Which of the following is the additive inverse of −7/11?

Riya divided her pocket money of ₹240 equally into 5 parts. She donated 3 parts to a charity fund. The amount donated, expressed as a fraction of the total, is:

How many rational numbers lie between 1/3 and 1/2?

A school auditorium has 2025 chairs arranged in a square formation (equal rows and columns). The number of chairs in each row is:

Which of the following cannot be the units digit of a perfect square?

The smallest number by which 180 must be multiplied to make it a perfect square is:

Using the identity (a+b)² = a² + 2ab + b², the value of 103² is:

If x + 1/x = 6, then the value of x² + 1/x² is:

The product 49 × 51 using the identity (a+b)(a−b) = a²−b² equals:

A farmer has a trapezoidal field with parallel sides of 30 m and 20 m, and a height of 15 m. The area of the field is:

The total surface area of a cuboid with length = 8 cm, breadth = 5 cm, and height = 4 cm is:

A cylindrical water tank has radius = 7 m and height = 10 m. The volume of water it can hold (use π = 22/7) is:

The value of (2⁻³ × 3²) / (2² × 3⁻¹) is:

The mass of Earth is approximately 5,970,000,000,000,000,000,000,000 kg. In standard form (scientific notation), this is written as:

The factorised form of 4a² − 9b² is:

The common factor of 12a²b, 18ab², and 24a²b² is:

A car travels 240 km in 4 hours. If it maintains the same speed, the time taken to travel 360 km is:

If 8 workers can build a wall in 12 days, how many days will 16 workers take (assuming inverse variation)?

A point P lies on the y-axis. Its x-coordinate must be:

The graph of a direct proportion between two variables x and y always passes through:

The temperature in Shimla on Monday was −4.5°C. On Tuesday, it dropped further by 3/2°C and on Wednesday it rose by 7/4°C. What was the temperature on Wednesday? Express your answer as a fraction.

A gardener wants to fence a square plot of area 2116 m². Find the length of fencing wire required and the cost of fencing at ₹25 per metre.

Simplify and express with positive exponents:   [( 5⁻² × 3³) / (5³ × 3⁻²)]

Factorise completely:   15x²y − 20xy² + 25xy

A motorbike consumes 4 litres of petrol to cover 120 km. Using the concept of direct proportion, find how far it can travel on 11 litres of petrol. Set up the proportion clearly.

Plot the following points on the grid below and write the quadrant (or axis) each point lies in:
A(3, −2),   B(−4, 1),   C(0, 5),   D(−3, −3)

A water pipe fills 3/8 of a tank in 1 hour. Due to a leak, the tank loses 1/12 of its capacity per hour.
(a) What fraction of the tank is filled in 1 hour, considering the leak?
(b) How many hours will it take to fill the complete tank?
(c) Represent the net filling rate as a point on a number line (draw it).

[Internal Choice]
Find the square root of 108900 using the prime factorisation method. Also verify your answer.

OR

Find the least number that must be added to 6412 to make it a perfect square. Also find the square root of the resulting number using the long division method.

A rectangular garden has its length represented by (3x + 4) m and breadth by (2x − 1) m.
(a) Find its area in terms of x.
(b) If x = 5 m, find the actual area and perimeter.
(c) The cost of laying grass is ₹12 per m². Find the total cost.

[Internal Choice]
A swimming pool is 50 m long, 20 m wide, and 2.5 m deep. Find:

1. Volume of water it can hold (in litres; 1 m³ = 1000 litres)
2. The curved surface area of the four walls
3. Cost of painting the walls and floor at ₹8 per m²

OR

A solid iron cylinder has a diameter of 14 cm and height of 20 cm. Find its total surface area and volume (use π = 22/7).

A scientist measures two microscopic particles:
Particle A: diameter = 4.5 × 10⁻⁷ m  |  Particle B: diameter = 9 × 10⁻⁵ m
(a) How many times larger is Particle B than Particle A?
(b) Express the total combined diameter in standard form.
(c) Simplify: (3⁻² × 4³) ÷ (3² × 4⁻¹)

[Internal Choice]
Factorise the following completely, using suitable methods:
(a) x² + 8x + 15    (b) 49p² − 64q²    (c) a²b − ab² + 2ab

OR

Divide (4x³ − 8x² + 6x) by 2x using the division algorithm, and verify your answer.

Study the table and answer the questions:

Number of workers (x)	4	6	8	12
Days to complete a job (y)	24	?	?	8

(a) Is this direct or inverse variation? Justify.
(b) Find the missing values.
(c) How many workers are needed to complete the job in 6 days?

