Class 10 Maths Solution WBBSE : Download PDF

The Class 10 Maths syllabus for WBBSE is designed to build a strong foundation in various mathematical concepts. It includes topics like Algebra, Geometry, Trigonometry, Statistics, and Probability. Each of these topics is crucial for developing problem-solving skills and logical thinking.

Key Topics and Sub-Topics

Algebra

• Polynomials
• Pair of Linear Equations in Two Variables
• Quadratic Equations
• Arithmetic Progressions

Geometry

• Triangles
• Circles
• Constructions
• Coordinate Geometry

Trigonometry

• Introduction to Trigonometry
• Trigonometric Identities
• Heights and Distances

Statistics and Probability

• Mean, Median, and Mode of Grouped Data
• Probability

Number Systems

• Real Numbers

Exam Pattern Information

The Class 10 Maths exam under WBBSE consists of two papers: Paper 1 (Theory) and Paper 2 (Internal Assessment). The theory paper is worth 90 marks, and the internal assessment is worth 10 marks.

Theory Paper (90 Marks)

• Section A: Multiple Choice Questions (MCQs) – 20 Marks
• Section B: Short Answer Questions (SAQs) – 30 Marks
• Section C: Long Answer Questions (LAQs) – 40 Marks

Internal Assessment (10 Marks)

• Project Work
• Practical Work
• Viva Voce

Mathematical Formulas in Plain Text

Here are some essential formulas that are frequently used in Class 10 Maths. These formulas can be easily copied and pasted into the WordPress classic editor.

Algebra

1. Quadratic Equation: ax^2 + bx + c = 0
2. Sum of roots of a quadratic equation: -b/a
3. Product of roots of a quadratic equation: c/a
4. Arithmetic Progression nth term: a_n = a + (n-1)d
5. Sum of n terms of an arithmetic progression: S_n = n/2 * (2a + (n-1)d)

Geometry

1. Pythagorean Theorem: a^2 + b^2 = c^2
2. Area of a triangle: (1/2) * base * height
3. Area of a circle: π * r^2
4. Circumference of a circle: 2 * π * r

Trigonometry

1. sin^2A + cos^2A = 1
2. sec^2A – tan^2A = 1
3. cosec^2A – cot^2A = 1
4. sin(90° – A) = cosA
5. cos(90° – A) = sinA

Statistics and Probability

1. Mean of grouped data: Σ(f * x) / Σf
2. Mode of grouped data: L + (f1 – f0) / (2f1 – f0 – f2) * h
3. Median of grouped data: L + (n/2 – cf) / f * h
4. Probability of an event: Number of favorable outcomes / Total number of outcomes

Types of Questions

Multiple Choice Questions (MCQs)

• These questions have four options, and you need to choose the correct one. For example: What is the value of sin 30°? Options: a) 0.5 b) 0.866 c) 1 d) 0

Short Answer Questions (SAQs)

• These require brief answers. For example: Solve the quadratic equation x^2 – 5x + 6 = 0.

Long Answer Questions (LAQs)

• These require detailed solutions. For example: Prove that the sum of the angles in a triangle is 180°.

Sample Questions and Answers

Algebra

Question 1: Solve the quadratic equation x^2 – 7x + 10 = 0. Answer: The equation can be factored as (x – 5)(x – 2) = 0. So, x = 5 or x = 2.

Question 2: Find the 10th term of the arithmetic progression 2, 5, 8, 11, … Answer: Here, a = 2 and d = 3. Using the formula for the nth term: a_n = a + (n-1)d, we get a_10 = 2 + (10-1) * 3 = 2 + 27 = 29.

Geometry

Question 1: Prove that the diagonals of a rectangle are equal. Answer: Let ABCD be a rectangle with diagonals AC and BD. Since ABCD is a rectangle, we have AB = CD and AD = BC. In triangles ABD and CDB, we have AB = CD, AD = BC, and BD is common. Therefore, triangles ABD and CDB are congruent by the SAS criterion. Hence, AC = BD.

Question 2: Find the area of a circle with radius 7 cm. Answer: Using the formula for the area of a circle, π * r^2, we get the area as 22/7 * 7^2 = 154 cm^2.

Trigonometry

Question 1: Prove that sin^2A + cos^2A = 1. Answer: In a right-angled triangle, let the angle be A. By the definition of sine and cosine, sinA = opposite/hypotenuse and cosA = adjacent/hypotenuse. Squaring both sides and adding, we get (opposite/hypotenuse)^2 + (adjacent/hypotenuse)^2 = 1, which simplifies to sin^2A + cos^2A = 1.

Question 2: Find the value of tan 45°. Answer: tan 45° = sin 45° / cos 45° = 1.

Statistics and Probability

Question 1: Find the mean of the following data: 5, 10, 15, 20, 25. Answer: The mean is the sum of the observations divided by the number of observations. Mean = (5 + 10 + 15 + 20 + 25) / 5 = 75 / 5 = 15.

Question 2: A box contains 3 red balls, 2 blue balls, and 5 green balls. What is the probability of drawing a red ball? Answer: The probability of an event is the number of favorable outcomes divided by the total number of outcomes. Probability of drawing a red ball = 3 / (3+2+5) = 3 / 10 = 0.3.

Best 100 Example Questions and Answers for Class 10 Maths Solution for WBBSE

Question: Find the area of a rectangle with length 10 cm and breadth 5 cm.

Answer: Area = Length × Breadth = 10 cm × 5 cm = 50 cm²

Question: Find the perimeter of a rectangle with length 10 cm and breadth 5 cm.

Answer: Perimeter = 2 × (Length + Breadth) = 2 × (10 cm + 5 cm) = 30 cm

Question: Calculate the area of a triangle with base 8 cm and height 5 cm.

Answer: Area = 1/2 × Base × Height = 1/2 × 8 cm × 5 cm = 20 cm²

Question: Calculate the perimeter of an equilateral triangle with side 6 cm.

Answer: Perimeter = 3 × Side = 3 × 6 cm = 18 cm

Question: Find the circumference of a circle with radius 7 cm.

Answer: Circumference = 2 × π × Radius = 2 × 3.14 × 7 cm = 43.96 cm

Question: Find the area of a circle with radius 7 cm.

Answer: Area = π × Radius² = 3.14 × (7 cm)² = 153.86 cm²

Question: Calculate the volume of a cube with side 4 cm.

Answer: Volume = Side³ = (4 cm)³ = 64 cm³

Question: Find the surface area of a cube with side 4 cm.

Answer: Surface Area = 6 × Side² = 6 × (4 cm)² = 96 cm²

Question: Calculate the volume of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.

Answer: Volume = Length × Breadth × Height = 5 cm × 3 cm × 2 cm = 30 cm³

Question: Find the surface area of a cuboid with length 5 cm, breadth 3 cm, and height 2 cm.

Answer: Surface Area = 2 × (Length × Breadth + Breadth × Height + Height × Length) = 2 × (5 cm × 3 cm + 3 cm × 2 cm + 2 cm × 5 cm) = 62 cm²

Question: Calculate the area of a parallelogram with base 12 cm and height 8 cm.

Answer: Area = Base × Height = 12 cm × 8 cm = 96 cm²

Question: Find the perimeter of a square with side 9 cm.

Answer: Perimeter = 4 × Side = 4 × 9 cm = 36 cm

Question: Calculate the area of a square with side 9 cm.

Answer: Area = Side² = (9 cm)² = 81 cm²

Question: Find the volume of a cylinder with radius 5 cm and height 10 cm.

Answer: Volume = π × Radius² × Height = 3.14 × (5 cm)² × 10 cm = 785 cm³

Question: Calculate the surface area of a cylinder with radius 5 cm and height 10 cm.

Answer: Surface Area = 2 × π × Radius × (Radius + Height) = 2 × 3.14 × 5 cm × (5 cm + 10 cm) = 471 cm²

Question: Find the area of a trapezium with bases 8 cm and 5 cm and height 6 cm.

Answer: Area = 1/2 × (Base1 + Base2) × Height = 1/2 × (8 cm + 5 cm) × 6 cm = 39 cm²

Question: Calculate the distance between two points (3, 4) and (6, 8).

Answer: Distance = √((x2 – x1)² + (y2 – y1)²) = √((6 – 3)² + (8 – 4)²) = √(9 + 16) = √25 = 5

Question: Find the midpoint of the line segment joining the points (2, 3) and (4, 5).

Answer: Midpoint = ((x1 + x2)/2, (y1 + y2)/2) = ((2 + 4)/2, (3 + 5)/2) = (3, 4)

Question: Solve for x: 3x + 5 = 20.

Answer: 3x + 5 = 20 => 3x = 20 – 5 => 3x = 15 => x = 15/3 => x = 5

Question: Solve for y: 2y – 7 = 13.

Answer: 2y – 7 = 13 => 2y = 13 + 7 => 2y = 20 => y = 20/2 => y = 10

Question: Solve for x: 5x – 9 = 21.

Answer: 5x – 9 = 21 => 5x = 21 + 9 => 5x = 30 => x = 30/5 => x = 6

Question: Solve for y: 4y + 3 = 19.

Answer: 4y + 3 = 19 => 4y = 19 – 3 => 4y = 16 => y = 16/4 => y = 4

Question: Solve for x: 7x – 2 = 26.

Answer: 7x – 2 = 26 => 7x = 26 + 2 => 7x = 28 => x = 28/7 => x = 4

Question: Solve for y: 9y + 4 = 40.

Answer: 9y + 4 = 40 => 9y = 40 – 4 => 9y = 36 => y = 36/9 => y = 4

Question: Find the quadratic roots of the equation x² – 5x + 6 = 0.

Answer: x² – 5x + 6 = 0 => (x – 2)(x – 3) = 0 => x = 2, x = 3

Question: Find the quadratic roots of the equation x² – 7x + 12 = 0.

Answer: x² – 7x + 12 = 0 => (x – 3)(x – 4) = 0 => x = 3, x = 4

Question: Find the quadratic roots of the equation x² – 9x + 20 = 0.

Answer: x² – 9x + 20 = 0 => (x – 4)(x – 5) = 0 => x = 4, x = 5

Question: Find the quadratic roots of the equation x² – 11x + 28 = 0.

Answer: x² – 11x + 28 = 0 => (x – 4)(x – 7) = 0 => x = 4, x = 7

Question: Find the quadratic roots of the equation x² – 13x + 36 = 0.

Answer: x² – 13x + 36 = 0 => (x – 4)(x – 9) = 0 => x = 4, x = 9

Question: Find the quadratic roots of the equation x² – 15x + 50 = 0.

Answer: x² – 15x + 50 = 0 => (x – 5)(x – 10) = 0 => x = 5, x = 10

Question: Solve for x in the equation 3x² – 12x + 9 = 0.

Answer: 3x² – 12x + 9 = 0 => x² – 4x + 3 = 0 => (x – 1)(x – 3) = 0 => x = 1, x = 3

Question: Solve for x in the equation 2x² – 8x + 6 = 0.

Answer: 2x² – 8x + 6 = 0 => x² – 4x + 3 = 0 => (x – 1)(x – 3) = 0 => x = 1, x = 3

Question: Solve for x in the equation x² – 6x + 5 = 0.

Answer: x² – 6x + 5 = 0 => (x – 1)(x – 5) = 0 => x = 1, x = 5

Question: Solve for x in the equation x² – 8x + 15 = 0.

Answer: x² – 8x + 15 = 0 => (x – 3)(x – 5) = 0 => x = 3, x = 5

Question: Solve for x in the equation x² – 10x + 24 = 0.

Answer: x² – 10x + 24 = 0 => (x – 4)(x – 6) = 0 => x = 4, x = 6

Question: Solve for x in the equation x² – 12x + 35 = 0.

Answer: x² – 12x + 35 = 0 => (x – 5)(x – 7) = 0 => x = 5, x = 7

Question: Solve for x in the equation x² – 14x + 48 = 0.

Answer: x² – 14x + 48 = 0 => (x – 6)(x – 8) = 0 => x = 6, x = 8

Question: Solve for x in the equation x² – 16x + 63 = 0.

Answer: x² – 16x + 63 = 0 => (x – 7)(x – 9) = 0 => x = 7, x = 9

Question: Solve for x in the equation x² – 18x + 80 = 0.

Answer: x² – 18x + 80 = 0 => (x – 8)(x – 10) = 0 => x = 8, x = 10

Question: Solve for x in the equation x² – 20x + 99 = 0.

Answer: x² – 20x + 99 = 0 => (x – 9)(x – 11) = 0 => x = 9, x = 11

Question: Solve for x in the equation x² – 22x + 120 = 0.

Answer: x² – 22x + 120 = 0 => (x – 10)(x – 12) = 0 => x = 10, x = 12

Question: Solve for x in the equation x² – 24x + 143 = 0.

Answer: x² – 24x + 143 = 0 => (x – 11)(x – 13) = 0 => x = 11, x = 13

Question: Solve for x in the equation x² – 26x + 168 = 0.

Answer: x² – 26x + 168 = 0 => (x – 12)(x – 14) = 0 => x = 12, x = 14

Question: Solve for x in the equation x² – 28x + 195 = 0.

Answer: x² – 28x + 195 = 0 => (x – 13)(x – 15) = 0 => x = 13, x = 15

Question: Solve for x in the equation x² – 30x + 224 = 0.

Answer: x² – 30x + 224 = 0 => (x – 14)(x – 16) = 0 => x = 14, x = 16

Question: Solve for x in the equation x² – 32x + 255 = 0.

Answer: x² – 32x + 255 = 0 => (x – 15)(x – 17) = 0 => x = 15, x = 17

Question: Solve for x in the equation x² – 34x + 288 = 0.

Answer: x² – 34x + 288 = 0 => (x – 16)(x – 18) = 0 => x = 16, x = 18

Question: Solve for x in the equation x² – 36x + 323 = 0.

Answer: x² – 36x + 323 = 0 => (x – 17)(x – 19) = 0 => x = 17, x = 19

Question: Solve for x in the equation x² – 38x + 360 = 0.

Answer: x² – 38x + 360 = 0 => (x – 18)(x – 20) = 0 => x = 18, x = 20

Question: Solve for x in the equation x² – 40x + 399 = 0.

Answer: x² – 40x + 399 = 0 => (x – 19)(x – 21) = 0 => x = 19, x = 21

Question: Solve for x in the equation x² – 42x + 440 = 0.

Answer: x² – 42x + 440 = 0 => (x – 20)(x – 22) = 0 => x = 20, x = 22

Question: Solve for x in the equation x² – 44x + 483 = 0.

Answer: x² – 44x + 483 = 0 => (x – 21)(x – 23) = 0 => x = 21, x = 23

Question: Solve for x in the equation x² – 46x + 528 = 0.

Answer: x² – 46x + 528 = 0 => (x – 22)(x – 24) = 0 => x = 22, x = 24

Question: Solve for x in the equation x² – 48x + 575 = 0.

Answer: x² – 48x + 575 = 0 => (x – 23)(x – 25) = 0 => x = 23, x = 25

Question: Solve for x in the equation x² – 50x + 624 = 0.

Answer: x² – 50x + 624 = 0 => (x – 24)(x – 26) = 0 => x = 24, x = 26

Question: Solve for x in the equation x² – 52x + 675 = 0.

Answer: x² – 52x + 675 = 0 => (x – 25)(x – 27) = 0 => x = 25, x = 27

Question: Solve for x in the equation x² – 54x + 728 = 0.

Answer: x² – 54x + 728 = 0 => (x – 26)(x – 28) = 0 => x = 26, x = 28

Question: Solve for x in the equation x² – 56x + 783 = 0.

Answer: x² – 56x + 783 = 0 => (x – 27)(x – 29) = 0 => x = 27, x = 29

Question: Solve for x in the equation x² – 58x + 840 = 0.

Answer: x² – 58x + 840 = 0 => (x – 28)(x – 30) = 0 => x = 28, x = 30

Question: Solve for x in the equation x² – 60x + 899 = 0.

Answer: x² – 60x + 899 = 0 => (x – 29)(x – 31) = 0 => x = 29, x = 31

Question: Solve for x in the equation x² – 62x + 960 = 0.

Answer: x² – 62x + 960 = 0 => (x – 30)(x – 32) = 0 => x = 30, x = 32

Question: Solve for x in the equation x² – 64x + 1023 = 0.

Answer: x² – 64x + 1023 = 0 => (x – 31)(x – 33) = 0 => x = 31, x = 33

Question: Solve for x in the equation x² – 66x + 1088 = 0.

Answer: x² – 66x + 1088 = 0 => (x – 32)(x – 34) = 0 => x = 32, x = 34

Question: Solve for x in the equation x² – 68x + 1155 = 0.

Answer: x² – 68x + 1155 = 0 => (x – 33)(x – 35) = 0 => x = 33, x = 35

Question: Solve for x in the equation x² – 70x + 1224 = 0.

Answer: x² – 70x + 1224 = 0 => (x – 34)(x – 36) = 0 => x = 34, x = 36

Question: Solve for x in the equation x² – 72x + 1295 = 0.

Answer: x² – 72x + 1295 = 0 => (x – 35)(x – 37) = 0 => x = 35, x = 37

Question: Solve for x in the equation x² – 74x + 1368 = 0.

Answer: x² – 74x + 1368 = 0 => (x – 36)(x – 38) = 0 => x = 36, x = 38

Question: Solve for x in the equation x² – 76x + 1443 = 0.

Answer: x² – 76x + 1443 = 0 => (x – 37)(x – 39) = 0 => x = 37, x = 39

Question: Solve for x in the equation x² – 78x + 1520 = 0.

Answer: x² – 78x + 1520 = 0 => (x – 38)(x – 40) = 0 => x = 38, x = 40

Question: Solve for x in the equation x² – 80x + 1599 = 0.

Answer: x² – 80x + 1599 = 0 => (x – 39)(x – 41) = 0 => x = 39, x = 41

Question: Solve for x in the equation x² – 82x + 1680 = 0.

Answer: x² – 82x + 1680 = 0 => (x – 40)(x – 42) = 0 => x = 40, x = 42

Question: Solve for x in the equation x² – 84x + 1763 = 0.

Answer: x² – 84x + 1763 = 0 => (x – 41)(x – 43) = 0 => x = 41, x = 43

Question: Solve for x in the equation x² – 86x + 1848 = 0.

Answer: x² – 86x + 1848 = 0 => (x – 42)(x – 44) = 0 => x = 42, x = 44

Question: Solve for x in the equation x² – 88x + 1935 = 0.

Answer: x² – 88x + 1935 = 0 => (x – 43)(x – 45) = 0 => x = 43, x = 45

Question: Solve for x in the equation x² – 90x + 2024 = 0.

Answer: x² – 90x + 2024 = 0 => (x – 44)(x – 46) = 0 => x = 44, x = 46

Question: Solve for x in the equation x² – 92x + 2115 = 0.

Answer: x² – 92x + 2115 = 0 => (x – 45)(x – 47) = 0 => x = 45, x = 47

Question: Solve for x in the equation x² – 94x + 2208 = 0.

Answer: x² – 94x + 2208 = 0 => (x – 46)(x – 48) = 0 => x = 46, x = 48

Question: Solve for x in the equation x² – 96x + 2303 = 0.

Answer: x² – 96x + 2303 = 0 => (x – 47)(x – 49) = 0 => x = 47, x = 49

Question: Solve for x in the equation x² – 98x + 2400 = 0.

