MATHS (Q)

Note: These questions are meant to cover a wide range of concepts, from basic understanding to application. They are divided into different categories for clarity.

Understanding Concepts:

1. What is a real number? Provide an example.
2. Differentiate between rational and irrational numbers with examples.
3. Is zero a rational number? Explain.
4. State the properties of real numbers.
5. Explain the closure property of addition for real numbers.
6. How is the commutative property of multiplication different from the commutative property of addition?
7. Give an example of a real number that is not a rational number.
8. Why is √2 considered an irrational number?
9. Explain why the sum of a rational number and an irrational number is irrational.
10. Can two irrational numbers add up to give a rational number? Justify your answer.
11. How does the distributive property work for real numbers?
12. Show that the sum of a rational and an irrational number is irrational.
13. Explain the associative property of addition for real numbers.
14. Provide an example of a real number that is neither rational nor irrational.

Performing Operations:

15. Calculate: 5+35+3​.
16. Evaluate: 25−525​−5​.
17. Simplify: 322​3​.
18. If �x is a rational number and �y is an irrational number, what can you say about �−�x−y?
19. Solve: 3�=5x3​=5, for �x.
20. Evaluate: 8228​​.
21. Simplify: 3+133+3​1​.
22. If �x is a rational number and �y is an irrational number, what can you say about �⋅�x⋅y?
23. Calculate: (2+7)2(2+7​)2.
24. Simplify: 522323​52​​.
25. If �a is a rational number and �b is an irrational number, what can you say about �+�a+b?
26. Evaluate: 273327​​.
27. Simplify: 45−155​4​−5​1​.
28. If �p is a rational number and �q is an irrational number, what can you say about �⋅�p⋅q?

Properties and Proofs:

29. Prove that the sum of two rational numbers is rational.
30. Prove that the sum of a rational number and an irrational number is irrational.
31. Prove that the product of a non-zero rational number and an irrational number is irrational.
32. Prove that the product of two irrational numbers can be rational.
33. Prove that 2+32​+3​ is irrational.
34. Prove that 55​ is irrational.
35. Prove that if �n is an odd integer, then �2n2 is odd.
36. Prove that if �n is an even integer, then �2n2 is even.
37. Prove that if �n is an odd integer, then �+2n+2 is odd.
38. Prove that the square of an even number is even.

Application:

39. If �x is a rational number and �2=9x2=9, find the value of �x.
40. If �y is an irrational number and �2=16y2=16, find the value of �y.
41. If �a is a rational number and �a​ is irrational, what can you say about �a?
42. The sum of two irrational numbers is rational. Is this statement true or false? Justify.
43. Solve for �x: �2−5�+6=0x2−5x+6=0.
44. If 1�+1�=1�x1​+y1​=z1​, where �,�,x,y, and �z are positive integers, find the relationship between �,x, �,y, and �z.
45. If �a is rational and �b is irrational, which of �+�a+b and �−�a−b is rational? Explain.
46. If �p is rational and �q is irrational, which of �⋅�p⋅q and ��pq is irrational? Explain.
47. If �x is rational and �3=8x3=8, find the value of �x.
48. If �a is a rational number and �a​ is rational, what can you say about �a?
49. If �x is an irrational number and �2=49x2=49, find the value of �x.

Word Problems:

50. The sum of two irrational numbers is 4. Can their product be rational?
51. The sum of a rational number and an irrational number is 7. Can their product be rational?
52. If a square number is subtracted from a cube number, is the result necessarily irrational? Explain.
53. The sum of two rational numbers is 3 and their product is 2. Find the numbers.
54. The sum of an irrational number and its additive inverse is 0. What could the number be?
55. An irrational number is multiplied by 5, and the result is a rational number. What could the irrational number be?
56. The sum of an irrational number and a rational number is 8. Can their product be rational?
57. If �a is a rational number and �b is an irrational number, find the conditions under which �⋅�a⋅b is rational.
58. If �x is a rational number and �2=25x2=25, find the value of �x.
59. The sum of an irrational number and its square is 6. What could the irrational number be?

Critical Thinking:

60. Can the square of a rational number be negative? Explain.
61. Can an irrational number raised to an irrational power be rational? Provide an example or counterexample.
62. If �x and �y are both irrational, is �+�x+y always irrational? Justify.
63. If �a is irrational and �2a2 is rational, what can you conclude about �a?
64. Can the sum of a rational number and its additive inverse be irrational? Explain.
65. Can a non-zero rational number be raised to an irrational power and result in a rational number? Explain.
66. Is the product of two irrational numbers always irrational? Provide examples to support your answer.
67. Can the sum of three rational numbers be irrational? Explain.

Mixed Practice:

68. Simplify: 32−2232​−22​.
69. Solve for �x: �=7x​=7.
70. Simplify: 2366​23​​.
71. If �m is a rational number and �n is an irrational number, what can you say about �⋅�m⋅n?
72. Evaluate: 162216​​.
73. Solve for �x: �=19x​=91​.
74. Simplify: 1055​10​​.
75. Solve for �x: 2�2=182x2=18.
76. Simplify: 4+5−54+5​−5​.
77. If �p is rational and �q is irrational, which of �⋅�p⋅q and ��pq is rational? Explain.
78. Solve for �x: �2−25=0x2−25=0.
79. If �a is a rational number and �b is an irrational number, find the conditions under which �+�a+b is rational.
80. Evaluate: 3636​.
81. Solve for �x: �2=49x2=49.
82. If �x is an irrational number and �3=27x3=27, find the value of �x.
83. Simplify: 23+3223​+32​.
84. Solve for �x: �2−16=0x2−16=0.
85. If �a is a rational number and �b is an irrational number, find the conditions under which �⋅�a⋅b is rational.
86. Evaluate: 8181​.
87. Solve for �x: �=3x​=3.
88. Simplify: 12−2712​−27​.
89. If �x is a rational number and �2=16x2=16, find the value of �x.
90. Solve for �x: �2+9=0x2+9=0.

Note: This question set covers a wide range of topics related to real numbers in Chapter 1 of Class 10 Mathematics. Depending on the duration and depth of your lessons, you can choose appropriate questions to use in your teaching and assessment.

Polynomial Basics:

1. Define a polynomial.
2. Differentiate between a monomial, binomial, and trinomial.
3. Give an example of a non-polynomial expression.
4. Identify the degree and coefficient of the term 3x² in the polynomial 4x⁴ – 3x² + 7x – 2.
5. Determine whether each of the following is a polynomial: a) √(2x + 1), b) 5x^3 + 2/x, c) 2x – 3.
6. If P(x) = 3x³ – 2x² + 5x – 1, find P(2).

Classifying Polynomials:

7. Classify the polynomial 4x² + 5x³ – 2x + 7 as monomial, binomial, or trinomial.
8. Classify the polynomial 8 – 3x as constant, linear, quadratic, or cubic.
9. Write a polynomial of degree 4 with 5 terms.
10. Give an example of a cubic polynomial with exactly one term.
11. Express the polynomial 2x² + 3x + 1 as the sum of two binomials.

