Following are complete up to date information and examples questions and answers for class X Math solutions for WBBSE (West Bengal Board of Secondary Education).

We are going to provide WBBSE class x math solution for maths subject here with sample questions and answers. You can download these sample questions and answers to study later.

**WBBSE Class X Math Solution For Each Topic**

- Number System
- Algebra
- Geometry
- Trigonometry
- Statistics
- Probability
- Coordinate Geometry
- Mensuration

**Number System**

The number system in Class X includes rational and irrational numbers, real numbers, and their properties. Here are ten important questions with solutions to help understand the concept better:

**Question:**Find the value of âˆš144.

**Answer:**âˆš144 = 12**Question:**Simplify 3âˆš2 Ã— 2âˆš3.

**Answer:**3âˆš2 Ã— 2âˆš3 = 6âˆš6**Question:**Express 0.000056 in scientific notation.

**Answer:**0.000056 = 5.6 Ã— 10^-5**Question:**Find the HCF of 24 and 36.

**Answer:**HCF of 24 and 36 is 12**Question:**Write the decimal expansion of 1/3.

**Answer:**1/3 = 0.333…**Question:**Are âˆš2 and âˆš3 rational or irrational numbers?

**Answer:**Both âˆš2 and âˆš3 are irrational numbers.**Question:**Simplify (7 + 3âˆš2)(7 – 3âˆš2).

**Answer:**(7 + 3âˆš2)(7 – 3âˆš2) = 49 – 18 = 31**Question:**Rationalize the denominator of 5/(2âˆš3).

**Answer:**5/(2âˆš3) = (5âˆš3)/6**Question:**Find the value of 2âˆš3 + 3âˆš3.

**Answer:**2âˆš3 + 3âˆš3 = 5âˆš3**Question:**Simplify the expression âˆš50 + âˆš18.

**Answer:**âˆš50 + âˆš18 = 5âˆš2 + 3âˆš2 = 8âˆš2

**Algebra**

Algebra involves solving equations and understanding polynomials. Let’s dive into some key questions:

**Question:**Solve for x: 2x + 3 = 7.

**Answer:**x = 2**Question:**Factorize: x^2 – 9.

**Answer:**x^2 – 9 = (x + 3)(x – 3)**Question:**Solve the quadratic equation: x^2 – 5x + 6 = 0.

**Answer:**x = 2 or x = 3**Question:**Find the roots of the equation: x^2 – 4x + 4 = 0.

**Answer:**x = 2 (repeated root)**Question:**Simplify: (x^2 + 2x + 1)/(x + 1).

**Answer:**(x^2 + 2x + 1)/(x + 1) = x + 1**Question:**Solve for y: 3y – 4 = 2y + 1.

**Answer:**y = 5**Question:**Expand: (x + 2)^2.

**Answer:**(x + 2)^2 = x^2 + 4x + 4**Question:**Solve for x: 5x – 2 = 3x + 6.

**Answer:**x = 4**Question:**If a = 2, b = 3, and c = -1, find the value of a^2 + b^2 + c^2.

**Answer:**a^2 + b^2 + c^2 = 4 + 9 + 1 = 14**Question:**Factorize: x^2 – 5x + 6.

**Answer:**x^2 – 5x + 6 = (x – 2)(x – 3)

**Geometry**

Geometry in Class X includes theorems and problems related to triangles, circles, and other shapes.

**Question:**What is the Pythagorean theorem?

**Answer:**In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a^2 + b^2 = c^2).**Question:**Find the area of a triangle with base 5 cm and height 10 cm.

**Answer:**Area = 1/2 Ã— base Ã— height = 1/2 Ã— 5 Ã— 10 = 25 cm^2**Question:**Calculate the circumference of a circle with radius 7 cm.

**Answer:**Circumference = 2Ï€r = 2Ï€ Ã— 7 = 44 cm**Question:**Prove that the sum of the angles in a triangle is 180 degrees.

**Answer:**The proof involves parallel lines and alternate angles, showing that all interior angles add up to 180 degrees.**Question:**Find the length of the diagonal of a rectangle with sides 3 cm and 4 cm.

**Answer:**Diagonal = âˆš(3^2 + 4^2) = âˆš(9 + 16) = âˆš25 = 5 cm**Question:**Calculate the area of a circle with diameter 14 cm.

**Answer:**Radius = 7 cm, Area = Ï€r^2 = Ï€ Ã— 7^2 = 154 cm^2**Question:**What is the volume of a cube with side length 3 cm?

**Answer:**Volume = side^3 = 3^3 = 27 cm^3**Question:**If two angles of a triangle are 45Â° and 45Â°, what is the measure of the third angle?

**Answer:**Third angle = 180Â° – 45Â° – 45Â° = 90Â°**Question:**What is the perimeter of a square with side length 6 cm?

**Answer:**Perimeter = 4 Ã— side = 4 Ã— 6 = 24 cm**Question:**Find the area of a parallelogram with base 8 cm and height 5 cm.

**Answer:**Area = base Ã— height = 8 Ã— 5 = 40 cm^2

**Trigonometry**

Trigonometry deals with the relationships between the angles and sides of triangles.

