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$\mathrm{1.666666......}$ is a rational number and can be expressed in $\frac{p}{q}$ form where $p$ and $q$ are integers. Then the value of $p+q$ is

Question 5 (i)
In the given figure, the arms of two angles are parallel. If $\Delta ABC={70}^{\circ }$, then find: $\angle DGC$

If there is a scalene ∆ABC in which all its angles have integral values, what would be the maximum possible value for ∠ABC? Which type of triangle would ∆ABC be, on the basis of its angles? [2 MARKS]

A circle is divided into 8 equal parts. Given that the area of the shaded portion is $\frac{10}{4}$ $m^2$. Find the area of the unshaded part of the circle.

[4 MARKS]

1. 24

A collection of numbers or characters that represent qualitative or quantitative information is called

Is it
possible to have a triangle with the following sides?

(i) 2 cm,
3 cm, 5 cm (ii) 3 cm, 6 cm, 7 cm

(iii) 6
cm, 3 cm, 2 cm

What will be the sign of the product if we multiply together 12 negative integers? [1 MARK]

For the following distribution, the modal class is

$\begin{array}{cc}Marks& Numberofstudents\\ Below10& 3\\ Below20& 12\\ Below30& 27\\ Below40& 57\\ Below50& 75\\ Below60& 80\end{array}$

Question 98

A girl is 28 years younger than her father. The sum of their ages is 50 years. Find the ages of the girl and her father.

Match each of the entries in Column I with the appropriate entries in Column II.
$\begin{array}{ccc}& & \\ \text{Column I}& & \text{Column II}\\ 12.5\%& \text{F.}& \text{Rs.}25\%\end{array}$

$△ABC$ is such that $AB=3cm,BC=2cm$ and $CA=2.5cm.$ $△DEF$ is similar to $△ABC.$ If $EF=4cm$, then the perimeter of $△DEF$ is ____.

Question 58 (f)

Subtract:

$-2a^2-2b^2$ from $-a^2-b^2+2ab.$

Question 1

A square is inscribed in an isosceles right triangle have one angle common. Show that the vertex of the square opposite the vertex of the common angle bisects the hypotenuse.

Solve the following problems.

Shylaja borrows a sum of Rs. 400 from her friend at 10% p.a simple interest. If she returns the money along with the interest after 146 days, how much will she pay altogether?

Question 49

In questions 24 to 59, fill in the blanks to make the statements true.
Interest on Rs. 12500 at 18 % per annum for a period of 2 yr and 4 months is ___ .

What of the following do we have to add with 280 to make it a perfect square nearest to it?

Raghavendra can cover a distance in 1 hr and 24 min by covering 2/3 of the distance at 4 kmph and the remaining at 5 kmph. Find the total distance covered by him.

Find the set corresponding to common elements between set A and set B in the following venn diagram.

The ratio of the number of boys and girls in a college is 3 : 4. If the percentage increase in the number of boys and girls be 60% and 50% respectively, what will be the new ratio?

Question 159(iii)

Find a single repeater machine that will do the same work as each hook-up.

The area (in sq. units) enclosed by the figure described by the equation $x^4+1=2x^2+y^2$ is

How to construct an angle of 50 degrees

Find the marked price.

Selling price = Rs. 2,400; rate of discount = 4%

In a hall, 324 chairs are arranged in such a way that the number of rows is equal to the number of columns. If one extra row and one extra column of chairs is added, find the new number of the chairs.

Which of the given objects has 3 faces, 2 edges, and no vertex?

A man runs in a circular path. He runs towards the center from the circumference and after reaching the center he suddenly changes his direction from his original path at 180 degrees to the original direction and stopped when he reached the circumference. Find the area and perimeter of the circle, given that, the man ran 8 meters in the above-described path? [4 MARKS]

Match each of the entries in Column I with the appropriate entries in Column II.
$\begin{array}{ccc}& & \\ \text{Column I}& & \text{Column II}\\ \text{Profit}\%\text{when CP = Rs.40 and SP = Rs.50}& \text{I.}& \text{Rs.159}\end{array}$

Find the sum total of 5, 7 and 6.

The subtraction of 2.998 from 1.76 results in a negative number. Which number lies to the left of this number on the number line?

Question 75(iii)
Study the bar graph given below and answer the questions that follow:

Calculate the average marks of the student.