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In the figure, there is a jogging track which consists of two semi-circular paths and two rectangle paths which have to be renovated. The cost of renovation is Rs. 15 per square meters. For the circular parts, the inner and outer radii are 6 m and 8 m respectively. Also, the thickness of the rectangular track is 2m. If the total cost of renovation is Rs. 2,520, find the length of AB. Also, find the difference between the outer and the inner perimeter of the track.

ABCD is a parallelogram, EBCF is a rectangle and BCG is a triangle between the same parallel lines. The ratio of area of parallelogram : area of rectangle : area of triangle is

What is the need of pi?

What does it actually mean?

State, in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v) The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii) Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) $\pi$ is irrational and $\frac{22}{7}$ is rational.

In the given figure, $AB$ and $CD$ are two chords of a circle, intersecting each other at a point $E.$ Prove that $\angle AEC=\frac{1}{2}$(angle subtended by arc $CXA$ at the centre $+$ angle subtended by arc $DYB$ at the centre).

$\text{Each of the equal sides of an isosceles triangle is 13 cm and its base is 24 cm. The area of the triangle is}\left(a\right)156c{m}^2\left(b\right)78c{m}^2\left(c\right)60c{m}^2\left(d\right)120c{m}^2$

Rationalize the denominator and simplify:

(i) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

(ii) $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}$

Assuming that x, y, z are positive real numbers, simplify each of the following:

(i) ${\left(\sqrt{x^{-3}}\right)}^5$

(ii) $\sqrt{x^3{y}^{-2}}$

(iii) $(x^{-2/3}{y}^{-1/2}{)}^2$

(iv) $(\sqrt{x}{)}^{-2/3}\sqrt{y^4}÷\sqrt{x{y}^{-1/2}}$

(v) $5\sqrt{243x^{10}{y}^5{z}^{10}}$

(vi) ${\left(\frac{x^{-4}}{y^{-10}}\right)}^{5/4}$

(vii) ${\left(\frac{\sqrt{2}}{\sqrt{3}}\right)}^5{\left(\frac{6}{7}\right)}^2$

Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden block covered with coloured paper with picture of Santa Claus on it. She must know the exact quantity of paper to buy for this purpose. If the box has length, breadth and height as 80 cm, 40 cm and 20 cm respectively. How many square sheets of paper of side 40 cm would she require?

If a - b = 5 and ab = 12, find the value of $a^2+b^2.$

The number of times a certain observation appears in the data is called its __.

If ${\left(\sqrt{1024}\right)}^3$= $8^x$, what is the value of x?

An equilateral triangle ABC, whose side is 6 cm, is inscribed in a circle. Find the radius of the circle.

What is Heron's formula?

Given that $sinA=\frac{1}{2}$ and $cosB=\frac{1}{\sqrt{2}}$, then find the value of $(A+B)$.

From Bangalore bus stand, if we buy 2 tickets to Malleshwaram and 3 tickets to Yeshwanthpur, the total cost is ₹ 46; but if we buy 3 tickets to Malleshwaram and 5 tickets to Yeshwanthpur, then the total cost is ₹ 74. Find the fares from Bangalore bus stand to Malleshwaram and to Yeshwanthpur respectively.

The sum of interior angles of a polygon with 12 sides is___

If I pick a red ball 10 times out of 30 times from a bag that contains red and black balls, then the probability of picking a black ball is _________.

The equation of the circle passing through (1, 1) and the points of intersection of $x^2+y^2+13x-3y=0$ and $2x^2+2y^2+4x-7y-25=0$ is

If $\frac{1}{lo{g}_3\pi }+\frac{1}{lo{g}_4\pi }>x$, then the biggest possible integer $x$ can take -

There are two lines, AB and CD, which are parallel to each other. ∠AMN= ${20}^{\circ }$. Find the value of x .

${}^n{C}_r{÷}^n{C}_{r-1}=$

[MP PET 1984]

Express y in the term of x given that 2 x - 5 y = 7 check weather the (-3,-2) lies on the graph of the given linear equation

If the radius of a hemisphere is 3.5 cm, its curved surface area is

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 4={45}^{\circ }$ then $\angle 3$ and $\angle 6$ are

The angle whose complement is one-third of its supplement will be

The value of $tan{60}^{\circ }cose{c}^2{45}^{\circ }+se{c}^2{60}^{\circ }tan{45}^{\circ }$ is

A curious 12th class student wants to know and collect the data regarding the percentage of students who got grade A1 in Mathematics during the last 10 years in Board examinations. This collected data is known as

The value of
$\frac{co{t}^2{30}^{\circ }+8si{n}^2{45}^{\circ }+\frac{3}{2}se{c}^2{30}^{\circ }+2co{s}^2{90}^{\circ }}{2sec{60}^{\circ }+3cosec{30}^{\circ }-\frac{7}{3}ta{n}^2{60}^{\circ }}$ is :

The perimeter of a square is 4(x+2y) cm. Its area is

The value $co{t}^2{30}^{\circ }-2co{s}^2{60}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }-4si{n}^2{30}^{\circ }$ is

Show that 1.27 is rational number

The points (6, 6), (0, 6) and (6, 0) are the vertices of a right triangle as shown in the figure. Find the distance between its centroid and D (point of median of AB).

A car travels 0.99 km distance in which each wheel makes 450 complete revolutions. Find the radius of its wheel in m.

In how many parts a circle divides a plane?

Question 9(a)
Use the sign of >, < or = in the box to make the statements true.
$(-8)+(-4)\square (-8)-(-4)$

The perimeter of triangular ground is 900m and its side are in the ratio 3:5:4.using herons formula.find the area of the ground