The following table shows the temperature (°C) of a city at different hours of a day:

Time (Hours)	6 AM	9 AM	12 PM	3 PM	6 PM
Temp (°C)	15	20	30	28	22

(a) Plot this data as a line graph on the grid below.
(b) Between which two time slots did the temperature rise the most?
(c) Find the average temperature for the day.

📖 Case: The residents of an apartment complex decided to build a community vegetable garden on a rectangular plot of land. The plot is (15/4) m long and (8/3) m wide. They divided it into sections:

• Tomatoes: 2/5 of the total area
• Spinach: 1/3 of the total area
• Carrots: remaining area

(a) Calculate the total area of the garden (in m²). [1 mark]
(b) Find the area used for tomatoes and spinach separately. [1 mark]
(c) What fraction of the total area is used for carrots? Find the area in m². [1 mark]
⭐ (d) HOT: If the cost of fencing the entire plot is ₹120 per metre, and they also want to put a divider between tomatoes and spinach (height = 1 m, length = breadth of garden), what is the total cost of fencing + divider at the same rate? [1 mark]

📖 Case: For the Annual Sports Day, the school ground needs to be prepared. A square running track is laid out such that its area is 12,769 m². A rectangular long-jump pit measures (x + 5) m × (x − 5) m. The school uses algebraic identities to calculate dimensions quickly.

(a) Find the side length of the square track using the square root method. [1 mark]
(b) Find the perimeter of the track and the cost of painting it at ₹18 per m. [1 mark]
(c) Using identity, find the area of the long-jump pit. What does the identity used tell us geometrically? [1 mark]
⭐ (d) HOT: If the area of the long-jump pit is 144 m², find the value of x and hence the actual dimensions of the pit. Verify using the identity. [1 mark]

📖 Case: A municipality plans to build two water storage structures:

• Structure A: Cuboidal tank — 12 m × 8 m × 6 m
• Structure B: Cylindrical tank — radius = 7 m, height = 6 m (use π = 22/7)

(a) Find the volume of each structure. Which one holds more water? [1 mark]
(b) Find the total surface area of Structure A (cuboid). [1 mark]
(c) Find the lateral (curved) surface area of Structure B. Cost of waterproofing the curved surface = ₹15 per m². Find total cost. [1 mark]
⭐ (d) HOT: If the cylindrical tank is melted and recast into a cuboid of length 11 m and breadth 7 m, find the height of the new cuboid. [1 mark]

📖 Case: In a school science lab, students are working on two experiments:

Experiment 1: Measuring microscopic distances. The diameter of a red blood cell is 8 × 10⁻⁶ m and the wavelength of green light is 5 × 10⁻⁷ m.

Experiment 2: Factorising polynomial expressions that model the shape of bacteria colony growth over time.

(a) How many times larger is the red blood cell than the wavelength of green light? Express in standard form. [1 mark]
(b) Simplify: [(2³ × 3²)² × (2⁻¹ × 3)³] / [2⁴ × 3⁵] [1 mark]
(c) Factorise the colony model expression: 6t² + 13t + 6 by splitting the middle term. [1 mark]
⭐ (d) HOT: The total area of a petri dish colony (cm²) at time t is given by A = 4t² − 20t + 25. Factorise this and find the value of t when A = 0. What does this represent in the context of the experiment? [1 mark]

📖 Case: The Sharma family is planning a road trip from Delhi to Jaipur. Study the data below and answer:

Speed (km/h)	40	60	80	120
Time taken (hours)	7.5	5	?	?

Also: The car gives a mileage of 15 km per litre. Petrol costs ₹106 per litre.

(a) What type of variation is shown between speed and time? Justify using the product rule. [1 mark]
(b) Complete the table by finding the missing values. [1 mark]
(c) Find the cost of petrol for the 300-km trip (at 60 km/h). [1 mark]
⭐ (d) HOT: If the family decides to increase speed by 50%, by what percentage does the travel time decrease? Show your calculation and state the type of variation used. [1 mark]

📖 Case: Aryan started a small business selling handmade items. The table below shows his monthly profit (in ₹ hundreds):

Month	Jan	Feb	Mar	Apr	May	Jun
Profit (₹ hundreds)	2	5	3	7	6	9

(a) Plot this data as a bar graph on the grid provided below. Label axes clearly. [2 marks]
(b) In which month was the profit the highest? By how much did it increase from January? [1 mark]
⭐ (c) HOT: Aryan notices that if he plots his cumulative (running total) profit as a line graph, the graph resembles a direct variation after March. Compute the cumulative profit for each month and check: Is there any evidence of direct variation in the data? Justify your reasoning. [1 mark]