Answer: x² – 98x + 2400 = 0 => (x – 48)(x – 50) = 0 => x = 48, x = 50

Question: Solve for x in the equation x² – 100x + 2499 = 0.

Answer: x² – 100x + 2499 = 0 => (x – 49)(x – 51) = 0 => x = 49, x = 51

Question: Solve for x in the equation x² – 102x + 2600 = 0.

Answer: x² – 102x + 2600 = 0 => (x – 50)(x – 52) = 0 => x = 50, x = 52

Question: Solve for x in the equation x² – 104x + 2703 = 0.

Answer: x² – 104x + 2703 = 0 => (x – 51)(x – 53) = 0 => x = 51, x = 53

Question: Solve for x in the equation x² – 106x + 2808 = 0.

Answer: x² – 106x + 2808 = 0 => (x – 52)(x – 54) = 0 => x = 52, x = 54

Question: Solve for x in the equation x² – 108x + 2915 = 0.

Answer: x² – 108x + 2915 = 0 => (x – 53)(x – 55) = 0 => x = 53, x = 55

Question: Solve for x in the equation x² – 110x + 3024 = 0.

Answer: x² – 110x + 3024 = 0 => (x – 54)(x – 56) = 0 => x = 54, x = 56

Question: Solve for x in the equation x² – 112x + 3135 = 0.

Answer: x² – 112x + 3135 = 0 => (x – 55)(x – 57) = 0 => x = 55, x = 57

Question: Solve for x in the equation x² – 114x + 3248 = 0.

Answer: x² – 114x + 3248 = 0 => (x – 56)(x – 58) = 0 => x = 56, x = 58

Question: Solve for x in the equation x² – 116x + 3363 = 0.

Answer: x² – 116x + 3363 = 0 => (x – 57)(x – 59) = 0 => x = 57, x = 59

Question: Solve for x in the equation x² – 118x + 3480 = 0.

Answer: x² – 118x + 3480 = 0 => (x – 58)(x – 60) = 0 => x = 58, x = 60

Question: Solve for x in the equation x² – 120x + 3599 = 0.

Answer: x² – 120x + 3599 = 0 => (x – 59)(x – 61) = 0 => x = 59, x = 61

Question: Solve for x in the equation x² – 122x + 3720 = 0.

Answer: x² – 122x + 3720 = 0 => (x – 60)(x – 62) = 0 => x = 60, x = 62

Question: Solve for x in the equation x² – 124x + 3843 = 0.

Answer: x² – 124x + 3843 = 0 => (x – 61)(x – 63) = 0 => x = 61, x = 63

Question: Solve for x in the equation x² – 126x + 3968 = 0.

Answer: x² – 126x + 3968 = 0 => (x – 62)(x – 64) = 0 => x = 62, x = 64

Question: Solve for x in the equation x² – 128x + 4095 = 0.

Answer: x² – 128x + 4095 = 0 => (x – 63)(x – 65) = 0 => x = 63, x = 65

Question: Solve for x in the equation x² – 130x + 4224 = 0.

Answer: x² – 130x + 4224 = 0 => (x – 64)(x – 66) = 0 => x = 64, x = 66

Question: Solve for x in the equation x² – 132x + 4355 = 0.

Answer: x² – 132x + 4355 = 0 => (x – 65)(x – 67) = 0 => x = 65, x = 67

Question: Solve for x in the equation x² – 134x + 4488 = 0.

Answer: x² – 134x + 4488 = 0 => (x – 66)(x – 68) = 0 => x = 66, x = 68

Question: Solve for x in the equation x² – 136x + 4623 = 0.

Answer: x² – 136x + 4623 = 0 => (x – 67)(x – 69) = 0 => x = 67, x = 69

Question: Solve for x in the equation x² – 138x + 4760 = 0.

Answer: x² – 138x + 4760 = 0 => (x – 68)(x – 70) = 0 => x = 68, x = 70

Question: Solve for x in the equation x² – 140x + 4899 = 0.

Answer: x² – 140x + 4899 = 0 => (x – 69)(x – 71) = 0 => x = 69, x = 71