Polynomial Operations:

12. Add: (3x² + 4x + 5) + (2x² – 3x + 1).
13. Subtract: (5x³ + 2x² – 3x – 1) – (3x³ – x² + 2x + 4).
14. Multiply: (x + 2)(x – 3).
15. Multiply: (2x² + 3)(x + 4).
16. Divide 6x³ – 5x² + 3x – 1 by x – 2 using long division.
17. Find the remainder when 2x³ – 3x² + 5x – 1 is divided by x + 1.

Factorization:

18. Factorize: 6x² – 11x + 4.
19. Factorize: x³ + 8.
20. Factorize: 4x⁴ – 25y².
21. Factorize completely: 2x² – 18.
22. Write (x – 3) as a factor of the polynomial x³ – 9x² + 24x – 18.
23. Find the common factors of 3x² + 9x.

Synthetic Division:

24. Use synthetic division to divide 2x³ + 3x² – 4x – 5 by x + 2.
25. Divide 3x⁴ – 8x³ + 7x² + 5x – 10 by x – 1 using synthetic division.

Finding Zeros and Roots:

26. Find the zeros of the polynomial x² – 4x + 3.
27. Solve the equation x³ – 6x² + 9x = 0.
28. If α is a zero of the polynomial p(x) = x³ + 2x² – 5x + 6, find the value of p(α).

Application Problems:

29. The length of a rectangular field is 3x + 2 meters and the width is x + 5 meters. Find the area of the field in terms of x.
30. The perimeter of a square is given by P = 4x + 12. Find the side length of the square in terms of x.
31. The sum of two numbers is 10, and their product is 21. Write a quadratic equation that represents this situation.
32. The product of two consecutive integers is 306. Write an equation and solve it to find the two integers.

Word Problems:

33. The area of a rectangular garden is given by the polynomial 2x² + 7x – 15 square meters. Find the dimensions of the garden.
34. A polynomial has a degree of 3. How many zeros can it have at most?
35. If (x – 3) is a factor of x³ – px² + qx – 9, find the values of p and q.
36. The sum of the cubes of two consecutive integers is 35. Find the integers.

Long Answer Problems:

37. Factorize: 9x⁴ – 4y⁴.
38. Divide 2x³ + 5x² – 3x + 4 by x + 2 using the long division method.
39. If α and β are the zeros of the polynomial p(x) = x² – 4x + 3, find an equation whose roots are α + 1 and β + 1.
40. Find the zeros of the polynomial 2x³ – 3x² – 5x + 6 and verify the relationship between the zeros and coefficients.

Remember, these questions are designed to cover a broad range of topics related to the chapter “Polynomials.” You can modify them or create variations to suit your teaching approach and your students’ needs.

Type 1: Multiple Choice Questions (MCQs)

1. What is the primary purpose of solving a pair of linear equations in two variables? a) Finding the product of the variables b) Solving for a single variable c) Determining the point of intersection d) Graphing a straight line
2. Which method involves replacing one variable in terms of the other in a pair of linear equations? a) Substitution method b) Elimination method c) Graphical method d) Factorization method
3. How many solutions can a consistent pair of linear equations have? a) 0 b) 1 c) 2 d) Infinite
4. In which quadrant do two intersecting lines typically have their point of intersection? a) First quadrant b) Second quadrant c) Third quadrant d) Fourth quadrant
5. Which method is most suitable for solving a pair of equations when the coefficients are simple integers? a) Substitution method b) Elimination method c) Graphical method d) Matrix method

Type 2: Fill in the Blanks

6. A pair of equations that has at least one solution is called ______________.
7. The solution to a system of linear equations lies at the ______________ of the lines.
8. In the elimination method, we add or subtract equations to eliminate one ______________.
9. The graphical representation of a pair of equations can have ______________, no solution, or a unique solution.
10. In the substitution method, we substitute the value of one variable into the other equation to find the ______________.

Type 3: Short Answer Questions

11. Define a consistent pair of linear equations.
12. What is the point of intersection of two lines?
13. Explain the substitution method for solving a pair of linear equations.
14. Briefly describe the elimination method.
15. How can you identify an inconsistent pair of linear equations graphically?

Type 4: Long Answer Questions

16. Solve the pair of equations: 2x + 3y = 10 and 4x – y = 5 using the substitution method.
17. Show that the pair of equations 3x + 2y = 8 and 6x + 4y = 16 are dependent.
18. Solve the system of equations 2x – 3y = 7 and 4x – 6y = 14 using the elimination method.
19. Graph the pair of equations 3x + 2y = 6 and x – y = 2 on the same coordinate plane and find their point of intersection.
20. A sum of money is divided between two friends A and B in the ratio 5:7. If A gets ₹300 more than B, find the total amount.

Type 5: Application-Based Questions

21. Raj and Kamal together have 60 marbles. If Raj gives Kamal 15 marbles, they will have an equal number of marbles. Represent this situation using a pair of linear equations and solve it.
22. The ages of father and son add up to 45 years. The father’s age is four times the son’s age. Find their ages using a pair of equations.
23. A shopkeeper sells pencils and erasers. He sold 20 items for ₹180. If pencils cost ₹8 each and erasers cost ₹10 each, find the number of pencils and erasers sold.
24. The perimeter of a rectangle is 50 cm. If the length is 15 cm more than the breadth, find the dimensions of the rectangle.

Remember, this is just a sample set of questions. You can create variations based on these question types, increasing or decreasing the complexity as required. Additionally, consider the CBSE guidelines and the specific needs of your students while designing the question paper.

Type 1: Multiple Choice Questions (MCQs)

1. Which of the following is a quadratic equation? a) 3x + 5 = 0 b) x^2 – 4x + 7 = 0 c) 2x – 1 = 3x^2 d) 5x^3 + 2x^2 – x = 0
2. The solutions of the quadratic equation x^2 – 9 = 0 are: a) x = 3 b) x = -3 c) x = ±3 d) x = 9
3. The value of ‘a’ in the quadratic equation ax^2 + 6x + 9 = 0 is: a) 0 b) 1 c) 6 d) 9

Type 2: Fill in the Blanks

4. The process of finding the factors of a quadratic expression is called ___________.
5. The standard form of a quadratic equation is ___________.

Type 3: True or False

6. A quadratic equation can have more than two solutions. (True/False)
7. The sum of the solutions of a quadratic equation ax^2 + bx + c = 0 is -b/a. (True/False)

Type 4: Short Answer Questions

8. Define a quadratic equation.
9. State the Zero Factor Property.
10. Solve the quadratic equation x^2 – 5x + 6 = 0.

Type 5: Long Answer Questions

11. Explain the process of completing the square to solve a quadratic equation.
12. Compare and contrast the methods of factorization and the quadratic formula for solving quadratic equations.

