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5times of 5 th term of an AP is equal to 8 times of 8 th term. Find its 13 the term

An equilateral triangle of side $9\text{cm}$ is inscribed in a circle. Find the radius of the circle.

Two AP's have the same common difference. The difference between their ${100}^{th}$ terms is 100, what is the difference between their ${1000}^{th}$ terms?

A company with 10000 shares of ₹ 100 each, declares an annual dividend of 5 %

(i) What is the total amount of dividend paid by the company

(ii) What would be the annual income of a man, who has 72 shares , in the company

(iii) If he received only 4 % on his investment , find the price he paid for each share

The difference of areas of two sectors of different circles is $77{\text{cm}}^2$. If the radii of the circles are $21\text{cm}$ and $14\text{cm}$ respectively, and corresponding angles of the sectors made at the centre are ${60}^{\circ }$and $\theta$, then the value of $\theta$ can be

A circle is inscribed in a $\Delta$ ABC touching AB, BC and AC at P, Q and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm, find the length of BC.

(A*B) = 27. HCF(A,B) = 3. Their LCM is ___.

Find the next term in the following sequence: a-2d, a-d, a, a+d,...

Every even positive integer is of the form (a) ___ and every positive odd integer is of the form (b) ___.

(x is any positive integer)

Arrange the steps in correct order to construct the circumcenter of a circle?

1. the point where they meet 'O' is the circumcenter.

2. Take the distance OA(or OB or OC) as radius and draw a circle.

3.Draw Triangle $△$ABC.

4. Draw the perpendicular bisectors for any two sides.

How many tangents can be drawn to a circle through the points A, B and C as shown?

What is the probability that an ordinary year has 53 Mondays?

A rope by which a cow is tethered is increased from 16 m to 23 m. How much additional ground does it have now to graze?

The sum of the 2 digit number and number obtained by reversing the order of the digit is 132 , if 12 is added to the number the new number becomes 5 times the sum of the digits . Find new number.

What would be the area of right isosceles triangle of base length 'a'?

1. 7

In a triangle $PQR,P$ is the largest angle and $\cos P=\frac{1}{3}.$ Further the incircle of the triangle touches the sides $PQ,QR$ and $RP$ at $N,L$ and $M$ respectively, such that the length of $PN,QL$ and $RM$ are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see the given figure). If ∠AOB = 30°, find the area of the shaded region.

Solve the equation $x^4-16x^3+86x^2-176x+105=0$ . If two roots being 1 and 7, Find the sum of the square of other two roots.

A man invested an amount at 10% per annum and another amount at 8% per annum simple interset.Thus,he received Rs.1350 as annual interest.Had he interchanged the amounts invested,he would have received Rs.45 less as interest.What amounts did he invest at different rates?

Prove that the lengths of tangents drawn from an external point to a circle are equal. Using the above do the following:

ABC is an isosceles triangle in which AB = AC, circumscribed about a circle as shown in the fig. Prove that the base is bisected by the point of contact.

Question 2

Find the area of a quadrilateral ABCD in which AB=3cm,BC=4cm,CD=4cm, DA = 5cm and AC= 5cm.

x(x+1) + (x+2)(x+3) = 42

The equation $3x-5y=15+3x$ has

Find three consecutive largest positive integers such that the sum of one-third of first, one-fourth of second and one-fifth of third is at most 20.