trains.

Conclusions:

I. Some stations are not trains.

II. Some radios are not tracks.

Question 2(d)
Give first the step you will use to separate the variable and then solve the equation:
4x=25

Additive inverse of $\frac{-5}{9}$ is

(a) $\frac{-9}{5}$

(b) 0

(c) $\frac{5}{9}$

(d) $\frac{9}{5}$

Why the area of a circle is pie r square

In a right triangle, if one angle is ${50}^{\circ }$, find its third angle.

Question 31

Number of pencils for Rs. $x$ at the rate of Rs. 2 per pencil is ___ .

1. 2.44

In the given figure, if $PQ\parallel RS,\angle MXQ={135}^{\circ }$, and $\angle MYR={40}^{\circ }$, find the measure of $\angle XMY$.

Multiply
and reduce to lowest form (if possible):

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

Rashmi has ₹ 5555.50 in her wallet. She bought a saree for ₹ 555.50 and bought an umbrella for ₹ 55.50. She paid ₹ 5.50 to the auto driver for dropping her home. What will be the total amount of money left with her?

Which of the following options show the correct match of parameters in column A with possible values in column B?

$\begin{array}{cc}ColumnA& ColumnB\\ 1.\text{Area}& a.67m\\ 2.\text{Perimeter}& b.Rs.6/m^2\\ 3.\text{Cost per}{m}^2& c.100m^2\\ & d.Rs.6m^2\\ & e.100/m^2\end{array}$

What is the difference between these two decimal numbers?

A) 4.176 B) $4.\overline{176}$

Question 5

To find the sum of three numbers 14, 27 and 13, we can have two ways:

(a) We may first add 14 and 27 to get 41 and then add 13 to it to get the total sum 54 or

(b) We may add 27 and 13 to get 40 and then add 14 to get the sum 54. Thus (14 + 27) + 13 = 14 + (27 + 13)

This can be done for any three numbers. This property is known as the associativity of addition of numbers. Express this property which we have already studied in the chapter on whole numbers, in a general way, by using variables a, b, and c.

Question 1(v)

Carry out the multiplication of the expressions in each of the following pairs:

pq+qr+rp,0

The value of x in the following figure is:

Two angles are complementary. If one measures ${80}^{\circ }$, then the measure of the other angle is:

Question 4 (iv)

Draw the number line and represent the following rational number on it:
$\frac{7}{8}$

-3-x=1+3x

$\frac{\left(a^m\right)\times \left(a^n\right)}{\left(a^p\right)}$ can be rewritten as:

What is the degree of the polynomial $\frac{7x^2+2x^5+4x}{3x}?$

A rectangular painting has an area equal to $45$ $uni{t}^2$. What are its possible integer dimensions?

Which of the following is a binomial?

A tin contains a mixture of two liquids $A$ and $B$ in the ratio $7:5.$ When $9$ litres of mixture are drawn off and the tin is filled with $B,$ the ratio of $A$ and $B$ becomes $7:9.$ How many litres of liquid $A$ was contained by the tin initially?

Question 33

In questions 24 to 59, fill in the blanks to make the statements true.
In a class of 50 students, 8 % were absent on one day. The number of students present on that day, was ___.

What is the name given to the graph representing numerical data with figures?

A Circle is inscribed in a Square. The side length of the square is 10 cm. The ratio of the circumference of circle to the Perimeter of square is