A message from Competitive Study! 2022 - 2023 Dear Candidate, We have prepared this data for you by using all our ability, after reading it you will surely crack the test, now only your hard work is left, if you prepare these questions, you will pass easily. May Allah make it easy for you. 1. For any complex number ๐, it is always true that |๐| is equal to: (a) |๐ง| (b) | − ๐ง| (c) | − ๐ง| (d) โ all of these 2. The numbers which can be written in the form of ๐ , ๐, ๐ ∈ ๐ , ๐ ≠ ๐ are : (a) โRational number (b) Irrational number (c) Complex number (d) Whole number 3. A decimal which has a finite numbers of digits in its decimal part is called______ decimal. (a) โTerminating (b) Non-Terminating (c) Recurring (d) Non recurring 4. ๐. ๐๐๐ …. Is (a) Rational (b) Irrational (c) an integer (d) a prime number 5. ๐ is (a) Rational (b) โ Irrational (c) Natural number (d) None 6. ๐๐ ๐ is (a) โRational (b) Irrational (c) an integer (d) a whole number 7. Multiplicative inverse of ′๐′ is (a) 0 (b) any real number (c) โ not defined (d) 1 8. If ๐ is any non-zero real number, then multiplicative inverse is (a) – ๐ (b) โ 1 ๐ (c) − 1 ๐ (d) not defined 9. For all ๐ ∈ , ๐ = ๐ is …. Property. (a) โReflexive (b) Symmetric (c) Transitive (d) Trichotomy 10. For all ๐, ๐ ∈ , ๐ = ๐ โน ๐ = ๐ is called….. property. (a) Reflexive (b) โ Symmetric (c) Transitive (d) Trichotomy 11. Golden rule of fraction is that for ๐ ≠ ๐, ๐ ๐ = (a) โ ๐๐ ๐๐ (b) ๐๐ ๐ (c) ๐๐ ๐ (d) ๐๐ ๐ 12. The set {๐, −๐} possesses closure property ๐. ๐. ๐ (a) ′ + ′ (b) โ ′ × ′ (c) ′ ÷ ′ (d) ′ − ′ 13. If ๐ < ๐ then (a) ๐ < ๐ (b) 1 ๐ < 1 ๐ (c) โ 1 ๐ > 1 ๐ (d) ๐ − ๐ > 0 14. The additive identity in set of complex number is (a) โ(0,0) (b) (0,1) (c) (1,0) (d) (1,1) 15. The multiplicative identity of complex number is (a) (0,0) (b) (0,1) (c) โ (1,0) (d) (1,1) 16. The modulus of ๐ = ๐ + ๐๐ is (a) √๐ + ๐ (b) โ√๐ 2 + ๐2 (c) ๐ − ๐ (d) √๐2 − ๐2 17. ๐ ๐๐ equals: (a) โ๐ (b) – ๐ (c) 1 (d) -1 18. The multiplicative inverse of (๐, −๐) is: (a) (− 4 65 , − 7 65 ) (b) (− 4 65 , 7 65 ) (c) ( 4 65 , − 7 65 ) (d) โ( 4 65 , 7 65 ) 19. (๐, ๐)(๐, ๐) = (a) 15 (b) โ-15 (c) −8๐ (d) 8๐ 20. (−๐) − ๐๐ ๐ = (a) ๐ (b) โ – ๐ (c) 1 (d) -1 21. √๐ is __________ (a) Rational (b) โ Irrational (c) Integer (d) Prime 22. Product √−๐ × √−๐ is equal to _____ (a) -2 (b) โ2 (c) 0 (d) 4 23. The imaginary part of the complex number ( , ๐) is _________ (a) โ๐ (b) ๐ (c) ๐๐ (d) None of these 24. If ๐ = −๐ − ๐ then ๐ =______ (a) (−1, −1) (b) โ(−1,1) (c) (1, −1) (d) (1,1) 25. The property ๐. ๐ + (−๐. ๐) = ๐ is______ (a) Commutative (b)‘.’ Inverse (c) โ ‘ + ’ inverse (d) Associative 26. If ๐ = ๐ then multiplicative inverse of ๐ is (a) 0 (b) 1 (c) 1 ๐ฅ (d) โ None of these 27. (−๐) ๐๐ =_______ (a) 1 (b) -1 (c) โ ๐ (d) – ๐ 28. ---------------------------------------------------------------------------------------------------------------------------------------- 1. If ๐ ∈ ๐ณ ∪ ๐ด then (a) ๐ฅ ∉ ๐ฟ ๐๐ ๐ฅ ∉ ๐ (b) ๐ฅ ∉ ๐ฟ ๐๐ ๐ฅ ∈ ๐ (c) ๐ฅ ∈ ๐ฟ ๐๐ ๐ฅ ∉ ๐ (d) โ๐ฅ ∈ ๐ฟ ๐๐ ๐ฅ ∈ ๐ 2. Total number of subsets that can be formed from the set {๐, ๐, ๐} is (a) 1 (b) โ 8 (c) 5 (d)2 3. If ๐ ∈ ๐ฉ′ = ๐ผ − ๐ฉ then (a) ๐ฅ ∈ ๐ต ๐๐๐ ๐ฅ ∈ ๐ (b) โ๐ฅ ∉ ๐ต ๐๐๐ ๐ฅ ∈ ๐ (c) ๐ฅ ∉ ๐ต ๐๐๐ ๐ฅ ∉ ๐ (d)๐ฅ ∈ ๐ต ๐๐๐ ๐ฅ ∉ ๐ 4. ๐ณ ∪ ๐ด = ๐ณ ∩ ๐ด then ๐ณ is equal to (a) โ๐ (b) ๐ฟ (c) ๐ (d) ๐′ 5. A set is a collection of objects which are (a) Well defined (b) โWell defined and distinct (c) identical (d) not defined 6. The set of odd numbers between 1 and 9 are (a) {1,3,5,7} (b) {3,5,7,9} (c) {1,3,5,7,9} (d) โ{3,5,7} 7. Every recurring non terminating decimal represents (a) โ๐ (b) ๐′ (c) ๐ (d) None 8. A diagram which represents a set is called______ (a) โVenn’s (b) Argand (c) Plane (d) None 9. ๐น − {๐} is a group ๐. ๐. ๐ the binary operation (a) + (b) โ × (c) ÷ (d)− 10. In a proposition if ๐ → ๐ ๐๐๐๐ ๐ → ๐ is called (a) Inverse of ๐ → ๐ (b) โ converse of ๐ → ๐ (c) contrapositive of ๐ → ๐ (d) None 11. If ๐จ and ๐ฉ are disjoint sets , then ๐จ ∩ ๐ฉ = (a) 0 (b) 1 (c) 2 (d) โ ๐ 12. ๐ → ๐ is called converse of (a) ~๐๐ (b) โ ๐ → ๐ (c) ๐ → ๐ (d) ~๐ →. If ๐จ ⊆ ๐ฉ then (๐จ ∩ ๐ฉ) = (a) โ(๐ด) (b) (๐ต) (c) (๐ด) + ๐(๐ต) (d) (๐ด). ๐(๐ต) 14. Inverse of any element of a group is: (a) Not unique (b) โunique (c) has many inverses (d) none of these 15. Every function is: (a) โRelation (b) inverse function (c) one to one (d) none of these 16. The number of all subsets of a set having three elements is: (a) 4 (b) 6 (c) โ 8 (d) 10 17. The graph of linear function is : (a) Circle ( b) โstraight line (c) parabola (d) triangle 18. Identity element in (๐ช, . ) is: (a) (0,0) (b) (0,1) (c) โ (1,0) (d) (1,1) 19. Squaring a number is a: (a) โUnary operation (b) binary operation (c) relation (d) Function 20. Which of the following is true: (a) ๐ ⊂ ๐ (b) ๐ ⊂ ๐ (c) ๐ ⊂ ๐ (d) โall of these 21. Set of integers is a group ๐. ๐. ๐ (a) โAddition (b) multiplication (c) subtraction (d) division 22. If ๐จ = ๐ then (๐จ) = (a) Empty set (b) {0} (c) โ {๐} (d) none of these 23. If ๐จ and ๐ฉ are disjoint sets then : (a) โ๐ด ∩ ๐ต = ๐ (b) ๐ด ∩ ๐ต ≠ ๐ (c) ๐ด ⊂ ๐ต (d) ๐ด − ๐ต = ๐ 24. The set of non-zero real numbers ๐. ๐. ๐ multiplication is: (a) Groupied (b) Semi-group (c) Monoied (d) โ Group 25. Which of the following is not a binary operation : (a) + (b) × (c) โ √ (d) – 26. If ๐ = √ , ๐ ≥ ๐ is a function, then its inverse is: (a) A line (b) a parabola (c) a point (d) โ not a function 27. An onto function is also called: (a) Injective (b) โ Surjective (c) Bijective (d) Inverse 28. A (๐ − ๐) function is also called: (a) โInjective (b) Surjective (c) Bijective (d) Inverse 29. For the propositions ๐ and ๐, (๐ ∧ ๐) → ๐ is: (a) โTautology (b) Absurdity (c) contingency (d) None of these 30. For the propositions ๐ and , ๐ → (๐ ∨ ๐) is: (a) โTautology (b) Absurdity (c) Contingency (d) None of these 31. If set ๐จ has 2 elements and ๐ฉ has 4 elements , then number of elements in ๐จ × ๐ฉ is : (a) 6 (b) โ 8 (c) 16 (d) None of these 32. Inverse of a line is : (a) โA line (b) a parabola (c) a point (d) not defined 33. The