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In Fig. there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate the cost of painting the shaded region at the rate of ₹25 per $c{m}^2$.

The coordinates of two points A and B are $(-3,5)$ and $(4,-9)$. Then the coordinates of the point P on AB such that AP:PB = 1:6 are

In a $\Delta ABC$, AD is the bisector of $\angle A$.

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

In the given fig. $\angle DAB$ = $\angle ABC$ = ${90}^{\circ }$. Also if $\alpha$ + $\phi$ = ${90}^{\circ }$ and α = 2$\phi$. Find the ratio of H and h.

___

How many terms are there in the AP 6, 10, 14, 18, ..., 174?

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

The 17th term of AP is 5 more than twice its 8th term. If the 11th term of the AP is 43, find its nth term.

$se{c}^2{60}^o$ - 1 = ?

(a) 2 (b) 3 (c) 4 (d) 0

Find the HCF of the following pairs of integers and express it as a linear combination of them.
(i) 963 and 657 (ii) 592 and 252 (iii) 506 and 1155
(iv) 1288 and 575

A bucket made of aluminium sheet is of height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs. 70 per 100 $c{m}^2$. (Use $\pi$ = 3.14).

A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find their present ages.A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find their present ages.

The hypotenuse of a right-angled triangle is 20 metres. If the difference between the lengths of the other sides be 4 metres, find the other sides.

Cards numbered 1 to 30 are put in a bag. A card is drawn at random fromthe bag. Find the probability that the number on the drawn card is (i) not divisible by 3, (ii) a prime number greater that 7, (iii) not a perfect square number.

Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8.

Water flows at the rate of 10 metre per minute from a cylindrical pipe 5mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?

If r is the radius of a circle such that $\pi r^2$= 2$\pi$r, what is the diameter of the circle?

The relative humidity (in %) of a certain city in a month of 30 days was as follows:
$\begin{array}{cccccccccc}98.1& 98.6& 99.2& 90.3& 86.5& 95.3& 92.9& 96.3& 94.2& 95.1\\ 89.2& 92.3& 97.1& 93.5& 92.7& 95.1& 97.2& 93.3& 95.2& 97.3\\ 96.2& 92.1& 84.9& 90.2& 95.7& 98.3& 97.3& 96.1& 92.1& 89\end{array}$

What is the range of this data?

A boat goes 12 km upstream and 40 km downstream in 8 hours. it can go 16 km upstream and 32 km downstream in the same time.Find the speed of the boat in still water and the speed of the stream.

A(7, -3), B(5, 3) and C(3,1) are the vertices of a $△ABC$ and AD is its median. Prove that the median AD divides $△ABC$ into two triangles of equal area.

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.

A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs.10 per 100 $c{m}^2$. (Use $\pi$ = 3.14).

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase if he makes 2 rounds of the fence. Also, find the cost of the rope, if it costs Rs. 4 per meter. $(Take\pi =\frac{22}{7})$

A wheat hut in the form of a cone has radius 3m and height 14 m. Find the capacity of the hut to store the wheat.

The image of a point P(x, y) when reflected in the origin is ___

In Fig. 8.61, a circle is inscribed in a quadrilateral ABCD in which $\angle B={90}^{\circ }$. If AD =23 cm, AB =29 cm and DS =5 cm, find the radius r of the circle.

Tickets numbered 2, 3, 4, 5,..., 100, 101 are placed in a box and mixed thoroughly. ONe ticket is drawn at random from the box. Find the probability that the number on the ticket is
(i) an even number
(ii) a number less than 16
(iii) a number which is a perfect square
(iv) a prime number less than 40.

If cosec $\theta =2$, show that $cot\theta +\frac{sin\theta }{1+cos\theta }$ = 2.

A circular disc of radius 6 cm is divided into three sectors with central angles ${90}^{\circ },{120}^{\circ }and{150}^{\circ }$. What part of the whole circle is the sector with central angle ${150}^{\circ }$? Also, calculate the ratio of the areas of the three sectors.

Question 27

$\frac{1}{9}of\frac{6}{5}$ is

ABC is an isosceles triangle and AC, BC are the tangents at M and N respectively. DE is the diameter of the circle. $\angle$ADP = $\angle$BEQ = ${100}^{\circ }$. What is value of $\angle$PRD?

Let $\left\{a_n\right\}$ be a non - constant arithmetic progression with $a_1=1$ and for any $n\ge 1$, the value $\frac{a_{2n}+a_{2n-1}+\cdots +a_{n+1}}{a_n+a_{n-1}+\cdots a_1}$ remains constant.

Then, $a_{15}$ will be?

Two numbers are in the ratio 3 : 5. If 8 is added to each number the ratio becomes 2 : 3. Find the numbers.

Find the indicated terms in each of the sequences in where $n^{th}$ terms are :

$a_n=4n-3;a_{17},a_{24}$

The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is:

If the sides of a quadrilateral ABCD touch a circle, prove that :

AB + CD = BC + AD.

0/2 is a rational number or not?

Two positions of a dice are shown. Which number will appear on the face opposite the one having 5?

In the figure, PQ is a tangent at a point R of the circle with centre O. If ∠TRQ = 30^o.The measure of ∠PRS is

The average marks of the students in Mathematics of class $8^{th}$ is 45. But most of the students were given 60 out of 100.The Median of the class would be___

Show that the square of any positive odd integer is of the form 8m+1

Understand in a more understanding way.

The rate at which the central bank lends money to member commercial banks against approved securities is known as

A conical tent is to accomodate 11 persons. Each person must have 4 m² of space on the ground and 20 m³ of air to breath. Find thw height of the cone.

Match the following with the midpoints of the line segment joining the given two points.

What is the relation between AM and MB in the given figure?

Show that $\tan {48}^{\circ }\tan {23}^{\circ }\tan {42}^{\circ }\tan {67}^{\circ }=1$

sin35° sec 55° + cos10° cosec80° - 3 = ___

What is the term for a cumulative frequency curve?