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Convert $0.08\overline{3}$ into $\frac{p}{q}$ form.

If a triangle and a square are on the same base and between the same parallels, then the ratio of area of triangle to the area of square is

O is the centre of the circle.Given that $\angle$OAB = 20${}^{\circ }$, $\angle$OCB = 55${}^{\circ }$. Find $\angle$BOC and $\angle$AOC in degree.
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The volume of a prism is 100 $m^3$ and its height is $\frac{4}{\sqrt{3}}m$. The base of the prism is an equilateral triangle. What is the length of each side of the triangle forming the base of the prism ?

Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides and is equal to half the difference of these sides. [4 MARKS]

Question 3

Find the total surface area of a hemisphere of radius 10 cm.

$[Use\pi =3.14]$

A match box measures 4 cm $\times$ 2.5 cm $\times$ 1.5 cm. Which of the following does not represent the volume of a packet containing 12 such boxes?

The inverse of the 2 $\times$ 2 matrix $\left[\begin{array}{cc}1& 2\\ 5& 7\end{array}\right]$ is

Without actually calculating the cubes, find the value of each of the following:

(i)

(ii)

In which of the following figures are the diagonals equal?

(a) Parallelogram

(b) Rhombus

(c) Trapezium

(d) Rectangle

In $△ABC$,
$sec\left(\frac{B+C}{2}\right)=$ _______.

Assertion: We find midpoints of a class interval with the following formula.
$\frac{upperclasslimit+lowerclasslimit}{2}$

Reason: To draw frequency polygons independently without drawing histogram it is required to have the class mark.

Which of the following is correct?

Given below are the steps for the construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following is wrong?

1:- Draw AB = 3.5 cm.

2:- Construct $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.

3:- Draw BC = 6.5 cm.

4:- At D construct $\angle ADC={120}^{\circ }$.

Complete the following table:

(A)

(B)

(C)

Give a method to find the centre of a given circle.

Burst the bubble if the rational number is terminating.

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. Find the volume of the solid formed.

In the _____ quadrant, the abscissa of the point is negative.

Simplify $\frac{a{b}^2{c}^3\times a^4{b}^5{c}^{-6}}{a^{-7}{b}^{-8}{c}^9\times a^{10}{b}^{11}{c}^{-12}\times a^{13}{b}^{-14}{c}^{15}}$

ABCD is a parallelogram. P is any point on CD. If ar$\left(△DPA\right)=25c{m}^2$ and ar$\left(△APC\right)=40c{m}^2$, then area$\left(△APB\right)$is

$△$ DEF and $△$ LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then are the two triangles congruent? Which condition do you use?
If $\angle F={40}^{\circ }$, what is the measures $\angle N$?

The point of intersection of axes is __.

If the number $91876y2$ is completely divisible by $8$, then the smallest whole number in place of $y$ will be: