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9th class maths MCQs by Ustani G.docx

  1. 1. (a) (b) (a) {0} (a) (c) π‘₯7 MULTIPLE CHOICE QUESTIONS CHAPTER 01 REAL AND COMPLEX NUMBERS Choose the correct answer from the options given in each question. βˆ’1 βˆ’ 2 (c) 𝑖 (d) βˆ’π‘– 8. Every real number is (a) a positive integer (b) a rational number (c) A negative integer (d) a complex number 9. Real part of 2π‘Žπ‘(𝑖 + 𝑖2) is (a) 2ab (b) βˆ’2ab (c) 2ab𝑖 (d) βˆ’2ab𝑖 10. Imaginary part of βˆ’π‘–(3𝑖 + 2) is (a) βˆ’2 (b) 2 (c) 3 (d) βˆ’3 11. Which of the following sets have the closure property w. r. t. addition 1. (27π‘₯ 3 √π‘₯2 ) 3 = √π‘₯3 (b) {0, βˆ’1} 9 3 √π‘₯2 (b) 9 √π‘₯3 (c) {0,1} (d) {1, 1 √2 , 1 } 2 (c) 8 (d) 8 12. Name the property of real numbers used in (βˆ’ √5) Γ— 1 = βˆ’ √5 2 2 2. Write 7√π‘₯ in exponential form (a) π‘₯ (b) π‘₯7 (a) Additive identity (b) Additive inverse (c) Multiplicative identity (d) Multiplicative inverse 1 2 3. Write 43 with radical sign 7 (d) π‘₯2 13. If π‘₯, 𝑦, 𝑧 ∈ R and 𝑧 < 0 then π‘₯ < 𝑦 ⇔ (a) π‘₯𝑧 < 𝑦𝑧 π‘₯𝑧 > 𝑦𝑧 3√42 (c) 2√43 4. In 3√35 the radicand is (b) √43 (d) √46 (c) π‘₯𝑧 = 𝑦𝑧 (d) none of these 14. If π‘Ž, 𝑏 ∈ R then only one of π‘Ž = 𝑏 or π‘Ž < 𝑏 or π‘Ž > 𝑏 holds is called (a) Trichotomy property (b) Transitive property (c) Additive property (d) Multiplicative property (a) 3 (b) 1 3 (d) none of these 1 25 βˆ’ 15. A non-terminating non-recurring decimal represents: (a) a natural number (b) A rational number (c) An irrational number (d) A prime number 5. ( ) 16 2 = 16. The union of the set of rational numbers and irrational number is known (a) 5 4 (c) βˆ’ 5 4 6. The conjugate of 5 + 4𝑖 is (d) βˆ’ 4 5 as set of (a) rational number (b) irrational (c) real number (d) whole number 17. √3. √3 is a number (a) βˆ’5 + 4𝑖 (b) βˆ’5 βˆ’ 4𝑖 (c) 5 βˆ’ 4𝑖 (d) 5 + 4𝑖 7. The value of 𝑖9 is (a) rational (b) irrational (c) real (d) none 18. π‘›βˆšπ‘Žπ‘ = (a) 1 (b) βˆ’1 𝑛 βˆšπ‘Ž 𝑛 βˆšπ‘ (b) βˆšπ‘Ž βˆšπ‘ (b) 4 5 (a) (c) 35
  2. 2. 1 a 2 c 3 a 4 c 5 b 6 c 7 c 8 d 9 b 10 a 11 a 12 c 13 b 14 a 15 c 16 c 17 c 18 a 19 a 20 a 21 a 22 a 23 b 24 a 25 a 26 a 27 c 28 a 29 c 30 b (c) 𝑛 βˆšπ‘Ž βˆšπ‘ (d) βˆšπ‘Ž 𝑛 βˆšπ‘ 19. 5βˆšβˆ’8 = 1 (a) (βˆ’8)5 (b) (βˆ’8)5 1 (c) βˆ’8 (d) (8)5 20. The value of 𝑖10 is: (a) βˆ’1 (b) 1 (c) βˆ’π‘– (d) 𝑖 21. The conjugate of 2 + 3𝑖 is (a) 2 βˆ’ 3𝑖 (b) βˆ’2 βˆ’ 3𝑖 (c) βˆ’2 + 3𝑖 (d) 2 + 3𝑖 2 22. Real part of (βˆ’1 + βˆšβˆ’2) is: (a) βˆ’1 (b) βˆ’2√2 (c) 1 (d) 2√2 2 23. Imaginary part of (βˆ’1 + βˆšβˆ’2) is: (a) βˆ’1 (b) βˆ’2√2 (c) 1 (d) 2√2 (a) π‘₯ = 4, 𝑦 = βˆ’3 (b) π‘₯ = 3, 𝑦 = 3 (c) π‘₯ = 3, 𝑦 = βˆ’3 (d) π‘₯ = 5, 𝑦 = βˆ’3 30. 𝑝 from of 0. 3 is π‘ž (a) 3 10 (c) 0.33 (d) 10 3 24. 𝑝 is a/an π‘ž number (a) irrational (b) rational (c) natural (d) whole 25. The value of 𝑖 (iota) is (a) βˆšβˆ’1 (b) βˆ’1 (c) 1 (d) (βˆ’1)2 26. In βˆ’2 + 3𝑖, 3 is called (a) imaginary part (b) real part (c) negative part (d) complex number 27. The set of natural number is (a) {0,1,2,3, … } (b) {2,4,6, … } (c) {1,2,3, … } (d) {2,3,5,7, … } 28. πœ‹, 𝑒, √2, √3 and √5 are called (a) irrational numbers (b) rational numbers (c) natural numbers (d) complex numbers 29. If π‘₯ + 𝑖𝑦 + 1 = 4 βˆ’ 3𝑖, then (b) 1 3
  3. 3. 𝑝 CHAPTER 02 LOGARITHMS 9. log𝑏 π‘Ž Γ— log𝑐 𝑏 can be written as (a) log𝑐 π‘Ž (b) logπ‘Ž 𝑐 (c) logπ‘Ž 𝑏 (d) log𝑏 𝑐 10. log𝑦 π‘₯ will be equal to (a) log𝑧 π‘₯ log𝑦 𝑧 (c) log𝑧 π‘₯ log𝑧 𝑦 (b) logπ‘₯ 𝑧 log𝑦 𝑧 (d) log𝑧 𝑦 log𝑧 π‘₯ Choose the correct answer from the options given in each question. 11. For common logarithm, the base is 1. If π‘Žπ‘₯ = 𝑛, then (a) 2 (b) 10 (a) π‘Ž = logπ‘₯ 𝑛 (c) π‘₯ = logπ‘Ž 𝑛 2. The relation of 𝑦 = log𝑧 π‘₯ implies (b) π‘₯ = log𝑛 π‘Ž (d) π‘Ž = log𝑛 π‘₯ (c) 𝑒 12. For natural logarithm, the base is (a) 10 (d) 1 (b) 𝑒 (a) 𝑦π‘₯ = 𝑧 (b) 𝑧𝑦 = π‘₯ (c) 2 (d) 1 (c) π‘₯𝑧 = 𝑦 (d) 𝑦𝑧 = π‘₯ 3. The logarithm of unity to any base is (a) 1 (b) 10 (c) 𝑒 (d) 0 4. The logarithm to any number to itself as base is (a) 1 (b) 0 (c) βˆ’1 (d) 10 5. log 𝑒 = where 𝑒 β‰ˆ 2.718 (a) 0 (b) 0.4343 (c) ∞ (d) 1 13. The integral part of the common logarithm of a number is called the (a) characteristic (b) mantissa (c) logarithm (d) none of these 14. The decimal part of the common logarithm of a number is called the (a) characteristic (b) mantissa (c) logarithm (d) none of these 15. If π‘₯ = log 𝑦, then 𝑦 is called the (a) antilogarithm (b) logarithm (c) characteristic (d) none of these 6. The value of log ( ) is π‘ž 16. 30600 in scientific notation is (a) 3.06 Γ— 104 (b) 3.006 Γ— 104 log 𝑝 βˆ’ log π‘ž (b) log 𝑝 log π‘ž (c) log 𝑝 + log π‘ž (d) log π‘ž βˆ’ log 𝑝 7. log 𝑝 βˆ’ log π‘ž is same as: (a) log ( π‘ž ) (b) log(𝑝 βˆ’ π‘ž) 𝑝 (c) 30.6 Γ— 104 (d) 306 Γ— 104 17. 6.35 Γ— 106 in ordinary notation is (a) 6350000 (b) 635000 (c) 6350 (d) 63500 18. A number written in the form of π‘Ž Γ— 10𝑛, where 1 ≀ π‘Ž ≀ 10 and 𝑛 is (c) log 𝑝 log π‘ž 8. log π‘šπ‘› can be written as (d) log 𝑝 π‘ž an integer is called (a) scientific notation (b) ordinary notation (a) (log π‘š)𝑛 (b) π‘š log 𝑛 (c) 𝑛 log π‘š (d) log(π‘šπ‘›) (c) logarithmic notation (d) none of these 19. common logarithm is also known as logarithm. (a) natural (b) simple MULTIPLE CHOICE QUESTIONS (a)