function ๐ = {(๐, ๐), ๐ = ๐} is : (a) โIdentity function (b) Null function (c) not a function (d) similar function 34. If ๐ = √๐, ๐ ≥ ๐ is a function, then its inverse is : (a) A line (b) a parabola (c) a point (d) โ not defined 35. Truth set of a tautology is (a) โUniversal set (b) ๐ (c) True (d) False 36. A compound proposition which is always true is called: (a) โTautology (b) contradiction (c) absurdity (d) contingency 37. A compound proposition which is always neither true nor false is called: (a) Tautology (b) contradiction (c) absurdity (d) โ contingency 38. A compound proposition which is always wrong is called: (a) Tautology (b) โ contradiction (c) absurdity (d) contingency 39. If ๐บ = { } , then order of set ๐บ is: (a) โ0 (b) 1 (c) Infinite set (d) not defined 40. The symbol which is used to denote negation of a proposition is (a) โ~ (b) → (c) ∧ (d) ∨ 41. Which of the following is true: (a) ๐ − ๐ด = ๐ (b) ๐ด ∪ ๐ด = ๐ด (c) ๐ด ∩ ๐ด = ๐ด (d) โAll of these 42. Which of the following is true: (a) ๐ด ∪ ๐ = ๐ด (b) ๐ด ∩ ๐ = ๐ (c) ๐ด − ๐ = ๐ด (d) โAll of these 43. If ๐ฉ ⊆ ๐จ, then (๐ฉ − ๐จ) is equal to: (a) (๐ด) (b) (๐ต) (c) (๐ด ∩ ๐ต) (d) โ 0 1. A rectangular array of numbers enclosed by a square brackets is called: (a) โMatrix (b) Row (c) Column (d) Determinant 2. The horizontal lines of numbers in a matrix are called: (a) Columns (b) โ Rows (c) Column matrix (d) Row matrix 3. The vertical lines of numbers in a matrix are called: (a) โColumns (b) Rows (c) Column matrix (d) Row matrix 4. If a matrix A has ๐ rows and ๐ columns , then order of A is : (a) โ๐ × ๐ (b) ๐ × ๐ (c) ๐ + ๐ (d) ๐๐ 5. The element ๐๐๐ of any matrix A is present in: (a) โ๐ ๐กโ row and ๐ ๐กโ column (b)๐ ๐กโ column and ๐ ๐กโ row (c) (๐ + ๐)โ row and column (d) (๐ + ๐)โ row and column 6. A matrix A is called real if all ๐๐๐ are (a) โReal numbers (b) complex numbers (c) 0 (d) 1 7. If a matrix A has only one row then it is called: (a) โRow vector (b) Column vector (c) square matrix (d) Rectangle matrix 8. If a matrix A has only one column then it is called: (a) Row vector (b) โ Column vector (c) square matrix (d) Rectangle matrix 9. If a matrix A has same number of rows and columns then A is called: (a) Row vector (b) Column vector (c) โsquare matrix (d) Rectangular matrix 10. If a matrix A has different number of rows and columns then A is called: (a) Row vector (b) Column vector (c) square matrix (d) โ Rectangular matrix 11. For the square matrix ๐จ = [๐๐๐]×๐ then ๐๐๐, ๐๐๐, ๐๐๐…๐๐๐ are: (a) โMain diagonal (b) primary diagonal (c) proceding diagonal (d) secondary diagonal 12. For a square matrix ๐จ = [๐๐๐]if all ๐๐๐ = ๐, ๐ ≠ ๐ and all ๐๐๐ = ๐(๐๐๐ − ๐๐๐๐) for ๐ = ๐ then A is called: (a) Diagonal matrix (b) โ Scalar Matrix (c) Scalar Matrix (d) Null matrix 13. For a square matrix ๐จ = [๐๐๐]if all ๐๐๐ = ๐, ๐ ≠ ๐ and at least ๐๐๐ ≠ ๐, ๐ = ๐ then A is called: (a) โDiagonal matrix (b) Scalar Matrix (c) Scalar Matrix (d) Null matrix 14. The matrix [๐] is : (a) Square matrix (b) row matrix (c) column