**Question:**What is sin 30Â°?

**Answer:**sin 30Â° = 1/2**Question:**Find cos 60Â°.

**Answer:**cos 60Â° = 1/2**Question:**Calculate tan 45Â°.

**Answer:**tan 45Â° = 1**Question:**If sin Î¸ = 3/5, find cos Î¸.

**Answer:**cos Î¸ = âˆš(1 – sin^2 Î¸) = âˆš(1 – 9/25) = âˆš(16/25) = 4/5**Question:**What is the value of cot 30Â°?

**Answer:**cot 30Â° = âˆš3**Question:**Simplify sin^2 Î¸ + cos^2 Î¸.

**Answer:**sin^2 Î¸ + cos^2 Î¸ = 1**Question:**Find sec 0Â°.

**Answer:**sec 0Â° = 1**Question:**If tan Î¸ = 1, what is Î¸?

**Answer:**Î¸ = 45Â°**Question:**What is the value of sin 90Â°?

**Answer:**sin 90Â° = 1**Question:**Find the value of cos 90Â°.

**Answer:**cos 90Â° = 0

**Statistics**

Statistics involves the collection, analysis, interpretation, and presentation of data.

**Question:**Find the mean of the data set: 4, 6, 8, 10, 12.

**Answer:**Mean = (4 + 6 + 8 + 10 + 12)/5 = 40/5 = 8**Question:**What is the median of the data set: 3, 5, 7, 9, 11?

**Answer:**Median = 7 (middle value)**Question:**Calculate the mode of the data set: 1, 2, 2, 3, 4.

**Answer:**Mode = 2 (most frequent value)**Question:**Find the range of the data set: 15, 20, 25, 30, 35.

**Answer:**Range = 35 – 15 = 20**Question:**What is the variance of the data set: 2, 4, 4, 4, 5, 5, 7, 9?

**Answer:**Variance = 4 (after calculating the mean and sum of squared deviations)**Question:**Find the standard deviation of the data set: 2, 4, 6, 8, 10.

**Answer:**Standard deviation = âˆš8 = 2.83 (after calculating the mean and variance)**Question:**If the mean of 6, 8, x, 14, 16 is 10, find x.

**Answer:**x = 2 (after setting up and solving the equation)**Question:**What is the interquartile range of the data set: 1, 3, 5, 7, 9, 11, 13?

**Answer:**Interquartile range = Q3 – Q1 = 11 – 3 = 8**Question:**Calculate the mean deviation of the data set: 10, 12, 14, 16, 18.

**Answer:**Mean deviation = 2.4 (after finding the mean and average absolute deviations)**Question:**Find the cumulative frequency of the data set: 5, 10, 10, 20, 5.

**Answer:**Cumulative frequency table:Value Frequency Cumulative Frequency 5 1 1 10 2 3 20 1 4 5 1 5

**Probability**

Probability measures the likelihood of an event happening.

**Question:**What is the probability of getting a head in a coin toss?

**Answer:**Probability = 1/2**Question:**Find the probability of rolling a 3 on a standard die.

**Answer:**Probability = 1/6**Question:**If a bag contains 5 red and 3 blue balls, what is the probability of drawing a red ball?

**Answer:**Probability = 5/8**Question:**What is the probability of drawing an ace from a standard deck of 52 cards?

**Answer:**Probability = 4/52 = 1/13**Question:**If two coins are tossed, what is the probability of getting two tails?

**Answer:**Probability = 1/4**Question:**Find the probability of rolling an even number on a standard die.

**Answer:**Probability = 3/6 = 1/2**Question:**What is the probability of drawing a king or a queen from a standard deck of cards?

**Answer:**Probability = 8/52 = 2/13**Question:**If a bag contains 4 red, 5 green, and 7 blue balls, what is the probability of drawing a green ball?

**Answer:**Probability = 5/16**Question:**Calculate the probability of getting a sum of 7 when two dice are rolled.

**Answer:**Probability = 6/36 = 1/6**Question:**What is the probability of selecting a vowel from the letters of the word “PROBABILITY”?

**Answer:**Probability = 4/11

**Coordinate Geometry**

Coordinate geometry involves the study of geometric figures through the use of a coordinate plane.

**Question:**Find the distance between the points (3, 4) and (7, 1).

**Answer:**Distance = âˆš((7-3)^2 + (4-1)^2) = âˆš(16 + 9) = âˆš25 = 5**Question:**What is the midpoint of the line segment joining (2, 3) and (4, 7)?

**Answer:**Midpoint = ((2+4)/2, (3+7)/2) = (3, 5)**Question:**Find the slope of the line passing through the points (1, 2) and (3, 6).

**Answer:**Slope = (6-2)/(3-1) = 4/2 = 2**Question:**What is the equation of the line with slope 2 and y-intercept 3?

**Answer:**Equation = y = 2x + 3**Question:**Determine the equation of the line passing through the points (0, 0) and (2, 4).

**Answer:**Slope = 4/2 = 2, Equation = y = 2x**Question:**Find the coordinates of the point which divides the line segment joining (1, 1) and (4, 5) in the ratio 2:3.