  4. 4. 1 c 2 b 3 d 4 a 5 b 6 a 7 d 8 c 9 a 10 c 11 b 12 b 13 a 14 b 15 a 16 a 17 a 18 a 19 d 20 d 21 d 22 a 23 a 24 b MULTIPLE CHOICE QUESTIONS (c) scientific 20. logπ‘Ž π‘š + logπ‘Ž 𝑛 is same as: decadic (a) logπ‘Ž(π‘š + 𝑛) (b) logπ‘Ž(π‘š Γ— 𝑛) (c) logπ‘Ž π‘š Γ— logπ‘Ž 𝑛 π‘š logπ‘Ž (𝑛 ) ALGEBRAIC EXPRESSION 21. John Napier prepared the logarithm tables to the base . (a) 0 (b) 1 (c) 10 (d) 𝑒 22. log2 3 in common log is written as . AND FORMULAS (a) log 3 log 2 (c) log 3 2 23. log𝑒 10 = (b) log 2 log 3 (d) log 23 Choose the correct answer from the options given in each question. 1. 4π‘₯ + 3𝑦 βˆ’ 2 is an algebraic (a) expression (b) sentence (a) 2.3026 (b) 0.4343 (c) 𝑒10 (d) 10 24. If log2 π‘₯ = 5 then π‘₯ is: (a) 25 (b) 32 (c) 10 (d) 25π‘₯ (c) equation (d) inequation 2. The degree of polynomial 4π‘₯4 + 2π‘₯2𝑦 is 6. 1 π‘Žβˆ’π‘ βˆ’ 1 π‘Ž+𝑏 is equal to (a) 2π‘Ž π‘Ž2βˆ’π‘2 (c) βˆ’2π‘Ž π‘Ž2βˆ’π‘2 7. π‘Ž 2βˆ’π‘2 is equal to π‘Ž+𝑏 (a) (π‘Ž βˆ’ 𝑏)2 (c) π‘Ž + 𝑏 8. (βˆšπ‘Ž + βˆšπ‘)(βˆšπ‘Ž βˆ’ βˆšπ‘) is equal to 2𝑏 π‘Ž2βˆ’π‘2 (d) βˆ’2𝑏 π‘Ž2βˆ’π‘2 (π‘Ž + 𝑏)2 π‘Ž βˆ’ 𝑏 (b) (d) (b) (d) (d) CHAPTER 03 (a) 1 (c) 3 3. π‘Ž3 + 𝑏3 is equal to (b) 2 (d) 4 (a) (π‘Ž βˆ’ 𝑏)(π‘Ž2 + π‘Žπ‘ + 𝑏2) (b) (π‘Ž + 𝑏)(π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2) (c) (π‘Ž βˆ’ 𝑏)(π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2) (d) (π‘Ž + 𝑏)(π‘Ž2 + π‘Žπ‘ βˆ’ 𝑏2) 4. (3 + √2)(3 βˆ’ √2) is equal to (a) 7 (b) βˆ’7 (c) βˆ’1 (d) 1 5. Conjugate of Surd π‘Ž + βˆšπ‘ is (a) βˆ’π‘Ž + βˆšπ‘ (b) π‘Ž βˆ’ βˆšπ‘ (c) βˆšπ‘Ž + βˆšπ‘ (d) βˆšπ‘Ž βˆ’ βˆšπ‘
  5. 5. 1 a 2 d 3 b 4 a 5 b 6 b 7 d 8 c 9 a 10 a 11 a 12 a 13 b 14 a 15 b 16 b 17 c 18 c 19 d 20 a 21 d (a) π‘Ž2 + 𝑏2 (b) π‘Ž2 βˆ’ 𝑏2 (c) π‘Ž βˆ’ 𝑏 (d) π‘Ž + 𝑏 9. The degree of the polynomial π‘₯2𝑦2 + 3π‘₯𝑦 + 𝑦3 is (a) 4 (b) 5 (c) 6 (d) 2 10. π‘₯2 βˆ’ 4 = (a) (π‘₯ βˆ’ 2)(π‘₯ + 2) (b) (π‘₯ βˆ’ 2)(π‘₯ βˆ’ 2) (c) (π‘₯ + 2)(π‘₯ + 2) (d) (π‘₯ βˆ’ 2)2 11. π‘₯3 + 1 1 ( ) 19. Which of the following is not surd? (a) √2 (b) √3 (c) √2 + 5 (d) βˆšπœ‹ 20. In the polynomial with the variable π‘₯, all the powers of π‘₯ are integers. (a) non-negative (b) negative (c) non-positive (d) none of these 21. Polynomial means an expression with: (a) one term (b) two terms π‘₯3 = (π‘₯ + π‘₯ ) (a) π‘₯2 βˆ’ 1 + 1 π‘₯2 (c) π‘₯2 + 1 βˆ’ 1 π‘₯2 … … … … … (b) π‘₯2 + 1 + 1 π‘₯2 (d) π‘₯2 βˆ’ 1 βˆ’ 1 π‘₯2 (c) three terms (d) many term 12. 1 = 2βˆ’βˆš3 (a) 2 + √3 (b) 2 βˆ’ √3 (c) βˆ’2 + √3 (d) βˆ’2 βˆ’ √3 13. (π‘Ž + 𝑏)2 βˆ’ (π‘Ž βˆ’ 𝑏)2 = (a) 2(π‘Ž2 + 𝑏2) (b) 4π‘Žπ‘ (c) 2π‘Žπ‘ (d) 3π‘Žπ‘ 14. A surd which contains a single term is called surd. (a) monomial (b) binomial (c) trinomial (d) conjugate 15. What is the leading coefficient of polynomial 3π‘₯2 + 8π‘₯ + 5? (a) 2 (b) 3 (c) 5 (d) 8 16. A surd which contains two terms is called surd. (a) monomial (b) binomial (c) trinomial (d) conjugate 17. Which of the following is polynomial? (a) 3π‘₯2 + 1 π‘₯ (b) 4π‘₯2 βˆ’ 3√π‘₯ (c) π‘₯2 βˆ’ 3π‘₯ + √2 (d) 2π‘₯2 + 3π‘₯βˆ’1 18. (3 + √3)(3 βˆ’ √3) = (a) 12 (b) 9 (c) 6 (d) 3
  6. 6. (c) 1 2 1 1 2 1 (3π‘₯ βˆ’ ) (9π‘₯ π‘₯ βˆ’ 3 + π‘₯2) (d) (3π‘₯ + π‘₯ ) ( 9 π‘₯ βˆ’ 3 + π‘₯2) FACTORIZATION 9. If π‘₯ βˆ’ 2 is a factor of 𝑝(π‘₯) = π‘₯2 + 2π‘˜π‘₯ + 8, then π‘˜ = (a) βˆ’3 (b) 3 (c) 4 (d) 5 10. 4π‘Ž2 + 4π‘Žπ‘ + (… ) is a complete square (a) 𝑏2 (b) 2𝑏 (c) π‘Ž2 (d) 4𝑏2 Choose the correct answer from the options given in each question. π‘₯2 𝑦2 1. The factor π‘₯2 βˆ’ 5π‘₯ + 6 are 11. 𝑦2 βˆ’ 2 + π‘₯2 = (a) π‘₯ + 1, π‘₯ βˆ’ 6 (b) π‘₯ βˆ’ 2, π‘₯ βˆ’ 3 (c) π‘₯ + 6, π‘₯ βˆ’ 1 (d) π‘₯ + 2, π‘₯ + 3 ( π‘₯ 𝑦 π‘₯ βˆ’ 𝑦 ) π‘₯ 𝑦 3 (b) ( π‘₯ 𝑦 π‘₯ + 𝑦 ) π‘₯ 𝑦 3 2. Factors 8π‘₯3 + 27𝑦3 are (c) ( βˆ’ ) 𝑦 π‘₯ (d) ( + ) 𝑦 π‘₯ (3π‘₯ βˆ’ ) ( 9 π‘₯ π‘₯ π‘₯3 + 3 + π‘₯2) (b) (3π‘₯ + π‘₯ ) ( 9 π‘₯ + 3 + π‘₯2) MULTIPLE CHOICE QUESTIONS (a) 2 2 CHAPTER 04 (a) (2π‘₯ + 3𝑦)(4π‘₯2 βˆ’ 9𝑦2) 12. (π‘₯ + 𝑦)(π‘₯2 βˆ’ π‘₯𝑦 + 𝑦2) = (b) (2π‘₯ βˆ’ 3𝑦)(4π‘₯2 βˆ’ 9𝑦2) (a) π‘₯3 βˆ’ 𝑦3 (b) π‘₯3 + 𝑦3 (c) (2π‘₯ + 3𝑦)(4π‘₯2 βˆ’ 6π‘₯𝑦 + 9𝑦2) (c) (π‘₯ + 𝑦)3 (d) (π‘₯ βˆ’ 𝑦)3 (d) (2π‘₯ βˆ’ 3𝑦)(4π‘₯2 + 6π‘₯𝑦 + 9𝑦2) 13. Factors of π‘₯4 βˆ’ 16 is 3. Factors 3π‘₯2 βˆ’ π‘₯ βˆ’ 2 are (a) (π‘₯ βˆ’ 2)2 (b) (π‘₯ βˆ’ 2)(π‘₯ + 2)(π‘₯2 + 4) (c) (π‘₯ βˆ’ 2)(π‘₯ + 2) (d) (π‘₯ + 2)2 (a) (π‘₯ + 1)(3π‘₯ βˆ’ 2) (b) (π‘₯ + 1)(3π‘₯ + 2) 14. Factors of 3π‘₯ βˆ’ 3π‘Ž + π‘₯𝑦 βˆ’ π‘Žπ‘¦ are (c) (π‘₯ βˆ’ 1)(3π‘₯ βˆ’ 2) 4. Factors of π‘Ž4 βˆ’ 4𝑏4 are (a) (π‘Ž βˆ’ 𝑏)(π‘Ž + 𝑏)(π‘Ž2 + 4𝑏2) (d) (π‘₯ βˆ’ 1)(3π‘₯ + 2) (b) (π‘Ž2 βˆ’ 2𝑏2)(π‘Ž2 + 2𝑏2) (a) (3 + 𝑦)(π‘₯ βˆ’ π‘Ž) (c) (3 βˆ’ 𝑦)(π‘₯ βˆ’ π‘Ž) 15. Factors of π‘π‘žπ‘Ÿ + π‘žπ‘Ÿ2 βˆ’ π‘π‘Ÿ2 βˆ’ π‘Ÿ3 is (b) (3 βˆ’ 𝑦)(π‘₯ + π‘Ž) (d) (3 + 𝑦)(π‘₯ + π‘Ž) (c) (π‘Ž βˆ’ 𝑏)(π‘Ž + 𝑏)(π‘Ž2 βˆ’ 4𝑏2) (d) (π‘Ž βˆ’ 2𝑏)(π‘Ž2 + 2𝑏2) (a) π‘Ÿ(𝑝 + π‘Ÿ)(π‘ž βˆ’ π‘Ÿ) (b) π‘Ÿ(𝑝 βˆ’ π‘Ÿ)(π‘ž + π‘Ÿ) 5. What will be added to complete the square of 9π‘Ž2 βˆ’ 12π‘Žπ‘? (c) π‘Ÿ(𝑝 βˆ’ π‘Ÿ)(π‘ž βˆ’ π‘Ÿ) (d) π‘Ÿ(𝑝 + π‘Ÿ)(π‘ž + π‘Ÿ) (a) βˆ’16𝑏2 (b) 16𝑏2 16. What is the value of 𝑝(π‘₯) = 6π‘₯4 + 2π‘₯3 βˆ’ π‘₯ + 2 at π‘₯ = 0? (c) 4𝑏2 (d) βˆ’4𝑏2 (a) 9 (b) 8 6. Find π‘š so that π‘₯2 + 4π‘₯ + π‘š is a complete square: (c) 2 (d) 7 (a) 8 (b) βˆ’8 17. π‘₯2 + 5π‘₯ + 6 = (c) 4 (d) 16 (a) (π‘₯ + 1)(π‘₯ βˆ’ 1) (b) (π‘₯ βˆ’ 2)(π‘₯ βˆ’ 3) 7. Factors of 5π‘₯2 βˆ’ 17π‘₯𝑦 βˆ’ 12𝑦2 are (c) (π‘₯ + 6)(π‘₯ βˆ’ 1) (d) (π‘₯ + 2)(π‘₯ + 3) (a) (π‘₯ + 4𝑦)(5π‘₯ + 3𝑦) (b) (π‘₯ βˆ’ 4𝑦)(5π‘₯ βˆ’ 3𝑦) 18. 4π‘Ž2 βˆ’ 16 = (c) (π‘₯ βˆ’ 4𝑦)(5π‘₯ + 3𝑦) (d) (5π‘₯ βˆ’ 4𝑦)(π‘₯ + 3𝑦) (a) (2π‘Ž + 8)(2π‘Ž βˆ’ 8) (b) 4(π‘Ž + 2)(π‘Ž βˆ’ 2) 8. Factors of 27π‘₯3 βˆ’ 1 are (a) 1 2 1 1 2 1 (c) 4(π‘Ž + 2)2 (d) 4(π‘Ž βˆ’ 2)2 19. How many factors of a cubic expression are there?
  7. 7. 1 b 2 c 3 d 4 b 5 c 6 c 7 c 8 a 9 a 10 a 11 a 12 b 13 b 14 a 15 a 16 c 17 d 18 b 19 d 20 a (b) 1 (d) 3 (a) zero (c) 2 20. (π‘₯ βˆ’ 𝑦)(π‘₯2 + π‘₯𝑦 + 𝑦2) = (a) π‘₯3 βˆ’ 𝑦3 (b) π‘₯3 + 𝑦3 (c) (π‘₯ + 𝑦)3 (d) (π‘₯ βˆ’ 𝑦)3 CHAPTER 05 ALGEBRAIC MANIPULATION Choose the correct answer from the options given in each question. 1. H.C.F. of 𝑝3π‘ž βˆ’ π‘π‘ž3 and 𝑝5π‘ž2 βˆ’ 𝑝2π‘ž5 is (a) π‘π‘ž(𝑝2 βˆ’ π‘ž2) (b) π‘π‘ž(𝑝 βˆ’ π‘ž) (c) 𝑝2π‘ž2(𝑝 βˆ’ π‘ž) (d) π‘π‘ž(𝑝3 βˆ’ π‘ž3) 2. H.C.F. of 5π‘₯2𝑦2 and 20π‘₯3𝑦3 is: (a) 5π‘₯2𝑦2 (b) 20π‘₯3𝑦3 (c) 100π‘₯5𝑦5 (d) 5π‘₯𝑦 3. H.C.F. of (π‘₯ βˆ’ 2) and (π‘₯2 + π‘₯ βˆ’ 6) is (a) π‘₯2 + π‘₯ βˆ’ 6 (b) π‘₯ + 2 (c) π‘₯ βˆ’ 2 (d) π‘₯ + 3 4. H.C.F. of (π‘Ž3 + 𝑏3) and (π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2) is (a) π‘Ž + 𝑏 (b) π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2 (c) (π‘Ž βˆ’ 𝑏)2 (d) π‘Ž2 + 𝑏2 5. H.C.F. of (π‘₯2 βˆ’ 5π‘₯ + 6) and (π‘₯2 βˆ’ π‘₯ βˆ’ 6) is: (a) π‘₯ βˆ’ 3 (b) π‘₯ + 2 (c) π‘₯2 βˆ’ 4 (d) π‘₯ βˆ’ 2 6. H.C.F. of (π‘Ž2 βˆ’ 𝑏2) and (π‘Ž3 βˆ’ 𝑏3) is: (a) π‘Ž βˆ’ 𝑏 (b) π‘Ž + 𝑏 (c) π‘Ž2 + π‘Žπ‘ + 𝑏2 (d) π‘Ž2 βˆ’ π‘Žπ‘ + 𝑏2 7. H.C.F. of (π‘₯2 + 3π‘₯ + 2) and (π‘₯2 + 4π‘₯ + 3) is: (a) π‘₯ + 1 (b) (π‘₯ + 1)(π‘₯ + 2) (c) (π‘₯ + 3) (d) (π‘₯ + 4)(π‘₯ + 1) 8. L.C.M. of 15π‘₯2, 45π‘₯𝑦 and 30π‘₯𝑦𝑧 is: (a) 90π‘₯𝑦𝑧 (b) 90π‘₯2𝑦𝑧 (c) 15π‘₯𝑦𝑧 (d) 15π‘₯2𝑦𝑧 MULTIPLE CHOICE QUESTIONS
  8. 8. 𝑏 (c) 1 π‘Ž (d) 9. L.C.M. of π‘Ž2 + 𝑏2 and π‘Ž4 βˆ’ 𝑏4 is: (a) π‘Ž2 + 𝑏2 (b) π‘Ž2 βˆ’ 𝑏2 (c) π‘Ž4 βˆ’ 𝑏4 (d) π‘Ž βˆ’ 𝑏 (a) Β±(2π‘₯ βˆ’ 3) (b) Β±(2π‘₯ + 3) (c) (2π‘₯ + 3)2 (d) (2π‘₯ βˆ’ 3)2 19. L.C.M. = 10. The product of two algebraic expression is equal to the H.C.F. and L.C.M. (a) sum (b) difference (c) product (d) quotient of their (a) 𝑝(π‘₯)Γ—π‘ž(π‘₯) H.C.F (c) 𝑝(π‘₯) π‘ž(π‘₯)Γ—H.C.F 20. H.C.F. = (b) 𝑝(π‘₯)Γ—π‘ž(π‘₯) L.C.M (d) π‘ž(π‘₯) 𝑝(π‘₯)Γ—H.C.F 11. π‘Ž 9π‘Ž2βˆ’π‘2 (a) 4π‘Ž 9π‘Ž2βˆ’π‘2 4π‘Ž+𝑏 9π‘Ž2βˆ’π‘2 + 1 = 3π‘Žβˆ’π‘ (b) 4π‘Žβˆ’π‘ 9π‘Ž2βˆ’π‘2 (d) 𝑏 9π‘Ž2βˆ’π‘2 (a) 𝑝(π‘₯)Γ—π‘ž(π‘₯) L.C.M (c) 𝑝(π‘₯) π‘ž(π‘₯)Γ—L.C.M 21. L. C. M Γ— H. C. F. = (b) 𝑝(π‘₯)Γ—π‘ž(π‘₯) H.C.F (d) L.C.M 𝑝(π‘₯)Γ—π‘ž(π‘₯) 12. π‘Ž2+5π‘Žβˆ’14 Γ— π‘Ž+3 = π‘Ž2βˆ’3π‘Žβˆ’18 π‘Žβˆ’2 (a) π‘Ž+7 π‘Žβˆ’6 (c) π‘Ž+3 π‘Žβˆ’6 13. π‘Ž3βˆ’π‘3 Γ· ( π‘Ž2+π‘Žπ‘+𝑏2 ) = (b) π‘Ž+7 π‘Žβˆ’2 (d) π‘Žβˆ’2 π‘Ž+3 (a) 𝑝(π‘₯) Γ— π‘ž(π‘₯) (b) 𝑝(π‘₯) Γ— H. C. F. (c) π‘ž(π‘₯) Γ— L. C. M (d) none of these 22. Any unknown expression may be found if of them are known by using the relation L. C. M Γ— H. C. F = p(π‘₯) Γ— π‘ž(π‘₯) (a) two (b) three π‘Ž4βˆ’π‘4 1 π‘Ž+𝑏 (c) π‘Žβˆ’π‘ π‘Ž2+𝑏2 π‘Ž2+𝑏2 (b) 1 π‘Žβˆ’π‘ (d) π‘Ž+𝑏 π‘Ž2+𝑏2 (c) four (d) none of these 23. The H.C.F of π‘₯2 βˆ’ 4, π‘₯2 + 4π‘₯ + 4 and 2π‘₯2 + π‘₯ βˆ’ 6 is: (a) π‘₯ βˆ’ 2 (b) π‘₯ + 2 (c) 2π‘₯ βˆ’ 3 (d) (π‘₯ βˆ’ 2)(π‘₯ + 2)(2π‘₯ βˆ’ 3) 14. ( 2π‘₯+𝑦 βˆ’ 1) Γ· (1 βˆ’ π‘₯ ) = π‘Ž+𝑏 π‘Ž2βˆ’π‘Žπ‘ (a) (c) π‘₯+𝑦 π‘₯ π‘₯+𝑦 𝑦 π‘₯+𝑦 (b) 𝑦 π‘₯+𝑦 π‘₯ 24. π‘Ž2βˆ’π‘2 Γ· π‘Ž2βˆ’2π‘Žπ‘+𝑏2 (a) π‘Ž (b) 𝑏 π‘Ž π‘₯ 𝑦 15. The square root of π‘Ž2 βˆ’ 2π‘Ž + 1 is 25. If 𝐴 = π‘Ž+𝑏 , then 1 is: (d) π‘Ž (a) Β±(π‘Ž + 1) (b) Β±(π‘Ž βˆ’ 1) (c) π‘Ž βˆ’ 1 (d) π‘Ž + 1 16. What should be added to complete the square of π‘₯4 + 64? (a) 8π‘₯2 (b) βˆ’8π‘₯2 (a) π‘Žβˆ’π‘ π‘Ž+𝑏 (c) π‘Žβˆ’π‘ π‘Žβˆ’π‘ π‘Žβˆ’π‘ 𝐴 (b) π‘Ž+𝑏 π‘Žβˆ’π‘ (d) π‘Ž+𝑏 π‘Ž+𝑏 (c) 16π‘₯2 (d) 4π‘₯2 17. The square root of π‘₯4 + 1 + 2 is: π‘₯4 26. How many methods are used to find H.C.F of given expression? (a) one (b) two (c) three (d) four (a) 1 Β± (π‘₯ + ) π‘₯ Β± (π‘₯2 + 1 ) π‘₯2 27. How many methods are used to find square root of given expression? (a) one (b) two (c) Β± (π‘₯ βˆ’ 1 ) (d) Β± (π‘₯2 βˆ’ 1 ) π‘₯ 18. The square root of 4π‘₯2 βˆ’ 12π‘₯ + 9 is: π‘₯2 (c) three (d) four 28. If π‘ž(π‘₯). π‘ž(π‘₯) = 𝑝(π‘₯), then π‘ž(π‘₯) is called of 𝑝(π‘₯). (b) (a) (c)
  9. 9. 1 b 2 a 3 c 4 b 5 a 6 a 7 a 8 b 9 c 10 c 11 c 12 a 13 a 14 d 15 b 16 c 17 b 18 a 19 a 20 a 21 a 22 b 23 b 24 c 25 a 26 c 27 c 28 b (b) (a) square (b) square root (c) L.C.M (d) H.C.F CHAPTER 06 LINEAR EQUATION AND LINEAR INEQUALITIES Choose the correct answer from the options given in each question. 1. Which of the following is the solution of the inequality 3 βˆ’ 4π‘₯ ≀ 11? (a) π‘₯ β‰₯ βˆ’8 (c) π‘₯ β‰₯ βˆ’ 14 3 π‘₯ β‰₯ βˆ’2 (d) none of these 2. A statement involving any of the symbols <, >, ≀ or β‰₯ is called (a) equation (b) identity (c) inequality (d) linear equation 3. π‘₯ = is a solution of the inequality βˆ’2 < π‘₯ < 3 2 (a) βˆ’5 (b) 3 (d) 5 2 4. If π‘₯ is no larger than 10, then: (a) π‘₯ β‰₯ 8 (b) π‘₯ ≀ 10 (c) π‘₯ < 10 (d) π‘₯ > 10 5. If the capacity x of an elevator is at most 1600 pounds, then (a) 𝑐 < 1600 (c) 𝑐 ≀ 1600 6. π‘₯ = 0 is a solution of the inequality: (b) 𝑐 β‰₯ 1600 (d) 𝑐 > 1600 (a) π‘₯ > 0 (b) 3π‘₯ + 5 > 0 (c) π‘₯ + 2 < 0 (d) π‘₯ βˆ’ 2 < 0 7. The linear equation in one variable π‘₯ is: (a) π‘Žπ‘₯ + 𝑏 = 0 (b) π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0 (c) π‘Žπ‘₯ + 𝑏𝑦 + 𝑐 = 0 (d) π‘Žπ‘₯2 + 𝑏𝑦2 + 𝑐 = 0 8. An inconsistent equation is that whose solution set is: (a) empty (b) not empty (c) zero (d) positive MULTIPLE CHOICE QUESTIONS (c) 0
  10. 10. 9. |π‘₯| = π‘Ž is equivalent to: (a) π‘₯ = π‘Ž or π‘₯ = βˆ’π‘Ž (b) π‘₯ = 1 or π‘₯ = βˆ’ 1 18. |π‘₯| = 0 has only solution (a) one (b) two (c) π‘₯ = π‘Ž or π‘₯ = βˆ’ 1 π‘Ž 10. A linear inequality in one variable π‘₯ is: π‘Ž π‘Ž (d) none of these (c) three (d) none of these 19. The equation |π‘₯| = 2 is equivalent to: (a) π‘₯ = 2 or π‘₯ = βˆ’2 (b) π‘₯ = βˆ’2 or π‘₯ = βˆ’2 (a) π‘Žπ‘₯ + 𝑏 > 0, π‘Ž β‰  0 (b) π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 < 0, π‘Ž β‰  0 (c) π‘₯ = 2 or π‘₯ = 1 2 (d) π‘₯ = 2 or π‘₯ = βˆ’ 1 2 (c) π‘Žπ‘₯ + 𝑏𝑦 + 𝑐 > 0, π‘Ž β‰  0 (d) π‘Žπ‘₯2 + 𝑏𝑦2 + 𝑐 < 0, π‘Ž β‰  0 11. Law of trichotomy is . (π‘Ž, 𝑏 ∈ R) (a) π‘Ž < 𝑏 or π‘Ž = 𝑏 or π‘Ž > 𝑏 (b) π‘Ž < 𝑏 or π‘Ž = 𝑏 (c) π‘Ž < 𝑏 or π‘Ž > 𝑏 (d) none of these 12. Transitive law is (a) π‘Ž < 𝑏 and 𝑏 < 𝑐, then π‘Ž < 𝑐 (b) π‘Ž > 𝑏 and 𝑏 < 𝑐, then π‘Ž > 𝑐 (c) π‘Ž > 𝑏 and 𝑏 < 𝑐, then π‘Ž = 𝑐 (d) none of these 13. If π‘Ž > 𝑏, 𝑐 > 0 then: (a) π‘Žπ‘ < 𝑏𝑐 (b) π‘Žπ‘ > 𝑏𝑐 (c) π‘Žπ‘ = 𝑏𝑐 (d) π‘Žπ‘ ≀ 𝑏𝑐 14. If π‘Ž > 𝑏, 𝑐 > 0 then 20. A/an is equation that is satisfied by every number for which both sides are defined: (a) identity (b) conditional (c) inconsistent (d) inequation 21. A/an equation is an equation whose solution set is the empty set: (a) identity (b) conditional (c) inconsistent (d) none 22. A/an equation is an equation that is satisfied by at least one number but is not an identity: (a) identity (b) conditional (c) inconsistent (d) none 23. π‘₯ + 4 = 4 + π‘₯ is equation: (a) identity (b) conditional (c) inconsistent (d) none (a) π‘Ž > 𝑏 (b) π‘Ž < 𝑏 24. 2π‘₯ + 1 = 9 is equation: 𝑐 𝑐 𝑐 𝑐 (c) π‘Ž = 𝑏 𝑐 𝑐 15. If π‘Ž > 𝑏, 𝑐 < 0 then (a) π‘Ž < 𝑏 (d) π‘Ž β‰  𝑏 𝑐 𝑐 (b) π‘Ž > 𝑏 (a) identity (b) conditional (c) inconsistent (d) none 25. π‘₯ = π‘₯ + 5 is equation: (a) identity (b) conditional 𝑐 𝑐 𝑐 𝑐 (c) π‘Ž = 𝑏 (d) π‘Ž ≀ 𝑏 (c) inconsistent (d) none 𝑐 𝑐 𝑐 𝑐 16. If π‘Ž, 𝑏 ∈ R, 𝑏 β‰  0 then 26. Equations having exactly the same solution are called solution. π‘Ž | | = 𝑏 |π‘Ž| |𝑏| (b) |π‘Žπ‘| = |π‘Ž| |𝑏| (a) equivalent (b) linear (c) inconsistent (d) inequation (c) |π‘Ž + 𝑏| = |π‘Ž| + |𝑏| (d) |π‘Ž βˆ’ 𝑏| = |π‘Ž| βˆ’ |𝑏| 17. When the variable in an equation occurs under a radical, the equation is called equation. (a) radical (b) absolute value (c) linear (d) none of these 27. A solution that does not satisfy the original equation is called solution. (a) extraneous (b) root (c) general (d) proper (a)
  11. 11. 1 b 2 c 3 c 4 b 5 c 6 d 7 a 8 a 9 a 10 a 11 a 12 a 13 b 14 a 15 a 16 a 17 a 18 a 19 a 20 a 21 c 22 c 23 a 24 b 25 c 26 a 27 a (b) (d) CHAPTER 07 LINEAR GRAPH AND THEIR APPLICATION Choose the correct answer from the options given in each question. 1. If (π‘₯ βˆ’ 1, 𝑦 + 1) = (0,0), then (π‘₯, 𝑦) is: (a) (1, βˆ’1) (b) (βˆ’1,1) (c) (1,1) (d) (βˆ’1, βˆ’1) 2. If (π‘₯, 0) = (0, 𝑦), then (π‘₯, 𝑦) is: (a) (0,1) (b) (1,0) (c) (0,0) (d) (1,1) 3. Point (2, βˆ’3) lies in quadrant. (a) I (b) II (c) III (d) IV 4. Point (βˆ’3, βˆ’3) lies in quadrant. (a) I (b) II (c) III (d) IV 5. If 𝑦 = 2π‘₯ + 1, π‘₯ = 2 then 𝑦 is: (a) 2 3 (c) 4 5 6. Which ordered pair satisfy the equation 𝑦 = 2π‘₯: (a) (1,2) (b) (2,1) (c) (2,2) (d) (0,1) 7. The real number π‘₯, 𝑦 of the ordered pair (π‘₯, 𝑦) are called of point 𝑃(π‘₯, 𝑦) in a plane. (a) co-ordinate (b) π‘₯ co-ordinate (c) 𝑦-co-ordinate (d) ordinate 8. Cartesian plane is divided into quadrants. (a) two (b) three (c) four (d) five MULTIPLE CHOICE QUESTIONS
  12. 12. 1 a 2 c 3 d 4 c 5 d 6 a 7 a 8 c 9 a 10 b 11 d 12 a 13 a 14 a 15 b 16 a 17 d 18 c 19 d 20 a 9. The point of intersection of two coordinate axes is called: (a) origin (b) centre (c) π‘₯-coordinate (d) ordinate 10. The π‘₯-coordinate of a point is called (a) origin (b) abscissa (c) 𝑦-coordinate (d) ordinate 11. The 𝑦-coordinate of a point is called (a) origin (b) π‘₯-coordinate (c) 𝑦-coordinate (d) ordinate 12. The set of points which lie on the same line are called points. (a) collinear (b) similar (c) common (d) none of these 13. The plane formed by two straight lines perpendicular to each other is called: (a) cartesian plane (b) coordinate axes (c) plane (d) none of these 14. An ordered pair is a pair of elements in which elements are written in specific: (a) order (b) array (c) point (d) none 15. Point (βˆ’1,2) lies in quadrant. (a) I (b) II (c) III (d) IV 16. Point (1,1) lies in quadrant. (a) I (b) II (c) III (d) IV 17. Point (1, βˆ’3) lies in quadrant. (a) I (b) II (c) III (d) IV 18. Which of the following points is one the origin? (a) (0,0) (b) (βˆ’2, βˆ’3) (c) (0,2) (d) (4,0) 19. Which of the following lines is parallel to π‘₯-axis? (a) π‘₯ = 0 (b) π‘₯ = βˆ’3 (c) π‘₯ = 3 (d) 𝑦 = βˆ’3 20. Which of the following lines is parallel to 𝑦-axis? (a) 𝑦 = 2π‘₯ (b) π‘₯ = βˆ’3 (c) 𝑦 = 3 (d) 𝑦 = 4π‘₯ + 1
  13. 13. (a) CHAPTER 08 QUADRATIC EQUATION (c) {Β±2} (d) Β±2 9. An equation of the form 2π‘₯4 βˆ’ 3π‘₯3 + 7π‘₯2 βˆ’ 3π‘₯ + 2 = 0 is called a/an: (a) reciprocal equation (b) radical equation (c) exponential equation (d) none of these 10. The solution set of 25π‘₯2 βˆ’ 1 = 0 is: 1 {Β± } 5 (b) 1 {βˆ’ } 5 Choose the correct answer from the options given in each question. (c) { 1 } 5 (d) none of these 1. Standard form of quadratic equation is: (a) 𝑏π‘₯ + 𝑐 = 0, 𝑏 β‰  0 (b) π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0, π‘Ž β‰  0 (c) π‘Žπ‘₯2 = 𝑏π‘₯, π‘Ž β‰  0 (d) π‘Žπ‘₯2 β‰  0, π‘Ž β‰  0 11. An equation of the form 22π‘₯ βˆ’ 3. 2π‘₯ + 5 = 0 is called a/an: (a) exponential equation (b) radical equation (c) reciprocal equation (d) none of these 2. The number of terms in a standard quadratic equation is: (a) 1 (b) 2 (c) 3 (d) 4 π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0 12. The solution set of the equation π‘₯2 βˆ’ 9 = 0 is: (a) {Β±3} (b) {3} (c) {βˆ’3} (d) {9} 13. An equation of the form π‘₯4 + π‘₯3 + π‘₯2 + π‘₯ + 1 = 0 is called a/an 3. The number of methods to solve a quadratic equation is: (a) 1 (b) 2 (c) 3 (d) 4 4. The quadratic formula is: equation: (a) radical (b) reciprocal (c) exponential (d) none of these 14. Solution set of the equation 51+π‘₯ + 51βˆ’π‘₯ = 26 is: βˆ’π‘Β±βˆšπ‘2βˆ’4π‘Žπ‘ (b) 2π‘Ž π‘Β±βˆšπ‘2βˆ’4π‘Žπ‘ 2π‘Ž (a) {1} (b) {Β±1} (c) {2} (d) {Β±2} (c) βˆ’π‘Β±βˆšπ‘2+4π‘Žπ‘ (d) π‘Β±βˆšπ‘2+4π‘Žπ‘ 15. The solution set of the equation 2 + 9π‘₯ = 5π‘₯2 is: 2π‘Ž 2π‘Ž 1 1 5. Two linear factors of π‘₯2 βˆ’ 15π‘₯ + 56 = 0 are: (a) (π‘₯ βˆ’ 7) and (π‘₯ + 8) (b) (π‘₯ + 7) and (π‘₯ βˆ’ 8) (c) {βˆ’ , 2} (b) { 5 5 1 , 2} 1 { , βˆ’2} (d) {βˆ’ 5 5 , βˆ’2} (c) (π‘₯ βˆ’ 7) and (π‘₯ βˆ’ 8) (d) (π‘₯ + 7) and (π‘₯ + 8) 6. An equation, which remains unchanged when π‘₯ is replaced by 1 is called π‘₯ a/an: (a) exponential equation (b) reciprocal equation (c) radical equation (d) none of these 7. An equation of the type 3π‘₯ + 32βˆ’π‘₯ + 6 = 0 is a/an: (a) exponential equation (b) reciprocal equation (c) radical equation (d) none of these 8. The solution set of equation 4π‘₯2 βˆ’ 16 = 0 is: (a) {Β±4} (b) {4} 16. The solution set of the equation 5π‘₯2 = 30π‘₯ is: (a) {5,30} (b) {0,6} (c) {0, βˆ’6} (d) {5,0} 17. The solution set of the equation π‘₯2 βˆ’ π‘₯ βˆ’ 2 = 0 is: (a) {2,1} (b) {βˆ’2,1} (c) {2, βˆ’1} (d) {βˆ’2, βˆ’1} 18. The solution set of the equation π‘₯2 βˆ’ 16 = 0 is: (a) {Β±4} (b) {4} (c) {βˆ’4} (d) none of these 19. The solution set of the equation π‘₯2 βˆ’ 7π‘₯ + 6 = 0 is: MULTIPLE CHOICE QUESTIONS (a) (a)
  14. 14. 1 b 2 c 3 c 4 a 5 C 6 b 7 a 8 c 9 a 10 A 11 a 12 a 13 b 14 b 15 A 16 b 17 c 18 a 19 a 20 A 21 A 22 c 23 c 24 b 25 B 26 B 27 b 28 a 29 b 30 A 31 B 32 a 33 d 34 a 35 C (a) {1,6} (b) {βˆ’1, βˆ’6} (c) {βˆ’1,6} (d) {1, βˆ’6} 20. The solution set of the equation 3π‘₯2 + 4π‘₯ = 5 is: (c) add 7 in both sides (d) subtract 7 from both sides 30. What should be done to make the coefficient of π‘₯2 to 1 in 3π‘₯2 + 7π‘₯ = 0? (a) { βˆ’2±√19 } (b) 2±√19 (a) multiply the equation by 1 (b) divide the equation by 1 3 { 3 } 3 3 4±√19 (c) add 1 in both sides (d) subtract 1 from both sides (c) { } (d) none of these 3 3 3 21. If 𝑏 = 0 in a quadratic equation π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0, then it is called: (a) pure quadratic equation (b) linear equation (c) quadratic equation (d) exponential equation 22. Sentences involving the sign between the algebraic expressions are called equations: (a) < (b) β‰₯ (c) = (d) < or > 23. The standard from of the quadratic equation is π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0 where 31. The value of variable of an equation not satisfying the equation is called: (a) root (b)extraneous root (c) exponent (d) solution set 32. The cancellation of π‘₯ on both sides of the equation π‘Žπ‘₯2 = 𝑏π‘₯ means the loss of one root. That root is always equal to: (a) 0 (b) 1 (c) A (d) b 33. If 𝑦 = π‘₯βˆ’1 and 3𝑦 = 5, the value of π‘₯ is: a, b, c are: (a) irrational numbers (b) rational numbers (c) real numbers (d) whole numbers (a) 5 3 (c) βˆ’ 3 5 34. If 2π‘₯ = 1, then π‘₯ = (b) βˆ’ 5 3 24. If π‘Ž = 0 in π‘Žπ‘₯2 + 𝑏π‘₯ + 𝑐 = 0, then it reduces to: (a) pure quadratic equation (b) linear equation (c) quadratic equations (d) exponential equation 25. How many linear factors a quadratic equation has? (a) 1 (b) 2 (c) 3 (d) 4 26. What is the degree of quadratic equation? (a) 1 (b) 2 (c) 3 (d) 4 27. The number of roots of a quadratic equation is: (a) 1 (b) 2 (c) 3 (d) 4 28. cancellation of π‘₯ on both sides of 5π‘₯2 = 30π‘₯ means: (a) the loss of one root (b) no loss of any root (c) gain of one root (d) undefined solution 29. What should be done to make the coefficient of π‘₯2 equal to 1, in 7π‘₯2 + 2π‘₯ βˆ’ 1 = 0? (a) multiply the equation by 7 (b) divide the equation by 7 (a) 0 (b) 1 (c) 2 (d) 3 35. If 𝑦 = 2π‘₯ and 8𝑦 = 1, then π‘₯ = . (a) 8 (b) 1 8 (d) βˆ’3 (d) 3 5 (c) 3
  15. 15. MULTIPLE CHOICE QUESTIONS CHAPTER 09 CONGRUENT TRIANGLES Choose the correct answer from the options given in each question. 1. triangle is an equiangular triangle. (c) β‰… (d) = 10. How many end points does a ray have? (a) 1 (b) 2 (c) 3 (d) 4 11. Symbolically two congruent triangles ABC and PQR are written as: (a) βˆ†ABC = βˆ†PQR (b) βˆ†ABC ∼ βˆ†PQR (c) βˆ†ABC β‰… βˆ†PQR (d) βˆ†ABC β‰  βˆ†PQR 12. Which of the following is possible? (a) S. S. S β‰… S. S. S (b) S. A. A β‰… S. A. A (a) a scalene (b) an isosceles (c) an equilateral (d) a right triangle 2. A has two end points. (a) line (b) line segment (c) ray (d) angle 3. Three points are said to be collinear if they lie on the same: (a) plane (b) line (c) interior (d) area 4. Two lines can intersect at: (a) one point (b) two points (c) no point (d) infinite points 5. Two lines cannot intersect each other: (a) perpendicular (b) parallel (c) non-parallel (d) coplanar 6. All the medians of triangle are equal in measure. (a) a scalene (b) an isosceles (c) an equilateral (d) a right angled 7. If two angles of a triangle are congruent then the sides opposite to them are (a) congruent (b) equal (c) non congruent (d) similar 8. symbol for congruent is: (a) ↔ (b) N (c) β‰… (d) = 9. symbol for correspondence is: (b) N (c) H. S β‰… H. S (d) S. A. S 13. If sum of measures of two angles is 180Β° then angles are angles. (a) complementary (b) supplementary (c) equal (d) right 14. If sum of measures of two angles is 90Β° then angles are angles. (a) complementary (b) supplementary (c) congruent (d) acute 15. Hypotenuse is a side opposite to in right angles triangle. (a) 30Β° (b) 60Β° (c) 90Β° (d) 120Β° 16. In equilateral triangle each angle is of . (a) 30Β° (b) 60Β° (c) 90Β° (d) 180Β° 17. Corresponding sides of congruent triangles are: (a) equal (b) different (c) perpendicular (d) parallel 18. Median bisecting the base angle of an isosceles triangle bisects the angle. (a) base (b) vertical (c) right (d) acute 19. The median bisecting the base of an isosceles triangle is to the base. (a) parallel (b) perpendicular (c) collinear (d) adjacent 20. Corresponding angles of congruent triangles are: (a) ↔