matrix (d) โ all of these 15. If a matrix of order ๐ × ๐ then the matrix of order ๐ × ๐ is : (a) โTranspose of A (b) Inverse of A (c) Main diagonal of A (d) Adjoint of A 16. For any two matrices A and B ,(๐จ + ๐ฉ) ๐ = (a) ๐ต ๐ก๐ด ๐ก (b) ๐ด ๐ก๐ต ๐ก (c) โ๐ด ๐ก + ๐ต๐ก (d) ๐ต ๐ก + ๐ด๐ก 17. Let A be a matrix and ๐ is an integer then ๐จ + ๐จ + ๐จ + โฏ to ๐ terms (a) โ๐๐ด (b) ๐ + ๐ด (c) ๐ − ๐ด (d) ๐ด ๐ 18. If order of ๐จ is ๐ × ๐ and order of B is ๐ × ๐ then order of AB is (a) ๐ × ๐ (b) ๐ × ๐ (d) ๐ × ๐ (d) โ๐ × 19. If ๐๐๐ ๐จ = [ −๐ −๐ ๐ ๐ ] then matrix ๐จ is (a) [ −1 −2 4 3 ] (b) [ 4 2 3 −1] (c) [ −4 3 −2 −1] (d) โ [ 4 2 −3 −1] 20. If ๐จ is non-singular matrix then ๐จ −๐ = (a) โ 1 |๐ด| ๐๐๐๐ด (b) − 1 |๐ด| ๐๐๐๐ด (c) |๐ด| ๐๐๐๐ด (d) 1 |๐ด|๐๐๐๐ด 21. If ๐จ๐ฟ = ๐ฉ then ๐ฟ is equal to: (a) ๐ด๐ต (b) โ ๐ด −1๐ต (c) ๐ต −1๐ด (d) ๐ต๐ด 22. Inverse of a matrix exists if it is: (a) Singular (b) Null (c) Rectangular (d) โ Non-singular 23. Which of the property does not hold matrix multiplication? (a) Associative (b) โ Commutative (c) Closure (d) Inverse 24. For any matrix A , it is always true that (a) ๐ด = ๐ด๐ก (b) – ๐ด = ๐ดฬ (c) โ|๐ด| = |๐ด๐ก | (d) ๐ด −1 = 1 ๐ด 25. If all entries of a square matrix of order ๐ is multiplied by ๐, then value of |๐๐จ| is equal to: (a) ๐|๐ด| (b) ๐ 2 |๐ด| (c) โ๐ 3 |๐ด| (d) |๐ด| 26. For a non-singular matrix it is true that : (a) (๐ด −1) −1 = ๐ด (b) (๐ด ) ๐ก = ๐ด (c) ๐ดฬฟ= ๐ด (d) โall of these 27. For any non-singular matrices A and B it is true that: (a) (๐ด๐ต) −1 = ๐ต−1๐ด −1 (b) (๐ด๐ต) ๐ก = ๐ต๐ก๐ด ๐ก (c) ๐ด๐ต ≠ ๐ต๐ด (d) โ all of these 28. A square matrix ๐จ = [๐๐๐] for which ๐๐๐ = ๐, ๐ > ๐ then A is called: (a) โUpper triangular (b) Lower triangular (c) Symmetric (d) Hermitian 29. A square matrix ๐จ = [๐๐๐] for which ๐๐๐ = ๐, ๐ < ๐ then A is called: (a) Upper triangular (b) โLower triangular (c) Symmetric (d) Hermitian 30. Any matrix A is called singular if: (a) โ|๐ด| = 0 (b) |๐ด| ≠ 0 (c) ๐ด ๐ก = ๐ด (d) ๐ด๐ด−1 = ๐ผ 31. Which of the following Sets is a field. (a) R (b) Q (c) C (d) โall of these 32. Which of the following Sets is not a field. (a) R (b) Q (c) C (d) โZ 33. A square matrix A is symmetric if: (a) โ๐ด ๐ก = ๐ด (b) ๐ด ๐ก = −๐ด (c) (๐ด) ๐ก = ๐ด (d) (๐ด) ๐ก = −๐ด 34. A square matrix A is skew symmetric if: (a) ๐ด ๐ก = ๐ด (b) โ ๐ด ๐ก = −๐ด (c) (๐ด) ๐ก = ๐ด (d) (๐ด) ๐ก = −๐ด 35. A square matrix A is Hermitian if: (a) ๐ด ๐ก = ๐ด (b) ๐ด ๐ก = −๐ด (c) โ(๐ด) ๐ก = ๐ด (d) (๐ด) ๐ก = −๐ด 36. A square matrix A is skew- Hermitian if: (a) ๐ด ๐ก = ๐ด (b) ๐ด ๐ก = −๐ด (c) (๐ด) ๐ก = ๐ด (d) โ(๐ด) ๐ก = −๐ด 37. The main diagonal elements of a skew symmetric matrix must be: (a) 1 (b) โ 0 (c) any non-zero number (d) any complex number 38. The main diagonal elements of a skew hermitian matrix must be: (a) 1 (b) โ 0 (c) any non-zero number (d) any complex number 39. In echelon form of matrix, the first non zero entry is called: (a) โLeading entry (b) first entry (c) preceding entry (d) Diagonal entry 40. The additive inverse of a matrix exist only if it is: (a) Singular (b) non singular (c) null matrix (d) โ any matrix of order ๐ × ๐ 41. The multiplicative inverse of a matrix exist only if it is: (a) Singular (b) โ non singular (c) null matrix (d) any matrix of order ๐ × ๐ 42. The number of non zero rows in echelon form of a matrix is called: (a) Order of matrix (b) Rank of matrix (c) leading (d) leading row 43. If A is any square matrix then ๐จ + ๐จ๐ is a (a) โSymmetric (b) skew symmetric (c) hermitian (d) skew hermitian 44. If A is any square matrix then ๐จ − ๐จ๐ is a (a) Symmetric (b) โskew symmetric (c) hermitian (d) skew hermitian 45. If A is any square matrix then ๐จ + (๐จ) ๐ is a (a) Symmetric (b) skew symmetric (c) โ hermitian (d) skew hermitian 46. If A is any square matrix then ๐จ + (๐จ) ๐ is a (a) Symmetric (b) skew symmetric (c) hermitian (d) โ skew hermitian 47. If A is symmetric (Skew symmetric), then ๐จ ๐ must be (a) Singular (b) non singular (c) โsymmetric (d) non trivial solution 48. In a homogeneous system of linear equations , the solution (0,0,0) is: (a) โTrivial solution (b) non trivial solution (c) exact solution (d) anti symmetric 49. If ๐จ๐ฟ = ๐ถ then ๐ฟ = (a) ๐ผ (b) โ ๐ (c) ๐ด −1 (d) Not possible 50. If the system of linear equations have no solution at all, then it is called a/an (a) Consistent system (b)โ Inconsistent system (c) Trivial System (d) Non Trivial System 51. The value of ๐ for which the system ๐ + ๐๐ = ๐; ๐๐ + ๐๐ = −๐ does not possess the unique solution; (a) โ4 (b) -4 (c) ±4 (d) any real number 52. If the system ๐ + ๐๐ = ๐; ๐๐ + ๐๐ = ๐ has non-trivial solution, then ๐ is: (a) โ4 (b) -4 (c) ±4 (d) any real number 53. The inverse of unit matrix is: (a) โUnit (b) Singular (c) Skew Symmetric (d) rectangular 54. Transpose of a row matrix is: (a) Diagonal matrix (b) zero matrix (c) โ column matrix (d) scalar matrix 55. If | ๐ ๐ ๐ ๐๐| = ๐ ⇒ ๐ equals (a) โ2 (b) 4 (c) 6 (d) 8 1. The equation ๐๐๐ + ๐๐ + ๐ = ๐ will be quadratic if: (a) ๐ = 0, ๐ ≠ 0 (b) โ ๐ ≠ 0 (c) ๐ = ๐ = 0 (d) ๐ = any real number 2. Solution set of the equation ๐ ๐ − ๐๐ + ๐ = ๐ is: (a) {2, −2} (b) โ {2} (c) {−2} (d) {4, −4} 3. The quadratic formula for solving the equation ๐๐๐ + ๐๐ + ๐ = ๐; ๐ ≠ ๐ is (a) โ๐ฅ = −๐±√๐ 2−4๐๐ 2๐ (b) ๐ฅ = −๐±√๐2−4๐๐ 2๐ (c) ๐ฅ = −๐±√๐2−4๐๐ 2 (d) None of these 4. To convert ๐๐๐๐ + ๐๐๐ + ๐ = (๐ ≠ ๐) into quadratic form , the correct substitution is: (a) โ๐ฆ = ๐ฅ๐ (b) ๐ฅ = ๐ฆ๐ (c) ๐ฆ = ๐ฅ−๐ (d) ๐ฆ = 1 ๐ฅ 5. The equation in which variable occurs in exponent , called: (a) Exponential function (b) Quadratic equation (c) Reciprocal equation (d) โExponential equation 6. To convert ๐ ๐+๐ + ๐๐−๐ = ๐๐ into quadratic , the substitution is: (a) ๐ฆ = ๐ฅ1−๐ฅ (b) ๐ฆ = 41+๐ฅ (c) ๐ฆ = 4๐ฅ (d) ๐ฆ = 4−๐ฅ 7. The equations involving redical expressions of the variable are called: (a) Reciprocal equations (b) โ Redical equations (c) Quadratic functions (d) exponential equations 8. The cube roots of unity are : (a) โ1, −1+√3๐ 2 , −1+√3๐ 2 (b) 1, 1+√3๐ 2 , 1+√3๐ 2 (c) −1, −1+√3๐ 2 , −1+√3๐ 2 (d) −1, 1+√3๐ 2 , 1+√3๐ 2 9. Sum of all cube roots of 64 is : (a) โ0 (b) 1 (c) 64 (d) -64 10. Product of cube roots of -1 is: (a) 0 (b) -1 (c) โ1 (d) None 11. ๐๐๐๐ + ๐๐๐๐ = (a) 0 (b) โ -16 (c) 16 (d) -1 9 The sum of all four fourth roots of unity is: (a) Unity (b) โ0 (c) -1 (d) None 13. The product of all four fourth roots of unity is: (a) Unity (b) 0 (c) โ-1 (d) None 14. The sum of all four fourth roots of 16 is: (a) 16 (b) -16 (c) โ 0 (d) 1 15. The complex cube roots of unity are………………. each other. (a) Additive inverse (b) Equal to (c) โConjugate (d) None of these 16. The complex cube roots of unity are………………. each other. (a) Multiplicative inverse (b) reciprocal (c) square (d) โNone of these 17. The complex fourth roots of unity are ……. of each other. (a) โAdditive inverse (b) equal to (c) square of (d) None of these 18. If sum of all cube roots of unity is equal to ๐ ๐ + , then ๐ is equal to: (a) −1 (b) 0 (c) โ±๐ (d) 1 19. If product of all cube roots of unity is equal to ๐ ๐ + , then ๐ is equal to: (a) −1 (b) โ 0 (c) ±๐ (d) 1 20. The expression ๐ ๐ + ๐ ๐ − ๐ is polynomial of degree: (a) 2 (b) 3 (c) 1 (d) โ not a polynomial 21. If (๐) is divided by ๐ − ๐ , then dividend = (Divisor)(…….)+ Remainder. (a) Divisor (b) Dividend (c) โ Quotient (d) ๐ 22. If (๐) is divided by ๐ − ๐ by remainder theorem then remainder is: (a) โ (๐) (b) (−๐) (c) (๐) + ๐ (d) ๐ฅ − ๐ = ๐ 23. The polynomial (๐ − ๐) is a factor of (๐) if and only if (a) โ (๐) = 0 (b) (๐) = ๐ (c) Quotient = ๐ (d) ๐ฅ = −๐ 24. ๐ − ๐ is a factor of ๐ ๐ − ๐๐ + ๐, if ๐ is: (a) 2 (b) โ 4 (c) 8 (d) -4 25. If ๐ = −๐ is the root of ๐๐๐ − ๐๐๐ ๐ + ๐๐ = ๐, then ๐ = (a) 2 (b) -2 (c) 1 (d) โ -1 26. ๐ + ๐ is a factor of ๐ ๐ + ๐๐ when ๐ is (a) Any integer (b) any positive integer (c) โ any odd integer (d) any real number 27. ๐ − ๐ is a factor of ๐ ๐ − ๐๐ when ๐ is (a) โ Any integer (b) any positive integer (c) any odd integer (d) any real number 28. Sum of roots of ๐๐๐ − ๐๐ − ๐ = ๐ is (๐ ≠ ๐) (a) โ ๐ ๐ (b) – ๐ ๐ (c) ๐ ๐ (d) – ๐ ๐ 29. Sum of roots of ๐๐๐ − ๐๐ − ๐ = ๐ is (๐ ≠ ๐) (a) ๐ ๐ (b) – ๐ ๐ (c) ๐ ๐ (d) โ – ๐ ๐ 30. If 2 and -5 are roots of a quadratic equation , then equation is: (a) ๐ฅ 2 − 3๐ฅ − 10 = 0 (b) ๐ฅ 2 − 3๐ฅ + 10 = 0 (c) โ ๐ฅ 2 + 3๐ฅ − 10 = 0 (d) ๐ฅ 2 + 3๐ฅ + 10 = 0 31. If ๐ถ and ๐ท are the roots of ๐๐๐ − ๐๐ + ๐ = ๐, then the value of ๐ถ + ๐ท is: (a) โ 2 3 (b) − 2 3 (c) 4 3 (d) − 4 3 32. If roots of ๐๐๐ + ๐๐ + ๐ = ๐, (๐ ≠ ๐) are real , then (a) Disc≥ 0 (b) Disc< 0 (c) Disc≠ 0 (d) Disc≤ 0 33. If roots of ๐๐๐ + ๐๐ + ๐ = ๐, (๐ ≠ ๐) are complex , then (a) โDisc≥ 0 (b) โ Disc< 0 (c) Disc≠ 0 (d) Disc≤ 0 34. If roots of ๐๐๐ + ๐๐ + ๐ = ๐, (๐ ≠ ๐) are equal , then (a) โDisc= 0 (b) Disc< 0 (c) Disc≠ 0 (d) None of these 35. Graph of quadratic equation is: (a) Straight line (b) Circle (c) square (d) โParabola 36. ๐๐๐ + ๐๐๐ + ๐ = (a) โ0 (b) 1 (c) -1 (d) ๐ 37. Synthetic division is a process of: (a) Addition (b) multiplication (c) subtraction (d) โ division 38. Degree of quadratic equation is: (a) 0 (b)1 (c) โ2 (d) 3 39. Basic