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Solve
and check result: 5x
+ 9 = 5 + 3x

The coordinates of a point which lies on y-axis at a distance of 5 units in the negative direction of y-axis is?

What is the area of the rhombus ABCD below if AC=12 cm and BE= 8 cm?

Can you draw a line of length 2.25 centimetres using a ruler? How about using ruler and compass?

Maria did a survey where she asked all the children in her school to name their favourite pet. The results are shown in the pie chart.

If 720 children said their favourite pet was a Dog, how many children said their favourite pet was a Rabbit?

A system of simultaneous linear equations has infinitely many solutions if two lines:

A polyhedron with 4 faces and 6 edges, has ___ vertices.

What is the last step in constructing quadrilateral with 3 sides and 2 included angles given?

The angles of triangle are x − 40°, x − 20° and. Find the value of x.

Question 86 (ix)

Using suitable identities, evaluate the following:

$105\times 95$

Find the value of m
$5^{m+2}$ $\times$ $5^4$ = $5^3$.

Question 94

Solve the following:

Express $\frac{27}{64}$ and $\frac{-27}{64}$ as powers of a rational number.

Question 1(i)

State whether the number given below is a perfect cube or not.

216

The given figure shows a square and a regular pentagon put together. Which of the following statements is true?

Question 55

State whether the following statement is true or false:

The surface area of a cuboid formed by joining face-to-face 3 cubes of side x is 3 times the surface area of a cube of side x.

What is the number of faces in a triangular pyramid?

__

Question 20

A recent survey found that ages of workers in a factory as follows:



$\begin{array}{cccccc}\text{Age(in years)}& 20-29& 30-39& 40-49& 50-59& 60\text{and above}\\ \text{Number of}& 38& 27& 86& 46& 3\\ \text{workers}& & & & & \end{array}$



If a person is selected at random, find the probability that the person is:

(i) 40 years or more.

(ii) Under 40 years.

(iii) Having age from 30 - 39 years.

(iv) Under 60 but over 39 years.

Construct the quadrilateral $DEAR$ where $DE=4cm,EA=5cm,AR=4.5cm,\angle E={60}^{\circ },\angle A={90}^{\circ }$

Among the following properties, which are not true for a polygon?

Question 79(ii)

In the given figure, P, Q and R are collinear points and TQ $\perp$ PR. Name two pairs of supplementary angles,

Which of the following is correct for a parallelogram?

आशय स्पष्ट कीजिए -

(क) नम आँखों को गिनना स्याही फैलाना है।

(ख) फ़ादर को याद करना एक उदास शांत संगीत को सुनने जैसा है।

Question 93 (iv)

The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.

$x^2+19x-20$

27 - 125a³-135a + 225a² factorize

Write the following numbers in generalised form:

39, 52, 106, 359, 628, 3458, 9502, 7000

Construct a quadrliateral ABCD; if:

(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and $\angle$ ABC = ${75}^{\circ }$.

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and $\angle \text{BCD}={60}^{\circ }$

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, $\angle \text{A}={60}^{\circ }$ and $\angle \text{B}={75}^{\circ }$.

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, $\angle \text{B}={75}^{\circ }$ and $\angle \text{C}={120}^{\circ }$

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

Abhishek has three containers:

a)Cylindrical container A having radius r and height 2r

b)Cubical container B of edge $\frac{3}{4}r$

c)Cuboidal container C having dimensions $r\times \frac{5}{4}r\times \frac{7}{3}r$

Arrange of the containers in the increasing order of their volume.

Question 5

Plot the points A (1, -1) and B(4, 5).

(i) Draw the line segment joining these points. Write the coordinate of a point on this line segment between the point A and B.

(ii) Extend this line segment and write the coordinates of a point on this line which lies outside the line segment AB.

State which of the following are polygons :

If the given figure is a polygon, name it as convex or concave.

Find the value of x in the given figure