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The given figure shows a pentagon ABCDE. EG,drawn parallel to DA,meets BA produced at G,and CF,drawn parallel to DB,meets AB produced at F.Show that ar(pentagon ABCDE)=ar($△DGF$).

Question 30

$\frac{2}{5}$ of 25 is equal to ___

1. 3000

In the figure, $AB$ divides $\angle DAC$ in the ratio $1:3$ and $AB=DB$. Determine the value of $x.$

BAD is the ___arc

The product of $(3x+5)(x-4)$ is .

Two different positions of the same die are shown. Which number will appear on the face opposite to the face with the number $4$?

A metal sheet of width $1m$ is kept in a roll. A worker needs to make a box of dimensions $50cm\times 30cm\times 45cm$. Find the length of the sheet required to make the box.

In the figure, O is the centre of the circle and the length of are AB is twice the length of are BC. If angle AOB = ${108}^o$, find :

(i) $\angle$ CAB,

(ii) $\angle$ ADB.

In a quadrilateral PQRS, PQ = 3 cm, QR = 4 cm and PS = 5 cm. Also, $\angle SPQ$ = ${70}^{\circ }$ and $\angle PQR$ = ${90}^{\circ }$. Which of the following options is the approximate the value of $\angle QRS$?

What is the total surface area of a cube of side 5 m?

The bar graph given below shows the sales of newspapers (in million number) from six branches of a publishing company during two consecutive years 2013 and 2014.

i) What is the average sale of all the branches (in million numbers) for the year 2014?

ii) What is the total sales of NP1, NP3 and NP5 for both years?

For universal set U, and sets A, B which are subsets of U, the following information is given

n(U) = 47

n(A) = 18

n(B) = 11, n(A ∩ B) = 10

Then, the number of elements that are neither in A nor B is__

Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4 m × 3 m?

In the figure, ABCD is a ||gm . O is any point on AC. PQ || AB and LM || AD. Prove that ar (||gm DLOP) = ar(||gm BMOQ).

Which of the following measurements of side lengths can be used to construct a triangle?

In which quadrant or on which axis do each of the points (3, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane
[4 MARKS]

Find two rational numbers between √ 2 and √ 5

In figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [4 MARKS]

The value of $\sqrt{5+2\sqrt{6}}$ is

(a)$\sqrt{5}+\sqrt{6}$ (b)$\sqrt{5}-\sqrt{6}$ (c)$\sqrt{3}+\sqrt{2}$ (d)$\sqrt{3}-\sqrt{2}$

The standard form of a linear equation in two variables x and y, whose respective coefficients are 2 and -3 and has the constant as 4 is ____.

The value of $0.\overline{23}$ + $0.\overline{22}$ is

If (x,y) are the coordinates of any point P, at the same time if (x,y) = (y,x), which of following options must hold true?

ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCD respectively, then EF =

A $10$ inches long pencil $AB$ with mid point $C$ and a small eraser $P$ are placed on the horizontal top of a table such that $PC=\sqrt{5}$ inches and $\angle PCB={\tan }^{-1}\left(2\right).$

The acute angle through which the pencil must be rotated about $C$ so that the perpendicular distance between eraser and pencil becomes exactly $1$ inch is