  16. 16. 1 c 2 b 3 b 4 a 5 b 6 c 7 a 8 c 9 a 10 a 11 c 12 d 13 b 14 a 15 c 16 b 17 a 18 b 19 b 20 a 21 b 22 c MULTIPLE CHOICE QUESTIONS (a) congruent (b) non- congruent (c) unequal (d) supplementary 21. Any two medians of an triangle equal in measure. (a) isosceles (b) equilateral (c) acute (d) obtuse 22. Sum of all the interior angles of a triangle is: (a) 90Β° (b) 150Β° (c) 180Β° (d) 360Β° CHAPTER 10 PARALLELOGRAMS AND TRIANGLES Choose the correct answer from the options given in each question. 1. In a parallelogram opposite sides are (a) different (b) perpendicular (c) congruent (d) intersecting 2. In a parallelogram opposite angles are (a) parallel (b) congruent (c) complementary (d) adjacent 3. Diagonals of a parallelogram each other. (a) perpendicular (b) intersect (c) equal to (d) parallel 4. Medians of triangle are . (a) equal (b) concurrent (c) congruent (d) parallel 5. Diagonal of a parallelogram divides the parallelogram into triangles. (a) two equal (b) two different (c) three different (d) three equal 6. In a parallelogram show in figure, 𝑦0 = (a) 115Β° (b) 90Β° (d) 105Β° (c) 75Β°
  17. 17. 1 c 2 b 3 b 4 b 5 a 6 c 7 d 8 b 9 c 10 b 11 a 12 a (a) 8 (c) 2 7. In a parallelogram shown in figure, π‘₯0 = (a) 115Β° (b) 90Β° (c) 75Β° (d) 105Β° 8. In a parallelogram shown in figure, π‘₯0 = (a) 55Β° (c) 44Β° (d) 125Β° 9. In a parallelogram shown in figure, π‘š = (b) 10 (d) 4 10. In a βˆ†ABC, ED||BC where E and D are midpoints of the sides AB and AC respectively. Find the value of π‘šDE. (a) 6 cm (b) 9 cm (c) 18 cm (d) 10 cm 11. In parallelogram, congruent parts are: (a) opposite sides (b) diagonals (c) opposite angles (d) opposite sides and angles 12. Alternate angles on parallel lines intersected by a transversal are . (a) congruent (b) non-congruent (c) complementary (d) supplementary (b) 5Β°
  18. 18. 1 a 2 a 3 a 4 a 5 a 6 c 7 b 8 c 9 a 10 c 11 a 12 b 13 c 14 b MULTIPLE CHOICE QUESTIONS CHAPTER 11 LINE BISECTORS AND ANGLE BISECTORS Choose the correct answer from the options given in each question. 1. Bisection means to divide into equal parts. 8. If ⃑ C Μ…Μ…D Μ…β†’ is right bisector of line segment AB then π‘šAQ = (a) π‘šOA (b) π‘šOB (c) π‘šBQ (d) π‘šOD 9. The right bisectors of the sides of an acute triangle intersects each other the triangle. (a) inside (b) outside (c) midpoint (d) none 10. The right bisectors of the sides of a right triangle intersect each other on the . (a) vertex (b) midpoint (c) hypotenuse (d) none (a) two (b) three 11. The right bisectors of the sides of an obtuse triangle intersect each other (c) four (d) five the triangle. 2. of line segment means to draw perpendicular which passes through the midpoint of line segment. (a) right bisection (b) bisection (c) congruent (d) mid-point 3. Any point on the of a line segment is equidistant from its end points. (a) right bisector (b) median (c) angle bisector (d) altitude 4. Any point equidistant from the end points of line segment is on the _. (a) right bisector (b) median (c) angle bisector (d) altitude 5. The bisectors of the angles of a triangle are: (a) concurrent (b) congruent (c) parallel (d) none of these 6. Bisection of an angle means to draw a ray to divide the given angle into equal parts. (a) four (b) three (c) two (d) five 7. If ⃑ C Μ…Μ…D Μ…β†’ is right bisector of line segment AB then π‘šOA = (a) π‘šOQ (b) π‘šOB (c) π‘šAQ (d) π‘šBQ (a) outside (b) inside (c) midpoint (d) none 12. The point of line segment through which the right bisector passes is called its point. (a) end (b) mid (c) non-collinear (d) trisection 13. The point of intersection of right bisectors of sides of a triangle is equidistant from the of triangle. (a) sides (b) vertices (c) centre (d) angles 14. The altitudes of a triangle are . (a) congruent (b) concurrent (c) equal (d) parallel
  19. 19. (b) 90Β° MULTIPLE CHOICE QUESTIONS CHAPTER 12 SIDES AND ANGLES OF A TRIANGLE Choose the correct answer from the options given in each question. 1. Which of the following sets of lengths can be lengths of the sides of a triangle: (a) greater (b) smaller (c) equal (d) none 9. The distance between a line and a point on it is . (a) zero (b) one (c) equal (d) none 10. The difference of two sides of a triangle is the third side. (a) greater than (b) smaller than (c) equal to (d) congruent to 11. In a triangle, the side opposite to greater angle is . (a) smaller (b) greater (c) equal (d) congruent 12. In a triangle the angles opposite to congruent sides are . (a) 2cm, 3cm, 5cm (b) 3cm, 4cm, 5cm (c) 2cm, 4cm, 7cm (d) 1cm, 2cm, 3cm 2. Two sides of a triangle measure 10cm and 15cm. Which of the following measure is possible for the third side (a) 5 cm (b) 20 cm (c) 25 cm (d) 30 cm 3. The angle opposite to the longer side is (a) greater (b) shorter (c) equal (d) none 4. In right angle triangle greater angle of: (a) 60Β° (b) 30Β° (c) 75Β° (d) 90Β° 5. In an isosceles right-angles triangle angles other than right angle are each of: (a) 40Β° (b) 45Β° (c) 50Β° (d) 55Β° 6. A triangle having two congruent sides is called triangle. (a) equilateral (b) isosceles (c) right (d) none (a) congruent (b) concurrent (c) unequal (d) none 13. In a triangle, the side opposite to smaller angle is . (a) smaller (b) greater (c) congruent (d) concurrent 14. An exterior angle of a triangle is non-adjacent interior angle. (a) equal to (b) smaller than (c) greater than (d) congruent to 15. For a βˆ†ABC, which of the following is true? (a) π‘šAB + π‘šBC < π‘šCA (b) π‘šAB βˆ’ π‘šBC > π‘šCA (c) π‘šAB + π‘šBC > π‘šCA (d) π‘šAB + π‘šBC π‘˜ π‘šCA 16. What is the supplement of a right angle? (a) 60Β° (c) 120Β° (d) 180Β° 17. The sum of the measures of two sides of a triangle is greater than the measure of the median which bisects the third side. (a) twice (b) thrice (c) hypotenuse (d) angles 18. In an obtuse angled triangle, the side opposite to the obtuse angle is 7. Perpendicular to line from an angle of . than each of the other two sides. (a) 30Β° (b) 60Β° (c) 90Β° (d) 120Β° 8. Sum of two sides of triangle is than the third. (a) smaller (b) longer (c) twice (d) thrice
