Multiple choice questions of all chapters of STD -9 Maths textbook part 1

PAIR OF EQUATIONS

1. Which of the following pairs of equations is dependent?

A) x + y = 3, 2x + 2y = 6

B) x - y = 2, x + y = 4

C) x + y = 2, x - y = 2

D) x + y = 1, x - y = 3

2. What is the solution to the pair of equations:

x + 3y = 7

2x - 3y = -3

A) (2, 1)

B) (1, 2)

C) (3, 1)

D) (1, 1)

3. Which method is used to eliminate the variable in the pair of equations?

A) Substitution method

B) Elimination method

C) Graphical method

D) Algebraic method

4. What is the solution to the pair of equations:

2x + y = 5

x - 2y = -3

A) (2, 1)

B) (1, 2)

C) (3, 1)

D) (1, 1)

5. Which of the following pairs of equations has infinitely many solutions?

A) x + y = 3, x - y = 1

B) x + y = 2, x + y = 4

C) x - y = 2, x + y = 2

D) x + y = 1, x - y = 1

6. What is the solution to the pair of equations:

x + 2y = 4

3x - 2y = 6

A) (2, 0)

B) (0, 2)

C) (1, 1)

D) (3, 1)

7. Which of the following is the correct substitution for the equation x + y = 3?

A) x = 3 - y

B) x = 3 + y

C) y = 3 - x

D) y = 3 + x

8. What is the solution to the pair of equations:

x - 3y = -2

2x + 3y = 7

A) (1, 1)

B) (2, 1)

C) (3, 1)

D) (1, 2)

9. Which of the following pairs of equations is inconsistent?

A) x + y = 2, x - y = 2

B) x + y = 2, x + y = 4

C) x - y = 2, x + y = 2

D) x + y = 1, x - y = 3

10. What is the solution to the pair of equations:

2x + y = 3

x - 2y = -1

A) (1, 1)

B) (2, 1)

C) (3, 1)

D) (1, 2)

11. Which method is used to find the solution to the pair of equations graphically?

A) Substitution method

B) Elimination method

C) Graphical method

D) Algebraic method

12. What is the solution to the pair of equations:

x + 4y = 5

2x - 4y = -2

A) (1, 1)

B) (2, 1)

C) (3, 1)

D) (1, 2)

13. Which of the following pairs of equations has a unique solution?

A) x + y = 3, x - y = 1

B) x + y = 2, x + y = 4

C) x - y = 2, x + y = 2

D) x + y = 1, x - y = 1

14. What is the solution to the pair of equations:

x - 2y = -1

3x + 2y = 7

A) (1, 1)

B) (2, 1)

C) (3, 1)

D) (1, 2)

15. Which of the following is the correct elimination for the equations:

x + 2y = 4

3x - 2y = 6

A) 4x = 10

B) 4x = 12

C) 5x = 10

D) 5x = 12

IRRATIONAL NUMBERS:

1. What is an irrational number?

A) A number that can be expressed as a finite decimal

B) A number that cannot be expressed as a finite decimal

C) A number that is a perfect square

D) A number that is a perfect cube

Answer: B) A number that cannot be expressed as a finite decimal

2. Which of the following is an example of an irrational number?

A) 1/2

B) 3/4

C) √2

D) 2/3

Answer: C) √2

3. What is the decimal representation of an irrational number?

A) Finite and repeating

B) Finite and non-repeating

C) Infinite and non-repeating

D) Infinite and repeating

Answer: C) Infinite and non-repeating

4. Which of the following is a characteristic of irrational numbers?

A) They can be expressed as a ratio of integers

B) They cannot be expressed as a ratio of integers

C) They are always positive

D) They are always negative

Answer: B) They cannot be expressed as a ratio of integers

5. What is the value of √(2/3)?

A) 1/√3

B) √3/2

C) √6/3

D) √2/3

Answer: C) √6/3

6. Is π an irrational number?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

7. What is the decimal representation of π?

A) 3.14159 (finite and repeating)

B) 3.14159... (infinite and non-repeating)

C) 3.14 (finite and non-repeating)

D) 3 (finite and repeating)

Answer: B) 3.14159... (infinite and non-repeating)

