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A man walked 5 km towards North then 8 km towards South. What is his final position with respect to his initial position?

If two angles in a triangle are 55${}^{\circ }$ and 45${}^{\circ }$, then what would be the third angle?

In the $△$ given below, find the value of x.

For principal $P,$ rate of interest $R,$ and time period $N$ (in years), what is the simple interest?

The variable in the expression {9$x$ +32} $÷$ 9 is ___ .

Question 40

$8.4÷$ ___ $=2.1$

The common factor in the expression $4a+6a^2$ is ___.

On a number line mark the points $\frac{2}{3},\frac{-8}{3},\frac{7}{3},\frac{-2}{3}and-2.$

Question 28

Fill in the blanks to make the statement true.

Given, $\frac{-6}{7}=\frac{x}{42}$

Question 45

State whether the statement given is True or False.

Sum of $x^2+x$ and $y+y^2$ is $2x^2+2y^2$.

Question 131

A green grocer had a profit of Rs. 47 on Monday, a loss of Rs. 12 on Tuesday and loss of Rs. 8 on Wednesday. Find his net profit or loss in 3 days.

In a floral design made from tiles each of dimensions $40cm$ by $60cm$ (See figure), find the ratios of

a) The perimeter of the shaded portion to the perimeter of the whole design.

b) The area of the shaded portion to the area of the unshaded portion.

Verify each of the following :

(i) $\frac{3}{7}\times \frac{-5}{9}=\frac{-5}{9}\times \frac{3}{7}$

(ii) $\frac{-8}{7}\times \frac{13}{9}=\frac{13}{9}\times \frac{-8}{7}$

(iii) $\frac{-12}{5}\times \frac{7}{-36}=\frac{7}{-36}\times \frac{-12}{5}$

(iv) $-8\times \frac{-13}{12}=\frac{-13}{12}\times (-8)$

Question 83

Express $\frac{9}{40}$ as a per cent.

Question 90

Iron rods a, b, c, d, e and f are making a design in a bridge as shown in the given figure, in which a || b, c|| d and e || f. Find the marked angles between
(i) b and c
(ii) d and e
(iii) d and f
(iv) c and f

Question 43

In the given figure, M is the mid-point of both AC and BD. Then,

a) $\angle 1=\angle 2$
b) $\angle 1=\angle 4$
c) $\angle 2=\angle 4$
d) $\angle 1=\angle 3$

Question 25

In the given figure $\angle AOC$ and $\angle BOC$ form a pair of

(a) vertically opposite angles
(b) complementary angles
(c) alternate interior angles
(d) supplementary angles

Question 11

The marked price of an article is Rs 80 and it is sold at Rs 76, then the discount rate is
(a) 5%
(b) 95%
(c) 10%
(d) approx 11 %

Question 1

Which of the following statements are true:
(a) If a number is divisible by 3, it must be divisible by 9.
(b) If a number is divisible by 9, it must be divisible by 3.
(c) If a number is divisible by 18, it must be divisible by both 3 and 6.
(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.
(e) If two numbers are co-primes, at least one of them must be prime.
(f) All numbers which are divisible by 4 must also be divisible by 8.
(g) All numbers which are divisible by 8 must also be divisible by 4.
(h) If a number exactly divides two numbers separately, it must exactly divide their sum.
(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Question 96

Challenge

Write an expression for the sum of 1 and twice a number n, if you let n be any odd number, will the result always be an odd number?

Question 115
How many faces does figure have?

The diameter divides the circle into two equal parts, each part is ____.

The histogram below represents the Mathematics marks of a few students.

Find the total number of students with total marks above 40 and below 70.

Degree of the monomial '2abcy' is

Choose the correct statemet(s) about the below construction of ${60}^{\circ }$ using ruler and compass.

In the figure, AC = 10 cm, AB = 8 cm, PC = 15 cm, then PB = __ cm .

Question 56 (e)

Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.

$50x^3-21x+107+41x^3-x+1-93+71x-31x^3$

If the replacement set is the set of natural numbers (N), then find the solution set for the given inequation $1+9x\ge x+81$.

Bill wanted to find out the room into which the exited number went in. When he zoomed into the same premises of “The Hall of Operations” using his binoculars, he saw the following engravings on the walls of the halls:

Engraving 1: All natural numbers are rational numbers

Engraving 2: All natural numbers are rational numbers

Engraving 3: All integers are rational numbers

Help Bill by validating the engravings by selecting ALL the correct engravings, given in the options below:

Solve using suitable properties

$8\times 53\times (-125)$

Question 88(i)
The data given below shows the production of motorbikes in a factory for some months of two consecutive years.

Study the table given above and answer the following Questions:
Draw a double bar graph using appropriate scale to depict the above information and compare them.

A graph showing two sets of data simultaneously is known as:

Another name to describe average is ___.

1. mean

   
   

Subtract $x+4xy-y^2$ from $3x^2+8xy-6y^2+2y$

Convert $\frac{1}{5}:\frac{1}{3}$ into whole number ratio or ratio in simple form.

Write a pair of negative integers whose sum gives 8

ABCD is an isosceles trapezoid with DC as one of the bases.

$\angle$ D = (x + 60)${}^{\circ }$

$\angle$ B = (4x)${}^{\circ }$

DC = (x – 3) cm

What is the length of DC?

Which of the following properties are satisfied by addition of integers?

Ten observations 6, 14, 15, 17, x+1, 2x-13, 30, 32, 34, 43 are written in an ascending order. The median of data is 24. Find the value of x.

Find the value of each of the following
$\left(i\right)5^{\frac{1}{2}}\times 5^{\frac{3}{2}}$
$\left(ii\right)7^{\frac{4}{3}}\times 7^{\frac{2}{3}}$

Question 3 (v)

Subtract:

$-m^2+5mnfrom4m^2-3mn+8$