  20. 20. 1 b 2 b 3 a 4 d 5 b 6 b 7 c 8 a 9 a 10 b 11 b 12 a 13 a 14 c 15 c 16 b 17 a 18 b CHAPTER 13 PRACTICAL GEOMETRY- TRIANGLES Choose the correct answer from the options given in each question. 1. In a right angled triangle, the square of the length of hypotenuse is equal to the of the squares of the lengths of the other two sides. (a) sum (b) difference (c) zero (d) none of these 2. If the square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a triangle. (a) right angles (b) acute angled (c) obtuse angles (d) none of these 3. Let c be the longest of the sides a, b and c of a triangle. If π‘Ž2 + 𝑏2 = 𝑐2, then the triangle is : (a) right (b) acute (c) obtuse (d) none of these 4. Let c be the longest of the sides a, b and c of a triangle. If π‘Ž2 + 𝑏2 > 𝑐2, then the triangle is : (a) acute (b) right (c) obtuse (d) none of these 5. Let c be the longest of the sides a, b and c of a triangle. If π‘Ž2 + 𝑏2 < 𝑐2, then the triangle is : (a) acute (b) right (c) obtuse (d) none of these 6. If 3cm and 4cm are two sides of a right angled triangle, then hypotenuse is: (a) 5cm (b) 3cm (c) 4cm (d) 2cm 7. In right triangle is a side opposite to right angle. MULTIPLE CHOICE QUESTIONS
  21. 21. 1 a 2 a 3 a 4 a 5 c 6 a 7 c 8 b 9 c 10 b 11 c 12 b 13 a 14 c 15 b 16 b (a) base (b) perpendicular (c) hypotenuse (d) none 8. In the figure, the value of π‘₯ is (a) 6cm (b) 8cm (c) 10cm (d) 16cm 9. In the figure, the value of π‘₯ is (a) 5cm (b) 8cm (c) 12cm (d) 18cm 10. In the figure, the value of π‘₯ is (a) 2cm (b) 1cm (c) √2cm (d) 3cm 11. In right angles triangle greater angle is . (a) 30Β° (b) 60Β° (c) 90Β° (d) 120Β° 12. In right angled triangle on angle is 90Β° and other two angles are . (a) obtuse (b) acute (c) right (d) supplementary 13. If hypotenuse of an isosceles right angled triangle is √2 then each of other side is: (a) 1cm (b) 2cm (c) 3cm (d) 4cm 14. In right angled triangle which side is the longest side? (a) perpendicular (b) base (c) hypotenuse (d) none of these 15. In right angled triangle, if π‘šβˆ B = 90Β° then which of the following is true? (a) π‘Ž2 + 𝑏2 = 𝑐2 (b) π‘Ž2 + 𝑐2 = 𝑏2 (c) 𝑏2 + 𝑐2 = π‘Ž2 (d) π‘Ž2 βˆ’ 𝑐2 = 𝑏2 16. In an isosceles right angled triangle two acute angles are equal to: (a) 30Β° (b) 45Β° (c) 60Β° (d) 90Β°
  22. 22. THEOREMS CHAPTER 14 RELATED WITH (a) 18cm (b) 9cm (c) 18cm2 (d) 9cm2 8. Area of given figure is . AREA Choose the correct answer from the options given in each question. 1. the region enclosed by the bounding lines of a closed figure is called the of the figure: (a) area (b) circle (c) boundary (d) none of these 2. Base Γ— altitude = (a) 4 cm (b) 8cm2 (c) 16cm (d) 16cm2 9. Area of given figure is . (a) area of parallelogram (b) area of rectangular (c) area of square (d) area of triangle 3. The union of a rectangle and its interior is called: (a) circle region (b) rectangular region (c) triangle region (d) none of these 4. If a is the side of a square, its area will be equal to . (a) a square unit (b) π‘Ž2 square unit (c) π‘Ž3 square unit (d) π‘Ž4 square unit 5. The union of a triangle and its interior is called as: (a) 4cm2 (c) 32cm 10. Area of given figure is . 12cm2 32cm2 (a) triangular region (b) rectangular region (c) circle region (d) none of these 6. Altitude of a triangle means perpendicular distance to base from its opposite . (a) 160cm2 (b) 80cm2 (c) 80cm (d) 160cm 11. Area of triangle is . 1 A = (a) vertex (b) side Base Γ— Heigth (b) A = Base Γ— Heigth 2 (c) midpoint (d) none of these 7. Area of given figure is: (c) A = L Γ— W (d) A = L2 12. Area of square is . (a) A = 1 Base Γ— Heigth (b) A = Base Γ— Heigth 2 (c) A = L Γ— W (d) A = L2 13. Area of rectangle is . (a) A = 1 Base Γ— Heigth (b) A = Base Γ— Heigth 2 MULTIPLE CHOICE QUESTIONS (b) (d) (a)
  23. 23. 1 a 2 a 3 b 4 b 5 a 6 a 7 c 8 d 9 d 10 b 11 a 12 d 13 c 14 b 15 b 16 b 17 a 18 b MULTIPLE CHOICE QUESTIONS (c) A = L Γ— W (d) A = L2 (a) A = 1 Base Γ— Heigth (b) A = Base Γ— Heigth 2 (c) A = L Γ— W (d) A = L2 15. If the length and breadth of a rectangle are β€˜a’ and β€˜b’ then its area will be: (a) π‘Ž + 𝑏 (b) π‘Ž Γ— 𝑏 (c) π‘Ž βˆ’ 𝑏 (d) π‘Ž = 𝑏 16. In most cases similar figures have areas. (a) same (b) different (c) equal (d) congruent 17. All congruent figures have areas. (a) same (b) different (c) zero (d) non-congruent 18. Area of a geometrical figure is always real number. (a) zero (b) positive (c) negative (d) rational PROJECTION OF A SIDE OF A TRIANGLE Choose the correct answer from the options given in each question. 1. A triangle having two sides congruent is called . (a) scalene (b) right angled (c) equilateral (d) isosceles 2. A quadrilateral having each angle equal to 90Β° is called . (a) parallelogram (b) rectangle (c) trapezium (d) rhombus 3. The right bisectors of the three sides of a triangle are . (a) congruent (b) collinear (c) concurrent (d) parallel 4. The altitudes of an isosceles triangle are congruent: (a) two (b) three (c) four (d) none of these 5. A point equidistant from the end points of a line segment is on its . (a) bisector (b) right bisector (c) perpendicular (d) median 6. congruent triangles can be made by joining the midpoints of the sides of a triangle. (a) three (b) four (c) five (d) two 7. The diagonals of a parallelogram each other. (a) bisect (b) bisect at right angle (c) trisect (d) none of these 8. The medians of a triangle cut each other in the ratio: (a) 4: 1 (b) 3: 1 . 14. Area of parallelogram is CHAPTER 15
