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Arrange the following steps in the proper order to get a circumcircle from given regular polygon

(a): Mark the point of intersection of the angle bisector

(b): With the marked point as a centre and radius OA, draw the circle passing through the vertices of the given polygon

(c): Draw the right bisector of any two sides of the polygon drawn

(d): Construct the regular polygon

Solve and graph the solution set of :

(i) $3x-2>19or3-2x\ge -7;x\in R.$

(ii) $5>p-1>2or7\le 2p-1\le 17;p\in R.$

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the numebr.

A solid cylinder rolls down an inclined plane of height 6m and reaches the bottom of the plane with angular velocity of 2 rad/s. The radius of the cylinder must be

Identify the linear graph among the following.

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by these points (in ${cm}^2$).

One leg of a right angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

In the figure given below AB = 3, AC = 5 and AD = 4. Then, BD = (AD is median and AE is perpendicular to BC)

Identify two irrational numbers whose product is a rational number.

Which term of the arithmetic progressions 5, 10,15,.....will be 130 more than its ${31}^{st}$ term?

The catalogue price of a computer set is Rs.45,000. The shopkeeper gives a discount of 7% on the listed price. He further gives off season discount of 4% on the balance.

However sales tax at 4% is charged on the remaining amount. Find the final price he has to pay for the computer set.

Given x$\in${integers},find the solution set of:

$-5\le 2x-3<x+2$

Arush has a recurring time deposit account in a Bank. He deposits Rs 500 per month for a period of 4 years. If at the time of maturity he gets Rs 28410. Find the rate of interest.

A (1, 1), B (5, 1), C(4, 2) and D (2, 2) are vertices of a quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?

Find the annual income derived from 800, Rs 40 shares paying $25\%$ dividend.

What does a homogenous determinant mean?

One third of the total number of students in a class are in chemistry laboratory,one fourth are in physics laboratory,one sixth are in biology laboratory and 12 are in maths lab . How many students are there in the class?

In $\Delta ABC$, which is circumscribed by a circle ,$\angle A={45}^{\circ }$, BC =6 cm. The diameter of the circumcircle is equal to

cos$1^{\circ }$ $\times$ cos$2^{\circ }$ $\times$ cos$3^{\circ }$ $\times$……..$\times$ cos${180}^{\circ }$ is equal to:

The first term of the G.P is 1 . If ${(p+q)}^{th}$ term of G.P. is `a` and it's ${(p-q)}^{th}$ term is `b` where a, b ∈ $R^{+}$ then it's $p^{th}$ term is:

What is the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively?

The coordinates of the vertices of a triangle are (1,2),(2,3),(3,1). Find the coordinates of the centre of its circumcircle and the circumradius.

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

The slant height of a square pyramid is 10 cm and its surface area is 144 square centimetres. What is the volume of the square pyramid?

W. K. T

a=bq +r give examples of a and b, wherever possible, satisfying

1. If ais lesser than b then, what can be said about q and r

If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, then the radius of the sphere is

In the figure, ABCD is a cyclic quadrilateral with BC = CD. TC is tangent to the circle at point C and DC is produced to point G. If $\angle$ BCG =1${08}^o$ and O is the centre of the circle, find :

(i) angle BCT

(ii) angle DOC

The number 7 x 11 x 13 + 13 is :

Ice cream rates for a Strawberry brick for 12 months of the year are given :

January - Rs.190 , February - Rs.210 , March - Rs.250 , April - Rs.200 , May - Rs.225 , June - Rs.265 ,

July - Rs.270 , August - Rs.240 , September - Rs.217, October - Rs.203 , November - Rs.180, December - Rs.170

Find the Mean of the rates.

If two chords AB and CD intersect internally at P and if PA = 5, PB = 4, PD = 2, then PC =

Two pipes running together can fill a tank in $11\frac{1}{9}$ minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 $c{m}^2$ of the surface is 10 paise.Find the total cost to paint the vessel all over.

The mean of the following data is 42. Find the missing frequencies x and y if the sum of frequencies is 100.
$\begin{array}{ccccccccc}\text{Class interval}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70& 70-80\\ \text{Frequency}& 7& 10& x& 13& y& 10& 14& 9\end{array}$

Draw a line segment AB and by ruler and compasses, obtain a line segment of length $\frac{3}{4}\left(AB\right)$.

From an external point P, tangents PA and PB are drawn to a circle with centre O. At one point E on the circle tangent is drawn, which intersects PA and PB at C and D respectively. If $PA=14cm$, find the perimeter of $\Delta PCD.$

Show graphically that each of the following given systems of equations has infinitely many solutions:

$2x+y=6,6x+3y=18.$

In the given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.

[ Use $\pi$ = 3.14]

Sam plans to go by bus and walk back. If the speed of bus is 45 kms per hour and he can walk at the rate of 5 kms per hour, how far can he ride by bus if his total journey is of 12 hours?

In an equilateral triangle $PQR,$ if $p,q$ and $r$ denote the lengths perpendiculars from $P,Q,R$ respectively on the opposite sides, then

If $A=\left[\begin{array}{cc}1& 0\\ 2& 1\end{array}\right]\text{and}B=\left[\begin{array}{cc}3& 4\\ -5& 2\end{array}\right]$ Find AB

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.$[Use=\frac{22}{7}]$

If A(-3, 4) & B(9, -5) find distance AB & ratio in which line AB is divided by the – axis.