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In the given figure, the red line is:

Find the height (OC) of a square pyramid shaped toy with all equal edges of dimesion 15 in.

Two circles of radius 3 cm and 5cm have a common centre, O. AB is a chord to both the circles and length of CD is $2\sqrt{5}$ cm. Find the distance of the chord from the centre and the length AC.

A cuboidal water tank is $6m$ long, $5m$ wide and $4.5m$ deep. How many litres of water can it hold?

The sides of a triangle are 34 cm, 55 cm and 61 cm. The length of its longest altitude is

Two triangular parks are situated side by side. A gardener while planting along the periphery of the park, found that the sides of the first triangular park are in ratio 3:5:7, and walked 90 m to complete planting along the periphery. For the second triangular park, he found the ratio of sides as 3:4:5 and walked 60 m to complete planting along the periphery. Calculate the difference in areas of the two parks.

Question 1
Write whether the following statements are true or false? Justify your answer.
(i) Point (3,0) lies in the first quadrant.
(ii) Points (1, - 1) and (-1, 1) lie in the same quadrant.
(iii) The coordinates of a point whose ordinate is $-\frac{1}{2}$ and abscissa is 1 are $(-\frac{1}{2},1)$.
(iv) A point lies on Y-axis at a distance of 2 units from the X-axis, its coordinates are (2,0).
(v) (-1,7) is a point in the second quadrant.

1. 60

If two sides of a triangle are 8 cm and 6 cm and its perimeter is 26 cm. Find the third side of the triangle.

ABCD is a parallelogram. P is any point on CD. If ar($△$DPA) = 35 $c{m}^2$ and ar($△$APC) = 15 $c{m}^2$, then area of ($△$APB) is equal to

A vertical pole fixed to the ground is divided in the ratio 1 $:$ 9 by a mark on it with the lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, $15m$ away from the base of the pole, what is the height of the pole?

A metallic triangular prism has a height =15 cm and a base as a right angled triangle. The right angled triangle has the following dimensions: base = 3 cm & altitude = 4 cm. If the prism is melted and recast into cubes of side $1cm$, then what is the number of cubes that are cast?

In a \triangle ABC, P, and Q are respectively, the mid points of AB and BC and R is the mid point of AP. Prove that
$\left(i\right)ar\left(△PBQ\right)=ar\left(△ARC\right)\left(ii\right)ar\left(PRQ\right)=\frac{1}{2}ar\left(△ARC\right)\left(iii\right)ar\left(△RQc\right)=\frac{3}{8}ar\left(△ABC\right)$

What are the values of a, b and c for the equation $y=0.5x+\sqrt{7}$ when written in the standard form: $ax+by+c=0$ ?

1,2,3,4,5......

The above set of numbers are known as _______.

Find five rational numbers between.

In the adjoining figure,ABCD is a trapezium in which AB||DC and its diagonals AC and BD intersect at O.

Prove that $ar\left(△AOD\right)=ar\left(△BOC\right)$.

The highest common factor of ​$3x^{3}y,5x{y}^2,15xy$ is ____.

Select the shape which has only straight lines.

If $x=4+\sqrt{3},$ then find the value of $x^2+\frac{1}{x^2}$.

$△QRS$ is congruent to which of these triangles and what is the congruency condition being fulfilled?

Question 1 (i)

Write$\frac{36}{100}$ in decimal form and say what kind of decimal expansion it has.

The inner diameter of a well is 2.5 metres and it is 8 metres deep. What would be the cost of cementing its inside from the top to a depth of metres at the rate of 350 rupees per square metre?

By which rational number would you multiply $\frac{5}{12}$ , to get the product 1?
[1 MARK]

The given figure shows parallelogram ABCD. Diagonals AC and BD of the parallelogram intersect at point O.

What is the perimeter of ΔABD?

The two intersecting axes or fixed perpendicular lines divide the Cartesian plane into a fixed number of parts.



What are the parts called? Also, what's that 'fixed number'?

If V is the volume of a cuboid of dimentions x, y, z and A is its surface area, then $\frac{A}{V}$

Let $l\left(\stackrel{⌢}{AB}\right)$ be the length of the arc AB of a circle. In the given figure, A, B, D and C are points on the circle. If $l\left(\stackrel{⌢}{DC}\right)=l\left(\stackrel{⌢}{AB}\right)$, then which of the following can be concluded from Euclid's axioms?

Find the value of $a+b+c+d$ in the following figure.