8. Which of the following is an example of an irrational number?

A) 1/4

B) 3/5

C) √5

D) 2/7

Answer: C) √5

9. What is the value of (√3)/2?

A) 1/2

B) √3/4

C) √6/4

D) 3/4

Answer: B) √3/4

10. Can irrational numbers be added and subtracted?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

11. What is the result of adding two irrational numbers?

A) Always rational

B) Always irrational

C) Sometimes rational

D) Sometimes irrational

Answer: B) Always irrational

12. Can irrational numbers be multiplied and divided?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

13. What is the result of multiplying two irrational numbers?

A) Always rational

B) Always irrational

C) Sometimes rational

D) Sometimes irrational

Answer: B) Always irrational

14. What is the result of dividing two irrational numbers?

A) Always rational

B) Always irrational

C) Sometimes rational

D) Sometimes irrational

Answer: B) Always irrational

15. Are all non-repeating decimals irrational?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

16. Are all non-terminating decimals irrational?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

17. Can irrational numbers be expressed as a ratio of integers?

A) Yes

B) No

C) Sometimes

D) Always

Answer: B) No

18. What is the value of √(4/9)?

A) 2/3

B) 1/3

C) 4/9

D) 2/9

Answer: A) 2/3

19. Is the square root of a perfect square always rational?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

20. Can two irrational numbers be equal?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

Parallel Lines:

1. What are parallel lines?

A) Lines that intersect at a point

B) Lines that never intersect

C) Lines that are perpendicular

D) Lines that are skew

Answer: B) Lines that never intersect

2. What is the symbol for parallel lines?

A) ⊥

B) ∥

C) ≅

D) ∠

Answer: B) ∥

3. If two lines are parallel, what can be said about their slopes?

A) They are equal

B) They are opposite

C) They are perpendicular

D) They are undefined

Answer: A) They are equal

4. Which of the following is a property of parallel lines?

A) They intersect at a point

B) They never intersect

C) They are perpendicular

D) They are skew

Answer: B) They never intersect

5. If line A is parallel to line B, and line B is parallel to line C, what can be said about line A and line C?

A) They are perpendicular

B) They are parallel

C) They intersect at a point

D) They are skew

Answer: B) They are parallel

6. What is the distance between two parallel lines?

A) Always zero

B) Always equal

C) Always unequal

D) Always infinite

Answer: B) Always equal

7. Can two parallel lines be on the same plane?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

8. What is the intersection of two parallel lines?

A) A point

B) A line

C) A plane

D) None

Answer: D) None

9. Can parallel lines be congruent?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

10. What is the relationship between parallel lines and transversals?

A) They intersect at a point

B) They never intersect

C) They are perpendicular

D) They form corresponding angles

Answer: D) They form corresponding angles

11. Can parallel lines have the same equation?

A) Yes

B) No

C) Sometimes

D) Always

Answer: B) No

12. What is the difference between parallel lines and skew lines?

A) Parallel lines intersect, skew lines do not

B) Parallel lines do not intersect, skew lines intersect

C) Parallel lines are on the same plane, skew lines are not

D) Parallel lines are not on the same plane, skew lines are

Answer: C) Parallel lines are on the same plane, skew lines are not

13. Can parallel lines be graphed on a coordinate plane?

A) Yes

B) No

C) Sometimes

D) Always

Answer: A) Yes

14. What is the x-intercept of two parallel lines?

A) Always the same

B) Always different

C) Sometimes the same

D) Sometimes different

Answer: B) Always different

15. Can parallel lines have different slopes?

A) Yes

B) No

C) Sometimes

D) Always

Answer: B) No

16. What is the relationship between parallel lines and midpoint?

A) The midpoint is always on one of the lines

B) The midpoint is never on one of the lines

C) The midpoint is always equidistant from both lines

D) The midpoint is never equidistant from both lines

Answer: C) The midpoint is always equidistant from both lines

17. Can parallel lines be used to form a triangle?

A) Yes

B) No

C) Sometimes

D) Always

Answer: B) No

18. What is the sum of the interior angles of two parallel lines?

A) Always 180°

B) Always 360°

C) Sometimes 180°

D) Sometimes 360°

Answer: A) Always 180°

19. Can parallel lines be perpendicular to a third line?

A) Yes

B) No

C) Sometimes

D) Always

Answer: B) No

20. What is the relationship between parallel lines and congruent triangles?

A) Parallel lines form congruent triangles

B) Parallel lines never form congruent triangles

C) Sometimes parallel lines form congruent triangles

D) Sometimes parallel lines never form congruent triangles

Answer: A) Parallel lines form congruent triangles

IDENTITIES:

1. What is the expanded form of a(b + c)?

A) ab + ac

B) ab - ac

C) a + bc

D) a - bc

Answer: A) ab + ac

2. What is the expanded form of (a+b)(c+d)?

A) ac + ad + bc + bd

B) ac - ad - bc - bd

C) a + b + c + d

D) a - b - c - d

Answer: A) ac + ad + bc + bd

3. What is the value of 2(3 + 4)?

A) 2(3) + 2(4)

B) 2(3) - 2(4)

C) 2 + 3 + 4

D) 2 - 3 - 4

Answer: A) 2(3) + 2(4)

4. What is the value of (2+3)(4+5)?

A) 2(4) + 2(5) + 3(4) + 3(5)

B) 2(4) - 2(5) - 3(4) - 3(5)

C) 2 + 3 + 4 + 5

D) 2 - 3 - 4 - 5

Answer: A) 2(4) + 2(5) + 3(4) + 3(5)

5. What is the expanded form of 3(a + b)?

A) 3a + 3b

B) 3a - 3b

C) 3 + a + b

D) 3 - a - b

Answer: A) 3a + 3b

6. What is the value of (a+b)(c+d) if a = 2, b = 3, c = 4, and d = 5?

A) 2(4) + 2(5) + 3(4) + 3(5)

B) 2(4) - 2(5) - 3(4) - 3(5)

C) 2 + 3 + 4 + 5

D) 2 - 3 - 4 - 5

Answer: A) 2(4) + 2(5) + 3(4) + 3(5)

7. What is the expanded form of 2(x + y)?

A) 2x + 2y

B) 2x - 2y

C) 2 + x + y

D) 2 - x - y

Answer: A) 2x + 2y

8. What is the value of (x+y)(z+w) if x = 2, y = 3, z = 4, and w = 5?

A) 2(4) + 2(5) + 3(4) + 3(5)

B) 2(4) - 2(5) - 3(4) - 3(5)

C) 2 + 3 + 4 + 5

D) 2 - 3 - 4 - 5

Answer: A) 2(4) + 2(5) + 3(4) + 3(5)

9. What is the expanded form of 4(a + b)?

A) 4a + 4b

B) 4a - 4b

C) 4 + a + b

D) 4 - a - b

Answer: A) 4a + 4b

10. What is the value of (x+y)(z+w) if x = 1, y = 2, z = 3, and w = 4?

A) 1(3) + 1(4) + 2(3) + 2(4)

B) 1(3) - 1(4) - 2(3) - 2(4)

C) 1 + 2 + 3 + 4

D) 1 - 2 - 3 - 4

Answer: A) 1(3) + 1(4) + 2(3) + 2(4)

11. What is the expanded form of 3(a + b + c)?

A) 3a + 3b + 3c

B) 3a - 3b - 3c

C) 3 + a + b + c

D) 3 - a - b - c

Answer: A) 3a + 3b + 3c

12. What is the value of (a+b)(c+d+e) if a = 2, b = 3, c = 4, d = 5, and e = 6?

A) 2(4) + 2(5) + 2(6) + 3(4) + 3(5) + 3(6)

B) 2(4) - 2(5) - 2(6) - 3(4) - 3(5) - 3(6)

C) 2 + 3 + 4 + 5 + 6

D) 2 - 3 - 4 - 5 - 6

Answer: A) 2(4) + 2(5) + 2(6) + 3(4) + 3(5) + 3(6)

13. What is the expanded form of 2(x + y + z)?

A) 2x + 2y + 2z

B) 2x - 2y - 2z

C) 2 + x + y + z

D) 2 - x - y - z

Answer: A) 2x + 2y + 2z

Similar Triangles

Question 1: Two triangles are similar if:

a) Their corresponding angles are equal
b) Their corresponding sides are proportional
c) Both a and b
d) None of the above

Answer: c) Both a and b

Question 2: If two triangles are similar, the ratio of their areas is:

a) Equal to the ratio of their corresponding sides
b) Equal to the square of the ratio of their corresponding sides
c) Equal to the cube of the ratio of their corresponding sides
d) None of the above

Answer: b) Equal to the square of the ratio of their corresponding sides

Question 3: Triangle ABC is similar to triangle DEF. If AB = 4 cm, BC = 6 cm, CA = 8 cm, and DE = 8 cm, what is the length of EF?