Type 6: Application-Based Questions

13. A ball is thrown vertically upwards from the ground level. The height (in meters) of the ball after ‘t’ seconds is given by the equation h = 15t – 5t^2. Find the time it takes for the ball to reach the highest point.
14. The area of a rectangular garden is 72 square meters. If the length of the garden is 4 meters more than its width, find the dimensions of the garden.

Type 7: Higher-Order Thinking Questions

15. Solve the equation 2x^2 – 5x + 3 = 0 by using the quadratic formula.
16. Prove that the product of the roots of the quadratic equation ax^2 + bx + c = 0 is c/a.

Remember to mix and match these question types to create a well-rounded question set that covers various aspects of the chapter. Additionally, feel free to adjust the complexity of the questions based on the proficiency level of your students.

Type 1: Identification and Terminology

1. Define an arithmetic progression (AP).
2. In an AP, what is the common difference?
3. Identify the first term, common difference, and 5th term of the AP: 2, 5, 8, …
4. Determine whether the following sequence is an AP: 3, 7, 11, 15, …
5. Find the 20th term of the AP if the first term is 10 and the common difference is 3.

Type 2: Finding the nth Term

6. Find the 12th term of the AP: 3, 7, 11, 15, …
7. If the 6th term of an AP is 29 and the common difference is 4, find the first term.
8. The 3rd term of an AP is 21 and the 7th term is 37. Find the common difference.
9. The 10th term of an AP is 62 and the common difference is 3. Find the first term.
10. If the nth term of an AP is 2n – 1, find the 15th term.

Type 3: Finding Sum of First n Terms

11. Find the sum of the first 15 terms of the AP: 7, 12, 17, …
12. The sum of the first 20 terms of an AP is 450. If the common difference is 5, find the first term.
13. The sum of the first 10 terms of an AP is 105 and the common difference is 4. Find the first term.
14. If the sum of the first 25 terms of an AP is 625 and the common difference is 2, find the first term.
15. Find the sum of the first 30 terms of an AP if the first term is 10 and the common difference is 3.

Type 4: Word Problems

16. A ladder is placed such that its top reaches a window 17 feet above the ground. The ladder makes an angle of 60° with the ground. How far is the bottom of the ladder from the wall?
17. The first term of an AP is 5, and the common difference is 3. Find the 25th term.
18. The sum of the first ‘n’ terms of an AP is 315. If the common difference is 4 and the first term is 7, find ‘n’.
19. The first term of an AP is 12, and the common difference is 2. Find the sum of the first 18 terms.
20. The sum of the first 12 terms of an AP is 156, and the common difference is 4. Find the first term.

Type 5: Applications

21. A car’s odometer reads 75321 km, and the trip meter shows 158 km. Find the number of trips made assuming each trip is of equal distance.
22. An arithmetic sequence has a first term of 10 and a common difference of 3. Find the 50th term.
23. The ages of three siblings form an arithmetic sequence. If the middle child is 14 years old, and the common difference is 3, find the ages of the other two siblings.
24. A football team scored 120 goals in a season. The number of goals scored in each match forms an AP, with the first match recording 2 goals and each subsequent match increasing by 3 goals. How many matches were played?
25. A ladder is placed against a wall. The distance between the ladder’s foot and the wall decreases by 5 cm with each step the ladder takes. If the ladder’s foot covers 24 steps, find the initial distance between the ladder’s foot and the wall.

These questions cover a wide range of concepts and problem-solving approaches in the “Arithmetic Progressions” chapter. You can use these as a foundation and modify them to create additional questions for practice and assessment.

Multiple Choice Questions:

1. Which of the following is NOT a type of triangle? a) Equilateral b) Isosceles c) Rectangular d) Scalene
2. An equilateral triangle has ___________ equal angles. a) Three b) Two c) Four d) One
3. In an isosceles triangle, the angles opposite to the equal sides are ___________. a) Acute angles b) Obtuse angles c) Right angles d) Congruent angles
4. A triangle with one angle greater than 90 degrees is called ___________. a) Acute triangle b) Obtuse triangle c) Equilateral triangle d) Isosceles triangle
5. The sum of the angles in any triangle is always ___________ degrees. a) 90 b) 180 c) 270 d) 360

Fill in the Blanks:

6. In an isosceles triangle, the two equal sides are called ___________.
7. A triangle with all sides of different lengths is called a ___________ triangle.
8. The longest side of a right-angled triangle is called the ___________.
9. The angles of a triangle are named as ___________, ___________, and ___________.
10. In a right triangle, the side opposite the right angle is called the ___________.

True or False:

11. An equilateral triangle can also be an obtuse triangle. (True/False)
12. The hypotenuse is always the longest side of a triangle. (True/False)
13. An isosceles triangle can have all angles equal. (True/False)
14. The sum of any two sides of a triangle is always greater than the third side. (True/False)
15. A triangle can have more than one obtuse angle. (True/False)

Short Answer Questions:

16. State the Pythagoras theorem.
17. If one angle of a triangle is 60 degrees, what are the possible measures of the other two angles?
18. If two sides of a triangle are equal, what can you say about the angles opposite those sides?
19. Determine the type of triangle if its angles measure 45°, 45°, and 90°.
20. If the angles of a triangle are in the ratio 2:3:5, find the measures of the angles.

Problem-Solving Questions:

21. In a triangle ABC, if ∠A = 50° and ∠B = 70°, find the measure of ∠C.
22. The sides of a triangle are in the ratio 3:4:5. If the perimeter is 72 cm, find the lengths of the sides.
23. In a right triangle, the length of one leg is 8 cm and the hypotenuse is 17 cm. Find the length of the other leg.
24. An isosceles triangle has a base of 10 cm and the unequal side is 12 cm. Find the length of the equal sides.
25. The angles of a triangle are in the ratio 5:4:7. Find the measure of each angle.

Remember, these are just sample questions. You can modify and expand upon them to create a complete question set. Also, ensure that the questions match the difficulty level and format expected in CBSE Class 10 exams.

Knowledge and Understanding:

1. Define coordinate geometry.
2. What are the two perpendicular lines that form the coordinate plane?
3. State the significance of the x-axis and y-axis.
4. Explain what an ordered pair represents in coordinate geometry.
5. Differentiate between the x-coordinate and y-coordinate of a point.
6. Define the origin in the coordinate plane.
7. State the coordinates of the origin.
8. What do you understand by the first quadrant? How are its coordinates represented?
9. Explain the concept of the distance between two points on the coordinate plane.
10. What is the midpoint of a line segment? How is it calculated?