**Answer:**Coordinates = ((2*4 + 3*1)/(2+3), (2*5 + 3*1)/(2+3)) = (2.6, 2.6)**Question:**What is the area of the triangle formed by the points (1, 1), (4, 1), and (1, 5)?

**Answer:**Area = 1/2 * base * height = 1/2 * 3 * 4 = 6**Question:**Find the slope of a line perpendicular to the line with slope 3.

**Answer:**Slope = -1/3**Question:**What is the equation of the line passing through (2, 3) with slope -1?

**Answer:**Equation = y – 3 = -1(x – 2) => y = -x + 5**Question:**Determine the distance of the point (3, 4) from the x-axis.

**Answer:**Distance = 4 (y-coordinate)

**Mensuration**

Mensuration involves calculating areas, volumes, and surface areas of various geometric figures.

**Question:**Find the area of a square with side length 5 cm.

**Answer:**Area = side^2 = 5^2 = 25 cm^2**Question:**Calculate the volume of a sphere with radius 3 cm.

**Answer:**Volume = 4/3 Ï€r^3 = 4/3 Ï€ Ã— 3^3 = 113.1 cm^3**Question:**What is the surface area of a cube with side length 4 cm?

**Answer:**Surface area = 6 Ã— side^2 = 6 Ã— 16 = 96 cm^2**Question:**Find the area of a trapezium with bases 10 cm and 8 cm, and height 5 cm.

**Answer:**Area = 1/2 Ã— (base1 + base2) Ã— height = 1/2 Ã— (10 + 8) Ã— 5 = 45 cm^2**Question:**Calculate the volume of a cylinder with radius 7 cm and height 10 cm.

**Answer:**Volume = Ï€r^2h = Ï€ Ã— 7^2 Ã— 10 = 1540 cm^3**Question:**What is the total surface area of a right circular cone with radius 5 cm and slant height 13 cm?

**Answer:**Total surface area = Ï€r(l + r) = Ï€ Ã— 5 Ã— (13 + 5) = 282.74 cm^2**Question:**Find the volume of a rectangular prism with length 6 cm, width 4 cm, and height 3 cm.

**Answer:**Volume = length Ã— width Ã— height = 6 Ã— 4 Ã— 3 = 72 cm^3**Question:**What is the area of a rhombus with diagonals 6 cm and 8 cm?

**Answer:**Area = 1/2 Ã— diagonal1 Ã— diagonal2 = 1/2 Ã— 6 Ã— 8 = 24 cm^2**Question:**Calculate the circumference of a circle with diameter 10 cm.

**Answer:**Circumference = Ï€ Ã— diameter = Ï€ Ã— 10 = 31.42 cm**Question:**Find the lateral surface area of a cone with radius 4 cm and height 3 cm.

**Answer:**Slant height = âˆš(4^2 + 3^2) = âˆš25 = 5 cm, Lateral surface area = Ï€rl = Ï€ Ã— 4 Ã— 5 = 62.8 cm^2

**Exam Pattern**

The Class X mathematics exam under WBBSE is structured to assess students’ understanding of various mathematical concepts. The exam pattern typically includes:

**Multiple Choice Questions (MCQs):**These questions test the student’s basic understanding and quick problem-solving skills.**Short Answer Questions:**These questions require brief responses and test the ability to recall formulas and concepts.**Long Answer Questions:**These questions require detailed solutions and are meant to assess the student’s in-depth understanding and problem-solving abilities.**Practical Problems:**These questions involve real-life scenarios where students must apply mathematical concepts to find solutions.

**Formulas**

Here are some key formulas to remember:

**Pythagorean Theorem:**a^2 + b^2 = c^2**Quadratic Formula:**x = (-b Â± âˆš(b^2 – 4ac)) / 2a**Area of a Circle:**A = Ï€r^2**Circumference of a Circle:**C = 2Ï€r**Volume of a Sphere:**V = 4/3 Ï€r^3**Area of a Triangle:**A = 1/2 Ã— base Ã— height**Slope of a Line:**m = (y2 – y1) / (x2 – x1)**Distance Formula:**d = âˆš((x2 – x1)^2 + (y2 – y1)^2)**Midpoint Formula:**M = ((x1 + x2)/2, (y1 + y2)/2)**Surface Area of a Cube:**SA = 6a^2

**Types of Questions**

The types of questions that can be asked in the WBBSE Class X math exam include:

**Direct Formula-Based Questions:**These questions require the application of specific formulas.**Conceptual Questions:**These test the understanding of fundamental concepts.**Problem-Solving Questions:**These involve applying mathematical principles to solve complex problems.**Diagram-Based Questions:**These require interpretation of geometric figures and diagrams.**Data Interpretation Questions:**These involve analyzing and interpreting data from tables and graphs.

By understanding these topics and practicing the questions provided, students can prepare effectively for their Class X mathematics exam under the WBBSE.

We hope our Class X math solutions for WBBSE have made your studies easier. Keep practicing regularly, and don’t hesitate to revisit tough problems. Remember, math gets simpler with practice. Good luck with your exams, and always believe in your ability to succeed!