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Create an angle of ${120}^{\circ }$ by using angle bisection while also using protractor. [2 MARKS]

1. 3349

BC is a chord with centre O. A is a point on an arc BC as shown in the figure. Prove that:

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Match the following expressions with their factorised form.

In ΔABC, a line parallel to BC cuts AB and AC at P and Q. Show that.

The adjacent figure shows two arcs $P$ and $Q.$ Arc $P$ is part of the circle with centre $O$ and radius $OA=10cm$. Arc $Q$ is a part of the circle with centre $M$ and radius $AM=5cm,$ where $M$ is the mid-point of $AB.$ Area enclosed by the arc $P$ and chord, $AB$ is

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=a-b\sqrt{3}$, then

If two lines intersect each other, then the vertically opposite angles are ……….

If $A=(1,2,3)$ and $B(3,5,7)$ and $P,Q$ are the points on $AB$ such that $AP=PQ=QB,$ then the mid point of $PQ$ is

Which of the following polynomials represents the sequence 1, 8, 27, 64, 125...? ($x$ being a natural number)

In the$\Delta$ABC, if DE divides AB and AC in the same proportions, then:

the factors of $a^2-1-2x-x^2$ are

Can the square roots of non perfect squares be considered as polynomials?

standerd form of-51/84

The factors of the polynomial 4x ²+ 12x + 9 are

What is a sector?

‘p’ and ‘q’ are the zeroes of the polynomial,
$a{x}^2+bx+c=0$
The values of $a$ and $b$ are:

A bottle contains $\frac{1}{6}$ parts of water and $\frac{2}{3}$ parts of juice. So it contain parts of liquid altogether.

If $a$ and $b$ are rational numbers.
$\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}$
find $a$ and $b$.

Construct $\Delta$ ABC, given $\angle A={60}^{\circ },\angle B={30}^{\circ }$ and AB = 5.8 cm.

A paper file costs Rs0.80 and a plastic file Rs1.50. Suman bought $x$ paper files and $y$ plastic files. How many rupees should she pay the shopkeeper?

There is an equilateral triangle of side 5 cm. What is the length of the square whose area is equal to the area of the triangle ? (use construction)

(i) Find the number of cubes in the following structure.



(ii) If volume of each cube is 2 cu cm, find the volume of the structure.

Question 86 (xviii)

Using suitable identities, evaluate the following:

$(9.7{)}^2-(0.3{)}^2$

$\frac{sin{70}^{\circ }}{cos{20}^{\circ }}+\frac{sin{59}^{\circ }}{cos{31}^{\circ }}-8si{n}^2{30}^{\circ }=$____

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion:

$\frac{13}{3125}$ and $\frac{13}{21}$

Expand $(x-8)(x+10)$.

$\text{In the given figure,}\Delta ABD\text{is an isosceles triangle with}AB=AD.\text{A median is drawn from}A\text{to side}BD\text{at}C.\text{Which of the following option(s) is/are correct?}$

How much cloth 2.5 m wide will be required to make a conical tent having base redius 7 m and height 24 m ?

(a) 120 m (b) 180 m (c) 220 m (d) 550 m

In the figure triangle ABC is right-angled at B. Given that AB = 9 cm. AC = 15 cm and D, E are the mid points of the sides AB and AC respectively, calculate.

(i) The length of BC

(ii) The area of $\Delta ADE$

Find $\frac{(a^2-b^2{)}^3+(b^2-c^2{)}^3+(c^2-a^2{)}^3}{(a-b{)}^3+(b-c{)}^3+(c-a{)}^3}=$

In the given figure, AC and BD are two diagonals of the rectangle ABCD. They intersect at the point O. The length of the side AD = 8 cm and that of the side DC = 10 cm.

The area of the triangle OCD is