Application and Analysis:

11. Plot the points A(3, 4), B(-2, 5), C(0, -1) on the coordinate plane.
12. If the coordinates of a point are (5, -3), in which quadrant does the point lie?
13. Calculate the distance between the points P(2, 5) and Q(-3, -2).
14. Given A(1, 2) and B(5, 6), find the coordinates of the midpoint of the line segment AB.
15. Determine the coordinates of the point that divides the line segment joining (4, -1) and (-2, 3) in the ratio 3:2.
16. Find the coordinates of a point on the x-axis that is equidistant from (-3, 4) and (5, 4).
17. If the midpoint of a line segment AB with coordinates A(2, -1) and B(x, 4) is (1, 1), find the value of x.
18. A point P divides the line segment AB in the ratio 2:3. If A has coordinates (-2, 1) and B has coordinates (3, -4), find the coordinates of point P.
19. The length of a line segment AB is 10 units. If the coordinates of A are (3, -2) and B are (x, 5), find the value of x.
20. If the coordinates of two points A and B are (p, q) and (r, s) respectively, show that the mid-point of AB is [(p+r)/2, (q+s)/2].

Application and Comprehension:

21. Plot the points P(3, -2), Q(-1, 4), and R(6, 0) on the coordinate plane. In which quadrant do these points lie?
22. Given A(2, -5) and B(2, 3), find the distance between the two points.
23. The coordinates of the midpoint of a line segment AB are (-1, 2). If the coordinates of A are (-5, 3), find the coordinates of B.
24. Determine the midpoint of the line segment joining (1, -2) and (3, 4).
25. If A has coordinates (-2, 3) and B has coordinates (4, 1), calculate the distance AB.
26. In which quadrant does the point (0, -7) lie? Explain.
27. Find the coordinates of a point on the y-axis that is equidistant from (-3, 2) and (3, 2).
28. If the coordinates of a point P are (x, -3) and the coordinates of its midpoint Q are (1, -3), find the value of x.
29. Show that the points (2, -1), (5, 2), and (8, 5) are collinear.
30. Calculate the coordinates of a point P which divides the line segment joining (-3, 4) and (5, -2) in the ratio 2:3.

Application and Evaluation:

31. Given A(2, -3) and B(-5, 1), find the coordinates of the point that divides AB in the ratio 3:2.
32. Find the distance between the points A(-1, 4) and B(3, -2).
33. If the midpoint of the line segment joining (x, 2) and (4, -3) is (2, -1), determine the value of x.
34. A point P divides the line segment AB in the ratio 5:3. If A has coordinates (1, -4) and B has coordinates (7, 2), calculate the coordinates of point P.
35. Given A(3, 1) and B(7, -2), find the coordinates of the midpoint of AB.
36. The coordinates of the midpoint of a line segment PQ are (3, -2). If the coordinates of P are (-1, 1), determine the coordinates of Q.
37. Calculate the coordinates of a point that divides the line segment joining (-4, 3) and (6, -5) in the ratio 1:2.
38. If A(2, 3) and B(5, -2), determine the length of AB.
39. The length of a line segment AB is 12 units. If A has coordinates (1, 2) and B has coordinates (-3, y), find the value of y.
40. Show that the points (1, -2), (-2, 0), and (-5, 2) are collinear.

Synthesis and Evaluation:

41. Given A(2, 5) and B(7, -3), find the coordinates of the point that divides AB in the ratio 4:3 externally.
42. Calculate the distance between the points P(-2, 3) and Q(5, -4).
43. Determine the midpoint of the line segment joining (x, -1) and (3, 2). If the midpoint is (1, 0), find the value of x.
44. A point P divides the line segment AB in the ratio 2:7. If A has coordinates (-3, 4) and B has coordinates (6, -8), calculate the coordinates of point P.
45. Given A(4, -1) and B(1, 3), find the coordinates of the midpoint of AB.
46. The coordinates of the midpoint of a line segment MN are (-2, 3). If the coordinates of M are (1, -2), determine the coordinates of N.
47. Calculate the coordinates of a point that divides the line segment joining (-6, 4) and (8, -5) in the ratio 3:1.
48. If A(3, -2) and B(6, 5), determine the length of AB.
49. The length of a line segment AB is 15 units. If A has coordinates (2, 1) and B has coordinates (7, y), find the value of y.
50. Show that the points (0, -3), (3, -1), and (6, 1) are collinear.

Multiple Choice Questions (MCQs):

1. What is the significance of the x-coordinate in a point on the coordinate plane? a) It represents the distance from the y-axis. b) It represents the distance from the x-axis. c) It determines the quadrant in which the point lies. d) It has no significance.
2. The midpoint of a line segment with endpoints (3, 4) and (-1, 6) is: a) (1, 10) b) (2, 5) c) (2, 10) d) (4, 5)
3. The distance between points (2, 3) and (5, 8) is: a) √18 b) √20 c) √29 d) √34
4. If the point (4, y) lies on the x-axis, what is the value of y? a) 0 b) 4 c) -4 d) 1
5. Which quadrant contains points with positive x and negative y values? a) I b) II c) III d) IV

Fill in the Blanks:

6. The y-coordinate of a point is its distance from the _______.
7. The coordinates of the origin are _______.
8. The midpoint formula is [(x1 + x2)/2, _______].
9. The distance between points A(x1, y1) and B(x2, y2) is given by _______.
10. A point on the x-axis has a y-coordinate of _______.

True or False:

11. The x-coordinate of a point tells us how far the point is from the y-axis.
12. The coordinates of the origin are (0, 1).
13. The distance between two points can be negative.
14. The point (5, 3) lies in the second quadrant.
15. The x-coordinate of the midpoint of a line segment is the average of the x-coordinates of its endpoints.

Matching:

16. Match the quadrant with its description: a) First Quadrant i) Negative x and y values b) Second Quadrant ii) Positive x and y values c) Third Quadrant iii) Positive x and negative y values d) Fourth Quadrant iv) Negative x and positive y values

Short Answer Questions:

17. Explain the concept of a coordinate plane.
18. How do you find the distance between two points using the distance formula?
19. State the midpoint formula for a line segment with endpoints (x1, y1) and (x2, y2).
20. If the midpoint of a line segment is (3, 5) and one endpoint is (1, 2), what are the coordinates of the other endpoint?

Long Answer Questions:

21. Plot the points A(2, 3), B(5, -1), and C(-3, 4) on a coordinate plane. Calculate the lengths of AB and AC.
22. Show that the points (-2, 3), (1, 6), and (4, 9) are collinear.
23. Explain the concept of symmetry in the coordinate plane with suitable examples.
24. A line segment AB has endpoints A(-1, 2) and B(3, 6). Find the coordinates of the midpoint M of AB.
25. Prove that the points (x, y), (-y, -x), (-x, -y), and (y, x) are vertices of a rectangle.

Remember to adjust the difficulty level of questions according to the students’ proficiency. You can create more questions by modifying these examples and generating new scenarios related to the content of Chapter 7, “Coordinate Geometry.”

