- 22 Sections
- 33 Lessons
- Lifetime
- Section 1 : Number SystemBuild a strong foundation in Number System by mastering core concepts like divisibility, remainders, surds, and indices. Learn shortcut techniques and solve CAT-level questions with speed and accuracy.9
- Section 2 : mensuration 2dMensuration is a branch of Mathematics that deals with the measurement of geometric figures. When we talk about 2D mensuration, we focus on flat shapes (also called plane figures) that have only length and breadth, but no height or depth.🔹 What is 2D Mensuration? 2D mensuration involves calculating: Area → the space inside a shape Perimeter → the boundary or total length around a shape These concepts are based on Geometry.10
- trignometry3
- mensuration 3dMensuration 3D is the branch of mathematics that deals with measuring three-dimensional solids like cubes, cylinders, cones, and spheres. It focuses mainly on finding volume (space occupied) and surface area (outer covering) of these objects. It is widely used in real life for construction, storage, and solving competitive exam problems.16
- 4.1Cube
- 4.2Cube level 1 Quiz5 Minutes5 Questions
- 4.3Cuboid
- 4.4Cuboid level 110 Minutes10 Questions
- 4.5cuboid level 210 Minutes10 Questions
- 4.6cuboid level 310 Questions
- 4.7Cylinder
- 4.8Cone
- 4.9Sphere
- 4.10Hemisphere
- 4.11Prisms
- 4.12Pyramids
- 4.13Tetrahedron
- 4.14questions to practice
- 4.15Previous year questions
- 4.16dddd3 Questions
- AveragesAverages represent a central value of a group of numbers. This topic includes simple averages, weighted averages, and changes in average. It is widely used in real-life situations like marks, income, and statistics. It also helps in simplifying complex calculations.0
- AlligationsAlligation is a shortcut method used to solve mixture problems. It helps in finding ratios when two or more quantities are mixed. This topic is commonly used in problems involving price, concentration, and percentages. It saves time compared to traditional methods.0
- Ratio, Proportion & VariationThis topic explains how quantities are related and compared. Ratio compares two quantities, while proportion shows equality of ratios. It also includes direct and inverse variation. These concepts are widely used in real-life scenarios like sharing, scaling, and mixtures.0
- PercentagesPercentages express values as parts of 100. This topic is the foundation for many other chapters like profit & loss, interest, and data interpretation. It includes increase/decrease, successive percentages, and conversions. Strong understanding helps in solving many exam questions quickly.0
- Profit, Loss and DiscountThis chapter deals with buying and selling concepts. It includes cost price, selling price, marked price, profit, loss, and discounts. Questions often involve multiple transactions and percentage changes. It is one of the most important topics in competitive exams.0
- CI/SI InstalmentsThis topic focuses on financial mathematics. It includes Simple Interest (SI), Compound Interest (CI), and installment-based problems. It explains how money grows over time with interest. It is useful in banking, loans, and investment-related questions.0
- Time and WorkThis topic deals with efficiency and work completion. It explains how individuals or groups complete tasks over time. Includes concepts like work rates, pipes and cisterns, and alternate work. Logical thinking is key to solving these problems.1
- Time, Speed and DistanceThis chapter focuses on motion and travel problems. It includes speed, distance, and time relationships. Topics like trains, boats and streams, and relative speed are covered. It is widely used in real-life scenarios and exams.0
- GeometryGeometry deals with shapes, angles, lines, and their properties. It includes triangles, circles, polygons, and theorems. Visualization plays an important role in solving problems. It is a conceptual and scoring topic.0
- Elements of AlgebraThis topic introduces algebraic expressions and identities. It includes simplification, factorization, and basic equations. It forms the base for advanced algebra topics. Logical manipulation of expressions is key here.0
- Theory of EquationsThis chapter focuses on solving equations and understanding roots. It includes quadratic equations and relationships between roots and coefficients. It is useful for solving higher-level algebra problems. Concepts are both theoretical and application-based.0
- Set TheorySet theory deals with collections of elements. It includes operations like union, intersection, and complement. Venn diagrams are used to solve problems visually. It is widely used in logical reasoning and probability.0
- LogarithmLogarithms simplify calculations involving large numbers and exponents. This topic includes log rules, properties, and equations. It is helpful in algebra and exponential problems. Understanding properties is essential for quick solving.0
- Functions and GraphThis topic explains relationships between variables. Functions map inputs to outputs, and graphs help visualize them. It includes linear, quadratic, and other functions. Important for understanding trends and patterns.0
- Sequence, Series and ProgressionsThis chapter deals with ordered numbers and patterns. It includes Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP). It also covers sum of series. Useful in pattern-based questions.0
- Permutations & CombinationsThis topic focuses on counting arrangements and selections. Permutations deal with order, while combinations do not. It is widely used in probability problems. Logical counting methods are essential here.0
- ProbabilityProbability measures the chance of an event occurring. It includes basic rules, conditional probability, and independent events. It is widely used in real-life situations like games and predictions. Concept clarity is very important.0
- Coordinate GeometryThis topic uses a coordinate plane to study geometry. It includes distance formula, slope, and equations of lines. It connects algebra and geometry. Visualization and formulas both are important.0
Curriculum
height and distance
Type 1
1. 150 meter from the foot of a cliff on level ground, the
angle of elevation of the topis 30°. The height of the cliff is:
(a) 50√3 m (b) 40√3 m (c) 45√3 m (d) 60√3 m
2. From a point P on level ground, the angle of elevation of the top of a tower is 30°.
If the tower is 90√3 m high, the distance of P from the foot of the tower is:
(a) 270 m (b) 180 m (c) 90 m (d) 300 m
3. What is the angle of elevation of the sun when the shadow of a pole of height x m
is m ?
(a) 30° (b) 45° (c) 60° (d) 75°
4. A 12 metre ladder is placed against a wall making an angle of 30° with the ground.
Distance of the foot from the wall is:
(a) 10.39 m (b) 9 m (c) 8.5 m (d) 11 m
5. The shadow of a tower is twice its height. The angle of elevation of the sun is:
(a) 30° (b) 45° (c) 60° (d) 26.5°
6. A man 5 ft tall casts a shadow 3 ft long. At the same time a flag pole casts a shadow
45 ft long. Height of the pole is:
(a) 60 ft (b) 75 ft (c) 50 ft (d) 90 ft
7. If the length of the shadow of a boy is equal to his height, the angle of elevation of
the sun is:
(a) 30° (b) 45° (c) 60° (d) 75°
8. A kite is flying at a height of 60 m. If the string makes an angle of 30° with the
ground, the length of the string is:
(a) 120 m (b) 60√3 m (c) 90 m (d) 100 m
9. A tree 6 m high casts a shadow 10 m long. If another pole casts a shadow 15 m at
the same time, its height is:
(a) 9 m (b) 8 m (c) 10 m (d) 7 m
10. A girl 1.5 m tall sees the sun over a 4.5 m wall which is 3 m away. The angle of
elevation of the sun is:
(a) 30° (b) 45° (c) 60° (d) 75°
11. The shadow of a pole is 24 m. If secθ = , the height of the pole is:
(a) 18 m (b) 15 m (c) 20 m (d) 10 m