  24. 24. (c) 2: 1 (d) 1: 1 9. One angle on the base of an isosceles triangle is 30Β°. What is the measure of its vertical angle: (a) 30Β° (b) 60Β° (c) 90Β° (d) 120Β° 10. If the three altitudes of a triangle are congruent then triangle is: (a) equilateral (b) right angled (c) isosceles (d) acute angled 11. If two medians if a triangle are congruent then the triangle will be: (a) isosceles (b) equilateral (c) right angled (d) acute angled 12. a line segment joining a vertex of a triangle to the midpoint of its opposite side is called a of the triangle. (a) altitude (b) median (c) angle bisector (d) right bisector 13. A line segment from a vertex of triangle perpendicular to the line containing the opposite side, is called an of the triangle: (a) altitude (b) median (c) angle bisector (d) right bisector 14. The point of concurrency of the three altitudes of a βˆ† is called its . (a) ortho-centre (b) in-centre (c) circum-centre (d) none 15. The internal bisectors of the angles of a triangle meet at a point called the of the triangle. (a) in-centre (b) ortho-centre (c) circum-centre (d) none 16. The point of concurrency of the three perpendicular bisectors of the sides of (a) concurrent (b) congruent (c) mid-point (d) vertical angle 17. Point of concurrency of three medians of a triangle is called (a) in-centre (b) ortho-centre (c) centroid (d) circum-centre (a) 60Β° (b) 120Β° (c) 180Β° (d) 240Β° 19. The side opposite to right angle in right angled triangle is called . (a) base (b) perpendicular (c) hypotenuse (d) altitude 20. The altitudes of a right angled triangle are concurrent at the . (a) mid-point of hypotenuse (b) vertex of right angle (c) mid-point of base (d) vertical 21. The triangle are said to be if they are equiangular. (a) congruent (b) similar (c) equal (d) scalene 22. All the right bisectors of sides of triangle are concurrent. (a) one (b) two (c) three (d) four 23. All the three bisectors of angles of a triangle are . (a) congruent (b) concurrent (c) parallel (d) perpendicular 24. All the three medians of a triangle are . (a) congruent (b) concurrent (c) parallel (d) perpendicular 25. All the three altitudes of a triangle are . (a) congruent (b) concurrent (c) parallel (d) perpendicular 26. In-centre is the point of concurrency of three of triangle. (a) right bisectors (b) angle bisectors (c) altitudes (d) medians 27. Circum-centre is point of concurrency of three - of triangle. (a) right bisectors (b) angle bisectors (c) altitudes (d) medians 28. Centroid is the point of concurrency of three of triangle. (a) right bisectors (b) angle bisectors (c) altitudes (d) medians 29. Three or more than three line passing through the same point are called 18. sum of interior angles of a triangle is . lines.
  25. 25. 1 d 2 b 3 c 4 a 5 b 6 b 7 a 8 c 9 d 10 a 11 a 12 b 13 a 14 a 15 a 16 a 17 c 18 c 19 c 20 b 21 b 22 c 23 b 24 b 25 b 26 b 27 a 28 d 29 b 30 b 31 d 32 b (a) congruent (b) concurrent (c) parallel (d) perpendicular 30. The common point of three or more than three lines is called . (a) central point (b) point of concurrency (c) vertex (d) centroid 31. In right angled triangle if one angle is 30Β°, then other angle will be . CHAPTER 16 INTRODUCTION TO COORDINATE GEOMETRY/ (a) 15Β° (c) 45Β° 30Β° 60Β° ANALYTICAL GEOMETRY 32. In right angled triangle if one angle is 60Β°, then other angle will be . (a) 15Β° (b) 30Β° (c) 45Β° (d) 60Β° Choose the correct answer from the options given in each question. 1. Distance between points (0,0) and (1,1) is: (a) 0 (b) 0 (c) √2 (d) 2 2. Distance between points (1,0) and (0,1) is: (a) 0 (b) 0 (c) √2 (d) 2 3. Mid-point of the points (2,2) and (0,0) is: (a) (1,1) (b) (1,0) (c) (0,1) (d) (βˆ’1, βˆ’1) 4. Mid-point of the points (2, βˆ’2) and (βˆ’2,2) is: (a) (2,2) (b) (βˆ’2, βˆ’2) (c) (0,0) (d) (1,1) 5. A triangle having all sides equal is called: (a) isosceles (b) scalene (c) equilateral (d) none of these 6. A triangle having all sides different is called: (a) isosceles (b) scalene (c) equilateral (d) none of these 7. The points P, Q and R are collinear if: (a) |PQ| + |QR| = |PR| (b) |PQ| βˆ’ |QR| = |PR| (c) |PQ| + |QR| = 0 (d) none of these 8. The distance between points P(π‘₯1, 𝑦1) and P(π‘₯2, 𝑦2) in the coordinate plane is: 𝑑 > 0 MULTIPLE CHOICE QUESTIONS (b) (d)
  26. 26. 1 c 2 c 3 a 4 c 5 c 6 b 7 a 8 a 9 a 10 b 11 a 12 c 13 b 14 b 15 a 16 b (a) 𝑑 = √(π‘₯2 βˆ’ π‘₯1)2 + (𝑦2 βˆ’ 𝑦1)2 (b) 𝑑 = √(π‘₯1 βˆ’ π‘₯2)2 βˆ’ (𝑦1 βˆ’ 𝑦2)2 (c) 𝑑 = √(π‘₯2 βˆ’ π‘₯1)2 βˆ’ (𝑦2 βˆ’ 𝑦1)2 (d) 𝑑 = √(π‘₯1 + π‘₯2)2 βˆ’ (𝑦1 + 𝑦2)2 9. A triangle having two sides equal is called: (a) isosceles (b) scalene (c) equilateral (d) none of these 10. A right triangle is that in which one of the angles has measure equal to: (a) 80Β° (b) 90Β° (c) 45Β° (d) 60Β° 11. In a right angled triangle ABC, where π‘šβˆ ACB = 90Β°. (a) |AB|2 = |BC|2 + |CA|2 (b) |AB|2 = |BC|2 βˆ’ |CA|2 (c) |AB|2 + |BC|2 > |CA|2 (d) |AB|2 βˆ’ |BC|2 > |CA|2 12. In a βˆ†ABC, if |AB| = |BC| = |CA|, the triangle will be: (a) isosceles (b) scalene (c) equilateral (d) right-angled 13. If three or more than three points lie on the same line then points are called (a) non-collinear (b) collinear (c) parallel (d) perpendicular 14. A has two end points. (a) line (b) line segment (c) ray (d) triangle 15. A line segment has midpoint. (a) one (b) two (c) three (d) four 16. Each side of triangle has collinear vertices. (a) one (b) two (c) three (d) four

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