Type 1: Definitions and Concepts

1. Define sine, cosine, and tangent ratios.
2. What is the hypotenuse of a right triangle?
3. Explain the term ‘opposite side’ in a right triangle.
4. Differentiate between adjacent and opposite sides.
5. Define the term ‘angle of elevation.’

Type 2: Calculating Trigonometric Ratios 6. Calculate the sine of an angle in a right triangle given the lengths of the sides.

7. Find the cosine of an angle when the lengths of the sides are given.
8. If the tangent of an angle is 0.6, calculate the angle.
9. Given the hypotenuse and an acute angle, find the length of the opposite side.

Type 3: Applying Trigonometry in Real Life 10. A building casts a shadow of 25 meters when the angle of elevation of the sun is 30 degrees. Calculate the height of the building.

11. A ladder of length 10 meters makes an angle of 60 degrees with the ground when leaning against a wall. Calculate how high the ladder reaches on the wall.
12. An airplane is flying at an altitude of 10,000 meters. If the angle of depression to a city on the ground is 45 degrees, how far is the city from the airplane horizontally?

Type 4: Problem Solving 13. In a right triangle, the hypotenuse is 13 cm and one acute angle is 45 degrees. Calculate the lengths of the other two sides.

14. Given an angle of 30 degrees and the adjacent side as 8 cm, find the hypotenuse.
15. If the length of the opposite side is 15 cm and the hypotenuse is 17 cm, calculate the sine of the angle.
16. Solve for x: sin(x) = 0.5, where x is an acute angle.

Type 5: Word Problems Involving Trigonometric Ratios 17. A flagpole casts a shadow of 20 meters. If the angle of elevation of the sun is 60 degrees, find the height of the flagpole.

18. From the top of a lighthouse, an observer spots a boat at an angle of depression of 45 degrees. If the lighthouse is 100 meters tall, how far is the boat from the lighthouse?
19. An inclined plane has an angle of elevation of 20 degrees. If a box is being pulled up the plane and the vertical height it covers is 10 meters, calculate the distance along the plane.

Type 6: Multiple Choice Questions (MCQs) 20. In a right triangle, the length of the hypotenuse is always: a) Equal to the sum of the other two sides b) Equal to the difference of the other two sides c) Greater than the other two sides combined d) Smaller than the other two sides combined

21. The value of cos(90 degrees) is: a) 0 b) 1 c) -1 d) Undefined
22. If the tangent of an angle is 1.5, the angle is approximately: a) 30 degrees b) 45 degrees c) 60 degrees d) 75 degrees

Type 7: Practical Application 23. Visit a nearby location with elevation differences and calculate the height of an object using trigonometry.

24. Measure the length of your classroom, and then use trigonometry to calculate the height of a wall given an angle of elevation.

Remember to create questions of varying difficulty levels and encourage students to explain their reasoning when solving problems. This will help them develop a deeper understanding of the concepts.

Type 1: Finding Heights and Distances

1. If a ladder of 15 meters is leaning against a wall and makes an angle of 60° with the ground, find the distance of the ladder’s base from the wall.
2. A person on a 10-meter-high building observes a car at a 30° angle of elevation. Calculate the distance of the car from the building’s base.
3. A kite flying at an angle of elevation of 45° is attached to a string of 100 meters. Find the height at which the kite is flying.
4. A building casts a shadow of 20 meters when the angle of elevation of the sun is 60°. Determine the height of the building.
5. From the top of a 40-meter-high tower, the angle of depression to a point on the ground is 45°. Find the distance of that point from the tower’s base.

Type 2: Applications in Navigation

6. An airplane flies at an altitude of 10,000 meters. If the angle of depression to a point on the ground is 20°, find the distance of the airplane from that point.

7. A ship is located 15 kilometers away from a port. If the angle of elevation to the top of a lighthouse on the port is 10°, calculate the height of the lighthouse.
8. A man in a hot air balloon spots a landmark on the ground at an angle of depression of 30°. If the balloon is at a height of 500 meters, find the distance between the balloon and the landmark.
9. An observer in a control tower sees a plane at an angle of elevation of 25°. If the tower is 150 meters tall, how far is the plane from the tower?
10. A surveyor measures two sides of a triangular field. The angles of elevation from the ends of these sides to a point in the field are 45° and 60°. Find the distance between the two ends of the measured sides.

Type 3: Word Problems Involving Trigonometric Ratios

11. In a triangle, if the angle is 40° and the side opposite to it is 8 cm, find the length of the hypotenuse.

12. If the hypotenuse of a right-angled triangle is 13 cm and one of the angles is 30°, calculate the lengths of the other two sides.
13. A ladder of length 12 meters makes an angle of 75° with the ground. Find how high the ladder reaches on the wall.
14. If the height of a tower is 25 meters and the angle of elevation of its top from a point on the ground is 60°, find the distance of that point from the tower.
15. The length of the shadow of a tree is 15 meters when the angle of elevation of the sun is 45°. Calculate the height of the tree.

Type 4: Applications in Architecture

16. An architect needs to determine the length of a diagonal beam in a roof. If the height of the roof is 6 meters and the angle of elevation is 30°, find the length of the beam.

17. In a triangular window, one angle is 45° and the adjacent side is 8 feet long. Calculate the length of the hypotenuse.
18. A flagpole casts a shadow of 16 meters when the angle of elevation of the sun is 30°. Find the height of the flagpole.
19. An inclined road has an angle of inclination of 15°. If the road covers a vertical height of 100 meters, find the distance covered along the road.
20. A pyramid is 20 meters tall and has a square base. Calculate the slant height of the pyramid if the angle of elevation from a point on the ground to its top is 60°.

Type 5: Complex Applications and Problem Solving

21. A watchtower is situated on a hill. From the base of the hill, the angle of elevation to the top of the tower is 45°. If the hill is 300 meters high, find the height of the tower.

22. A man standing on the deck of a ship observes the top of a lighthouse at an angle of elevation of 12°. If the height of the lighthouse is 60 meters, find the distance between the ship and the lighthouse.
23. A bridge over a river makes an angle of 60° with the riverbanks. If the bridge is 40 meters long, calculate the width of the river.
24. An airplane at an altitude of 2,000 meters observes two points on the ground directly below it. The angles of depression to the points are 30° and 45°. Find the distance between the points.
25. A ladder leans against a wall. The foot of the ladder is 9 meters away from the wall. If the ladder makes an angle of 75° with the ground, find the length of the ladder.

Type 6: Constructing Problems

26. Construct a right-angled triangle ABC, where ∠A = 30° and AC = 10 cm.

27. Construct a triangle DEF in which ∠D = 45°, DE = 6 cm, and EF = 8 cm.
28. Construct a triangle XYZ, given ∠X = 60°, XY = 5 cm, and YZ = 7 cm.
29. Construct a triangle PQR, where ∠P = 75° and PQ = 9 cm.
30. Construct a triangle LMN, given ∠L = 90°, LN = 12 cm, and MN = 15 cm.