a) 6 cm
b) 9 cm
c) 12 cm
d) 16 cm

Answer: c) 12 cm

Question 4: If the ratio of the lengths of the corresponding sides of two similar triangles is 2:3, what is the ratio of their perimeters?

a) 2:3
b) 4:9
c) 8:27
d) None of the above

Answer: a) 2:3

Question 5: In two similar triangles, if the corresponding sides of one triangle are 5 cm, 7 cm, and 9 cm, and the corresponding sides of the other triangle are 10 cm, 14 cm, and 18 cm, what is the ratio of the areas of the triangles?

a) 1:2
b) 1:4
c) 1:8
d) 1:16

Answer: b) 1:4

Question 6: Triangle PQR is similar to triangle XYZ. If PQ = 12 cm, QR = 16 cm, and PR = 20 cm, and the perimeter of triangle XYZ is 60 cm, what is the perimeter of triangle PQR?

a) 24 cm
b) 30 cm
c) 48 cm
d) 60 cm

Answer: c) 48 cm

Question 7: In triangle ABC and triangle DEF, angle A = angle D, angle B = angle E, and AB = 6 cm, DE = 9 cm. What is the scale factor of triangle ABC to triangle DEF?

a) 2:3
b) 3:2
c) 1:2
d) 2:1

Answer: a) 2:3

Question 8: Triangle GHI is similar to triangle JKL. If GH = 8 cm, HI = 10 cm, IJ = 12 cm, and the ratio of the perimeters of triangle GHI to triangle JKL is 4:5, what is the length of KL?

a) 10 cm
b) 12.5 cm
c) 15 cm
d) 20 cm

Answer: c) 15 cm

Question 9: If two similar triangles have a scale factor of 3:5, what is the ratio of their corresponding altitudes?

a) 9:25
b) 3:5
c) 5:3
d) 25:9

Answer: b) 3:5

Question 10: Triangle MNO is similar to triangle PQR. If MN = 3 cm, NO = 4 cm, OM = 5 cm, and PR = 6 cm, what is the length of QR?

a) 8 cm
b) 9 cm
c) 10 cm
d) 12 cm

Answer: a) 8 cm

Question 11: The corresponding altitudes of two similar triangles are in the ratio of 2:3. What is the ratio of their areas?

a) 4:9
b) 2:3
c) 8:27
d) 1:2

Answer: a) 4:9

Question 12: If the sides of two similar triangles are in the ratio 1:√2, what is the ratio of their areas?

a) 1:2
b) 1:√2
c) 1:1
d) 1:3

Answer: a) 1:2

Question 13: Triangle ABC is similar to triangle DEF. If AB = 6 cm, BC = 8 cm, and CA = 10 cm, and the corresponding sides of triangle DEF are twice those of triangle ABC, what is the length of DE?

a) 12 cm
b) 16 cm
c) 20 cm
d) 24 cm

Answer: a) 12 cm

Question 14: Triangle ABC is similar to triangle XYZ. If the ratio of the areas of triangle ABC to triangle XYZ is 1:9, what is the ratio of the corresponding sides?

a) 1:3
b) 1:9
c) 1:27
d) 3:1

Answer: a) 1:3

Question 15: If the perimeters of two similar triangles are in the ratio 5:6, what is the ratio of their corresponding sides?

a) 5:6
b) 25:36
c) 6:5
d) 5:4

Answer: a) 5:6

Question 16: Triangle ABC is similar to triangle DEF. If the height from vertex A in triangle ABC is 9 cm and the corresponding height in triangle DEF is 12 cm, what is the ratio of the areas of triangle ABC to triangle DEF?

a) 3:4
b) 9:16
c) 3:2
d) 4:3

Answer: a) 3:4

Question 17: Two similar triangles have sides in the ratio 7:3. If the area of the smaller triangle is 27 square cm, what is the area of the larger triangle?

a) 63 square cm
b) 189 square cm
c) 441 square cm
d) 84 square cm

Answer: b) 189 square cm

Question 18: If triangle PQR is similar to triangle XYZ and the lengths of the sides of triangle PQR are 4 cm, 5 cm, and 6 cm respectively, and the shortest side of triangle XYZ is 10 cm, what is the length of the longest side of triangle XYZ?