Type 7: Problem Solving with Ambiguous Case 31. A triangle has an angle of 70° and two sides of length 8 cm and 12 cm. Determine the possible values for the third side and the other two angles.

32. Given a triangle with angles 40°, 70°, and a side of length 12 cm, find the possible lengths of the other sides.
33. In a triangle with angles 50° and 80°, one side is 15 cm. Find the possible values for the other sides and angles.
34. A triangle has an angle of 100° and two sides of length 10 cm and 15 cm. Determine the possible values for the third side and the other two angles.
35. Given a triangle with angles 35° and 85° and a side of length 20 cm, find the possible lengths of the other sides.

Type 8: Revision and Mixed Problems

36. If the angle of elevation of the sun is 30°, find the length of the shadow cast by a pole of height 10 meters.

37. A 20-meter-long ladder is placed against a wall, making an angle of 75° with the ground. Calculate the distance of the foot of the ladder from the wall.
38. From the top of a tower 80 meters high, a stone is dropped. Calculate the time it takes for the stone to reach the ground.
39. A tree casts a shadow of 24 meters when the angle of elevation of the sun is 60°. Find the height of the tree.
40. A boy on a 30-meter-high building observes a car at an angle of depression of 45°. Calculate the distance of the car from the building.

Type 9: Higher Order Thinking Questions

41. In a right-angled triangle, one acute angle is 35°. If the hypotenuse is 13 cm, find the lengths of the other two sides.

42. The length of the hypotenuse of a right-angled triangle is 17 cm. If one of the angles is 75°, calculate the lengths of the other two sides.
43. A ladder 25 meters long makes an angle of 45° with the ground. Find the distance from the top of the ladder to the wall.
44. From the top of a building 120 meters high, the angle of depression to the bottom of a tower is 30°. Calculate the height of the tower.
45. A building casts a shadow of 40 meters when the angle of elevation of the sun is 30°. Calculate the height of the building.

Type 10: Practical Applications and Real-World Scenarios

46. A helicopter is flying at an altitude of 500 meters. If the angle of depression to a target on the ground is 25°, find the distance between the helicopter and the target.

47. A tree leans at an angle of 60° with the ground. If its top touches the ground 15 meters away from its base, calculate the height of the tree.
48. A car moving on a straight road covers a distance of 500 meters. If the angle of elevation of the car changes from 5° to 20°, find the difference in the heights of the car.
49. An engineer needs to design a ramp for a truck to climb. If the truck needs to ascend to a height of 2 meters at an angle of 10°, determine the length of the ramp.
50. An observer at the top of a lighthouse sees a ship approaching the shore. The angle of depression to the ship changes from 30° to 60° as the ship gets closer. If the height of the lighthouse is 50 meters, find the distance between the ship and the lighthouse at the two different angles.

Type 11: Trigonometric Identities in Application

51. If cos θ = 5/13 and θ is an acute angle, find sin θ and tan θ.

52. Given that sec α = 17/8 and α is an acute angle, calculate cos α and cot α.
53. If tan β = 3/4 and β is an acute angle, determine sin β and sec β.
54. If cot γ = 7/24 and γ is an acute angle, find sin γ and cos γ.
55. Given that sin δ = 15/17 and δ is an acute angle, calculate cos δ and tan δ.

Type 12: Problem Solving with Trigonometric Identities

56. If cos θ = 12/13, find the values of sin θ, tan θ, sec θ, and cot θ.

57. If tan α = 24/7, determine the values of sin α, cos α, sec α, and cot α.
58. Given that sec β = 25/24, find the values of sin β, cos β, tan β, and cot β.
59. If cot γ = 7/24, calculate the values of sin γ, cos γ, tan γ, and sec γ.
60. If sin δ = 5/13, determine the values of cos δ, tan δ, sec δ, and cot δ.

Type 13: Problem Solving with Trigonometric Equations

61. Solve the equation 2sin x = 1 for 0° ≤ x ≤ 180°.

62. Solve the equation 3cos y = -1 for 0° ≤ y ≤ 360°.
63. Solve the equation 4tan z = -2 for 0° ≤ z ≤ 360°.
64. Solve the equation 5cot w = -4 for 0° ≤ w ≤ 180°.
65. Solve the equation 6sec t = -3 for 0° ≤ t ≤ 360°.

Type 14: Mixed Practice and Application

66. A ladder 18 meters long leans against a wall. If the angle of elevation is 60°, find the height the ladder reaches on the wall.

67. An airplane is flying at an altitude of 3,000 meters. If the angle of depression to a city on the ground is 45°, find the distance of the airplane from the city.
68. From a 15-meter-high building, the angle of elevation to the top of a tower is 30°. If the tower is further away from the building, find the height of the tower.
69. An archer aims at a target 40 meters away. If the arrow hits the target at an angle of 20°, find the height at which the arrow was aimed.
70. A ladder 10 meters long is resting against a wall. If the ladder makes an angle of 30° with the ground, find the distance of the foot of the ladder from the wall.

Type 15: Advanced Problem Solving and Analytical Thinking

71. An observer 100 meters above the level of a lake sees a boat approaching at an angle of depression of 15°. If the observer’s line of sight makes an angle of 45° with the lake’s surface, find the distance between the observer and the boat.

72. A pole is broken and the top touches the ground at a distance of 8 meters from the base. If the angle of elevation of the top is 60°, find the original height of the pole.
73. A staircase is such that its angle of inclination with the horizontal is 30°. If a person climbs 20 steps of the staircase, each 15 cm high, find the distance covered and the height gained.
74. A tower subtends an angle of 30° at a point on the ground. At a certain point, the angle of elevation to the top of the tower is 60°. Calculate the ratio of the tower’s height to the distance between the two points.
75. An airplane flying at an altitude of 5,000 meters has to cover a horizontal distance of 10,000 meters. Find the angle of depression that the line of sight from the airplane to the destination point makes with the horizontal.

Type 16: Complex Applications and Composite Figures

76. A ladder rests against a wall and touches the top of a box placed 5 meters from the wall. If the ladder makes an angle of 45° with the ground, find the length of the ladder.

77. A tree casts a shadow of 30 meters when the angle of elevation of the sun is 60°. At the same time, a pole casts a shadow of 20 meters. Determine the height of the tree and the pole.
78. A kite flying at an angle of elevation of 40° has a string 100 meters long. Find the height at which the kite is flying and the distance of the kite from the person holding the string.
79. A bridge across a river makes an angle of 60° with the riverbanks. If the bridge is 80 meters long, find the width of the river and the length of the diagonal of the parallelogram-shaped water body formed by the bridge and the riverbanks.
80. A 12-meter-long ladder is leaning against a wall in a garage. The garage’s roof and the ground form a right-angled triangle with the ladder. If the roof is 9 meters high, find the distance between the foot of the ladder and the wall.

Type 17: Mixed Problem Solving and Word Problems

81. A tree casts a shadow of 25 meters when the angle of elevation of the sun is 45°. Calculate the height of the tree.

82. A boy on a 15-meter-high building observes a car at an angle of depression of 30°. Find the distance of the car from the building.
83. A ladder of 10 meters is placed against a wall, making an angle of 60° with the ground. Determine the distance of the ladder’s base from the wall.
84. An observer at the top of a tower sees a boat at an angle of depression of 20°. If the tower is 50 meters high, find the distance between the observer and the boat.
85. From a 20-meter-high building, the angle of elevation to the top of a tower is 60°. If the tower is further away from the building, find the height of the tower.

Type 18: Problem Solving with Complex Figures

86. A ladder leans against a wall and makes an angle of 70° with the ground. If the ladder reaches a window 4 meters above the ground, find the length of the ladder.

87. A kite is flying at an angle of elevation of 60°. The length of the string is 150 meters. Calculate the height at which the kite is flying.
88. A 25-meter-high flagpole casts a shadow of 20 meters. Determine the angle of elevation of the sun.
89. A tree casts a shadow of 12 meters when the angle of elevation of the sun is 30°. Find the height of the tree.
90. A building casts a shadow of 40 meters when the angle of elevation of the sun is 60°. Calculate the height of the building.

Remember, the questions provided above cover various types of problems and applications related to the chapter “Some Applications of Trigonometry.” You can adjust the complexity of the questions based on your students’ understanding and the level of difficulty you want to introduce.

Multiple Choice Questions (MCQs):

1. What is the ratio of the circumference of a circle to its diameter? a) π b) 2π c) ½π d) π/2
2. Which of the following is the formula for the circumference of a circle? a) C = πr b) C = r² c) C = 2πr d) C = π/d
3. What is the diameter of a circle if its radius is 7 cm? a) 7 cm b) 14 cm c) 21 cm d) 28 cm
4. If the radius of a circle is 10 cm, what is its circumference? a) 20π cm b) 10π cm c) 30π cm d) 40π cm
5. What is the formula for the area of a circle? a) A = πd b) A = 2πr c) A = πr² d) A = r²
6. If the radius of a circle is 6 cm, what is its area? a) 12π cm² b) 36π cm² c) 72π cm² d) 18π cm²
7. What is the relationship between the radius and diameter of a circle? a) Diameter = 2 × Radius b) Diameter = Radius c) Diameter = Radius/2 d) Diameter = 3 × Radius
8. The circumference of a circle is 44 cm. What is its radius? a) 7 cm b) 11 cm c) 14 cm d) 22 cm
9. What is the area of a circle with a diameter of 12 cm? a) 6π cm² b) 36π cm² c) 72π cm² d) 144π cm²
10. The ratio of the circumference of two circles is 3:5. What is the ratio of their radii? a) 3:5 b) 5:3 c) 6:10 d) 10:6

Short Answer Questions:

11. Define a circle.
12. State the formula for calculating the circumference of a circle.
13. If the diameter of a circle is 14 cm, what is its radius?
14. Calculate the circumference of a circle with a radius of 9 cm.
15. What is the formula for calculating the area of a circle?
16. If the circumference of a circle is 44 cm, what is its diameter?
17. Calculate the area of a circle with a diameter of 10 cm.
18. Differentiate between the radius and diameter of a circle.
19. If the area of a circle is 154 cm², what is its radius?
20. Two circles have radii in the ratio 2:3. If the first circle has a circumference of 18.84 cm, find the circumference of the second circle.

Application-Based Problems:

21. A circular garden has a diameter of 28 m. Find its area.
22. A wheel has a circumference of 132 cm. Calculate its radius.
23. A circular race track has a circumference of 440 m. What is its diameter?
24. The area of a circular playground is 616 m². Calculate its radius.
25. The wheel of a bicycle makes 500 revolutions in moving 5 km. Find the diameter of the wheel.
26. A circular plot has an area of 616 m². What is its circumference?
27. The diameter of a circular pond is 14 m. Find the length of the string required to fence it around.
28. The circumference of a circular path is 88 m. Calculate its width if the path is 4 m wide.
29. The wheel of a car covers a distance of 2640 m in 15 minutes. If the radius of the wheel is 35 cm, find the number of revolutions made by the wheel.
30. The radius of a circular garden is 21 m. Find its area and the length of the fence required to enclose it.

Remember, these questions are intended to cover a range of topics and difficulty levels related to the chapter “Circles” in Class 10 Mathematics. You can use these questions for assessments, practice tests, or in-class discussions to reinforce the concepts taught in the chapter.

Concept: Area of a Circle (Using the formula A = πr^2)

1. Find the area of a circle with radius 7 cm.
2. If the area of a circle is 154 cm², find its radius.
3. The diameter of a circular garden is 14 m. Calculate its area.
4. The radius of a circle is 10.5 cm. Determine its area.
5. A circular table has a diameter of 1.2 m. What is its area?

Concept: Area of a Sector (Using the formula A = (θ/360)πr^2)

6. Calculate the area of a sector with radius 9 cm and central angle 60°.
7. If the radius of a sector is 5 cm and the area is 15π cm², find the central angle.
8. A sector of a circle has a central angle of 120° and area 48π cm². Find the radius.
9. What is the area of a sector with radius 6 cm and angle 45°?
10. A circular clock has a radius of 7 cm. Calculate the area of the sector representing 15 minutes.

Concept: Area of Segment (A = A of sector – A of triangle)

11. Find the area of a segment with radius 8 cm and central angle 90°.
12. In a circle with radius 10 cm, the central angle of a segment is 120°. Calculate the area of the segment.
13. A segment of a circle has a central angle of 60° and the radius is 5 cm. Determine its area.
14. Calculate the area of the shaded region in the figure, given that the radius is 12 cm and the angle is 75°.
15. A segment of a circle has an area of 16π cm². If the radius is 4 cm, find the central angle.

Concept: Mixed Questions and Real-life Applications

16. A circular garden has a circumference of 44 m. Calculate its radius and area.
17. Find the area of a circle which has the same circumference as a square with a side length of 8 cm.
18. The wheel of a bicycle has a diameter of 70 cm. Find its area of contact with the ground.
19. The minute hand of a clock is 10 cm long. Find the area swept by the minute hand in 20 minutes.
20. A circular track has a radius of 35 m. If a person covers one complete round, find the distance covered.

Concept: Word Problems and Problem-solving

21. The diameter of a circular field is 56 m. Find the cost of fencing it at ₹5 per meter.
22. A circular garden with a radius of 21 m is surrounded by a path of a width 7 m. Find the area of the path.
23. A sector of a circle has a radius of 9 cm and an area of 54π cm². Find the central angle and perimeter of the sector.
24. The area of a sector is 38.5 cm² and the radius is 7 cm. Find the central angle of the sector.
25. In a circular pond, the central angle of a sector is 72° and the area is 16π cm². Calculate the radius.

These are just 25 sample questions. You can create similar questions covering various aspects of the chapter, including calculating areas, central angles, radii, perimeters, and solving real-life problems. Additionally, you can vary the difficulty levels to challenge the students and cater to different learning abilities.

Multiple Choice Questions (MCQs):

1. The surface area of a cube with side length 5 cm is: a) 125 cm² b) 150 cm² c) 100 cm² d) 250 cm²
2. The volume of a cylinder with radius 7 cm and height 10 cm is: a) 1540 cm³ b) 1070 cm³ c) 220 cm³ d) 770 cm³
3. The curved surface area of a cone with radius 6 cm and slant height 10 cm is: a) 60 cm² b) 120 cm² c) 180 cm² d) 90 cm²
4. The surface area of a sphere with radius 4 cm is: a) 64π cm² b) 16π cm² c) 32π cm² d) 8π cm²

Fill in the Blanks:

5. The formula for the volume of a cuboid is ______.
6. The lateral surface area of a cylinder is also called its ______.
7. The volume of a cone with radius r and height h is (1/3)πr²h, which is (equal/greater/lesser) than the volume of a cylinder with the same dimensions.

True or False:

8. The base area of a cylinder and a cone with the same radius and height will be the same. (True/False)
9. The diagonal of a cube is the same as its edge length. (True/False)
10. The volume of a sphere is (4/3)πr³ where r is the radius. (True/False)

Short Answer Questions:

11. Explain the difference between the lateral surface area and the total surface area of a cylinder.
12. A rectangular tank has length 10 cm, width 6 cm, and height 8 cm. Calculate its volume and surface area.
13. How does increasing the radius of a cone affect its volume and curved surface area?

Long Answer Questions:

14. A cube has a surface area of 150 cm². Find its volume.
15. A cylindrical water tank has a diameter of 14 cm and a height of 21 cm. Calculate its volume and the total cost to paint the inner and outer surfaces at the rate of ₹5 per cm².

Word Problems:

16. A gift box in the shape of a cube has an edge length of 12 cm. Calculate its volume and the amount of wrapping paper needed to cover its entire surface.
17. A cylindrical container has a radius of 5 cm and a height of 18 cm. If it is filled with water, find the volume of water needed to fill it.

Remember, the above questions are just a sample set. You can mix and match question types and levels of difficulty to create a comprehensive question bank for your chapter on Surface Areas and Volumes in accordance with CBSE standards.

1. Multiple Choice Questions:

1. What is the term for a complete collection of all elements under study? a) Sample b) Mean c) Population d) Mode
2. Which measure of central tendency is most affected by extreme values? a) Mean b) Median c) Mode d) Range
3. The sum of all observations divided by the number of observations gives: a) Mode b) Median c) Mean d) Range
4. Which graph is best suited to represent categorical data? a) Histogram b) Pie Chart c) Line Graph d) Scatter Plot
5. If the range of a dataset is 25, and the maximum value is 45, what is the minimum value? a) 20 b) 25 c) 45 d) 70

2. Fill in the Blanks:

6. The value that appears most frequently in a dataset is called ______.
7. The difference between the highest and lowest values in a dataset is called ______.
8. The middle value of an ordered dataset is called the ______.
9. A graphical representation of data using vertical or horizontal bars is known as a ______.
10. The difference between the upper quartile and lower quartile is called the ______.

3. True or False:

11. The median is always the same as the mode. (True/False)
12. A bar graph and a histogram are the same thing. (True/False)
13. The range of a dataset can never be negative. (True/False)
14. The sum of all deviations from the mean is always zero. (True/False)
15. The mean is the best measure of central tendency for skewed data. (True/False)

4. Short Answer Questions:

16. Explain the concept of a sample and a population in statistics.
17. Calculate the mean, median, and mode of the following dataset: 12, 15, 18, 20, 22, 18, 15.
18. Define a histogram and explain its use in representing data.
19. How does an outlier affect the mean and median of a dataset?
20. What is the interquartile range, and why is it useful in data analysis?

5. Long Answer Questions:

21. Discuss the advantages and disadvantages of using the mean, median, and mode as measures of central tendency.
22. Compare and contrast bar graphs and pie charts as methods of representing data. Provide examples of when each would be appropriate.
23. Explain the steps you would take to create a frequency distribution table from a given dataset.
24. Describe the process of calculating the range and interquartile range for a dataset. Provide examples.
25. Discuss the importance of statistics in making informed decisions in real-life situations.

Remember to mix and match these question types to create a comprehensive question set that covers various aspects of the chapter. Additionally, make sure that the questions align with the level of complexity expected from CBSE class 10 standards.

Multiple Choice Questions (MCQs):

1. Which of the following is a rational number? a) √5 b) -3 c) π d) 0.777…
2. Which of the following is not a prime number? a) 2 b) 11 c) 15 d) 19
3. What is the decimal representation of the rational number 3/8? a) 0.375 b) 0.25 c) 0.5 d) 0.625

Fill in the Blanks:

4. A number that cannot be expressed as a fraction is called an ________ number.
5. The decimal representation of a rational number is either ________ or ________.

Matching:

6. Non-Terminating Repeating Decimal i) A number that can be expressed as a fraction of two integers.
7. Irrational Number ii) A decimal number that has an infinite number of digits after the decimal point.
8. Rational Number iii) A number that cannot be expressed as a fraction of two integers.

True or False:

9. Every integer is a rational number.
10. The square root of a negative number is always irrational.
11. Every rational number is a whole number.

Short Answer Questions:

12. Explain the difference between terminating and non-terminating decimals.
13. Give an example of a rational number that is not an integer.
14. If x is a rational number and y is an irrational number, what can you say about x + y?

Long Answer Questions:

15. Prove that the sum of a rational number and an irrational number is always irrational.
16. Explain how to find the HCF and LCM of two given numbers using prime factorization method.

Problem Solving:

17. If the sum of two rational numbers is -2/5 and their difference is 3/5, find the numbers.
18. A rectangular garden is 18 meters long and 12 meters wide. Find the length of the longest rod that can be placed in the garden without bending.

Application Based:

19. A shopkeeper gives a discount of 20% on the marked price of a shirt. If the marked price is ₹800, find the selling price.

Diagram-Based:

20. Draw a number line representing the set of all real numbers from -3 to 3.

Real-World Application:

21. If the temperature drops by 7 degrees Celsius in the morning and then rises by 5 degrees Celsius in the afternoon, what is the net temperature change?

Higher-Order Thinking:

22. Is zero a rational number? Justify your answer.

Remember, these are just examples to get you started. You can build upon these questions and create variations to reach your desired set of 90 questions. Don’t forget to include a mix of different types of questions to assess students’ understanding comprehensively.