techniques for solving quadratic equations are (a) 1 (b) 2 (c) โ3 (d) 4 40. ๐๐๐๐ + ๐๐๐๐ = (a) 0 (b) โ -16 (c) 16 (d) -1 1. An open sentence formed by using sign of “ = ” is called a/an (a) โEquation (b) Formula (c) Rational fraction (d) Theorem 2. If an equation is true for all values of the variable, then it is called: (a) a conditional equation (b) โ an identity (c) proper rational fraction (d) All of these 3. (๐ + ๐)(๐ + ๐) = ๐๐ + ๐๐ + ๐๐ is a/an: (a) Conditional equation (b) โan identity (c) proper rational fraction (d) a formula 4. The quotient of two polynomials (๐) ๐ธ(๐) , ๐ธ(๐) ≠ ๐ is called : (a) โRational fraction (b) Irrational fraction (c) Partial fraction (d) Proper fraction 5. A fraction (๐) ๐ธ(๐) , ๐ธ(๐) ≠ ๐ is called proper fraction if : (a) โDegree of (๐ฅ) < Degree of ๐(๐ฅ) (b) Degree of (๐ฅ) = Degree of ๐(๐ฅ) (c) Degree of (๐ฅ) > Degree of ๐(๐ฅ) (d) Degree of (๐ฅ) ≥ Degree of ๐(๐ฅ) 6. A fraction (๐) ๐ธ(๐) , ๐ธ(๐) ≠ ๐ is called proper fraction if : (a) Degree of (๐ฅ) < Degree of ๐(๐ฅ) (b) Degree of (๐ฅ) = Degree of ๐(๐ฅ) (c) Degree of (๐ฅ) > Degree of ๐(๐ฅ) (d) โ Degree of (๐ฅ) ≥ Degree of ๐(๐ฅ) 7. A mixed form of fraction is : (a) An integer+ improper fraction (b) a polynomial+improper fraction (c) โa polynomial+proper fraction (d) a polynomial+rational fraction 8. When a rational fraction is separated into partial fractions, then result is always : (a) A conditional equations (b) โan identity (c) a partial fraction (d) an improper fraction 9. The number of Partial fraction of ๐ ๐ (๐+๐)(๐๐−๐)are: (a) 2 (b) 3 (c) โ4 (d) None of these 10. The number of Partial fraction of ๐ ๐ (๐+๐)(๐๐−๐)are: (a) 2 (b) 3 (c) 4 (d) โ 6 11. Partial fractions of ๐ ๐ ๐−๐ are: (a) 1 2(๐ฅ−1) + 1 2(๐ฅ+1) (b) โ 1 2(๐ฅ−1) − 1 2(๐ฅ+1) (c) − 1 2(๐ฅ−1) + 1 2(๐ฅ+1) (d) − 1 2(๐ฅ−1) − 1 2(๐ฅ+1) 12. Conditional equation ๐๐ + ๐ = ๐ holds when ๐ is equal to: (a) โ− 3 2 (b) 3 2 (c) 1 3 (d) 1 13. Which is a reducible factor: (a) ๐ฅ 3 − 6๐ฅ2 + 8๐ฅ (b) ๐ฅ 2 + 16๐ฅ (c) ๐ฅ 2 + 5๐ฅ – 6 (d) โall of these 14. A quadratic factor which cannot written as a product of linear factors with real coefficients is called: (a) โAn irreducible factor (b) reducible factor (c) an irrational factor (d) an improper factor 15. ๐๐๐ ๐ ๐−๐ is an (a) Improper fraction (b) โ Proper fraction (c) Polynomial (d) equation 1. An arrangement of numbers according to some definite rule is called: (a) โSequence (b) Combination (c) Series (d) Permutation 2. A sequence is also known as: (a) Real sequence (b) โProgression (c) Arrangement (d) Complex sequence 3. A sequence is function whose domain is (a) ๐ (b) ๐ (c) ๐ (d) โ ๐ 4. As sequence whose range is ๐น ๐. ๐., set of real numbers is called: (a) โReal sequence (b) Imaginary sequence (c) Natural sequence (d) Complex sequence 5. If ๐๐ = {๐ + (−๐) ๐}, then ๐๐๐ = (a) 10 (b) โ 11 (c) 12 (d) 13 6. The last term of an infinite sequence is called : (a) ๐๐กโ term (b) ๐๐ (c) last term (d) โ does not exist 7. The next term of the sequence ๐, ๐, ๐๐, ๐, … is (a) โ112 (b) 120 (c) 124 (d) None of these 8. A sequence {๐๐} in which ๐๐ − ๐๐−๐ is the same number for all ๐ ∈ ๐ต, > 1 is called: (a) โA.P (b) G.P (c) H.P (d) None of these 9. ๐๐๐ term of an A.P is ๐๐ − ๐ then 10th term is : (a) 9 (b) โ 29 (c) 12 (d) cannot determined 10. ๐๐๐ term of the series ( ๐ ) ๐ + (๐ ๐ ) ๐ + (๐ ๐ ) ๐ + โฏ (a) โ ( 2๐−1 3 ) 2 (b) ( 2๐−1 3 ) 2 (c) ( 2๐ 3 ) 2 (d) cannot determined 11. If ๐๐−๐, ๐๐, ๐๐+๐ are in A.P, then ๐๐ is (a) โA.M (b) G.M (c) H.M (d) Mid point 12. Arithmetic mean between ๐ and ๐ is: (a) โ ๐+๐ 2 (b) ๐+๐ 2๐๐ (c) 2๐๐ ๐+๐ (d) 2 ๐+๐ 13. The arithmetic mean between √๐ and ๐√๐ is: (a) 4√2 (b) โ 4 √2 (c) √2 (d) none of these 14. The sum of terms of a sequence is called: (a) Partial sum (b) โ Series (c) Finite sum (d) none of these 15. Forth partial sum of the sequence {๐ } is called: (a) 16 (b) โ 1+4+9+16 (c) 8 (d) 1+2+3+4 16. Sum of ๐ −term of an Arithmetic series ๐บ๐ is equal to: (a) โ ๐ 2 [2๐ + (๐ − 1)] (b) ๐ 2 [๐ + (๐ − 1)] (c) ๐ 2 [2๐ + (๐ + 1)] (d) ๐ 2 [2๐ + ๐] 17. For any ๐ฎ. ๐ท., the common ratio ๐ is equal to: (a) ๐๐ ๐๐+1 (b) ๐๐−1 ๐๐ (c) โ ๐๐ ๐๐−1 (d) ๐๐+1 − ๐๐, ๐ ∈ ๐, ๐ > 1 18. No term of a ๐ฎ. ๐ท., is: (a) โ0 (b) 1 (c) negative (d) imaginary number 19. The general term of a ๐ฎ. ๐ท., is : (a) โ๐๐ = ๐๐๐−1 (b) ๐๐ = ๐๐๐ (c) ๐๐ = ๐๐๐+1 (d) None of these 20. The sum of infinite geometric series is valid if (a) |๐| > 1 (b) |๐| = 1 (c) |๐| ≥ 1 (d) โ |๐| < 1 21. For the series ๐ + ๐ + ๐๐ + ๐๐๐ + โฏ + ∞ , the sum is (a) -4 (b) 4 (c) 1−5๐ −4 (d) โ not defined 22. An infinite geometric series is convergent if (a) |๐| > 1 (b) |๐| = 1 (c) |๐| ≥ 1 (d) โ |๐| < 1 23. An infinite geometric series is divergent if (a) |๐| < 1 (b) |๐| ≠ 1 (c) ๐ = 0 (dโ) |๐| > 1 24. If sum of series is defined then it is called: (a) โConvergent series (b) Divergent series (c) finite series (d) Geometric series 25. If sum of series is not defined then it is called: (a) Convergent series (b) โ Divergent series (c) finite series (d) Geometric series 26. The interval in which series ๐ + ๐๐ + ๐๐๐ + ๐๐๐ + โฏ is convergent if : (a) −2 < ๐ฅ < 2 (b) โ − 1 2 < ๐ฅ < 1 2 (c) |2๐ฅ| > 1 (d) |๐ฅ| < 1 27. If the reciprocal of the terms a sequence form an ๐จ. ๐ท., then it is called: (a) โ๐ป. ๐ (b) ๐บ. ๐ (c) ๐ด. ๐ (d) sequence 28. The ๐๐๐ term of ๐ , ๐ ๐ , ๐ ๐ , … is (a) โ 1 3๐−1 (b) 3๐ – 1 (c) 2๐ + 1 (d) 1 3๐+1 29. Harmonic mean between ๐ and ๐ is: (a) โ5 (b) 16 5 (c) ±4 (d) 5 16 30. If ๐จ, ๐ฎ and ๐ฏ are Arithmetic , Geometric and Harmonic means between two positive numbers then (a) ๐บ 2 = ๐ด๐ป (b) โ๐ด, ๐บ, ๐ป ๐๐๐ ๐๐ ๐บ. ๐ (c) ๐ด > ๐บ > ๐ป (d) all of these 31. If ๐จ, ๐ฎ and ๐ฏ are Arithmetic , Geometric and Harmonic means between two negative numbers then (a) ๐บ 2 = ๐ด๐ป (b) ๐ด, ๐บ, ๐ป ๐๐๐ ๐๐ ๐บ. ๐ (c) ๐ด < ๐บ < ๐ป (d) โall of these 32. If ๐ and ๐ are two positive number then (a) ๐ด < ๐บ < ๐ป (b) โ ๐ด > ๐บ > ๐ป (c) ๐ด = ๐บ = ๐ป (d) ๐ด ≥ ๐บ ≥ ๐ป 33. If ๐ and ๐ are two negative number then (a) โ๐ด < ๐บ < ๐ป (b) ๐ด > ๐บ > ๐ป (c) ๐ด = ๐บ = ๐ป (d) ๐ด ≥ ๐บ ≥ ๐ป 34. If ๐ ๐+๐+๐๐+๐ ๐๐+๐๐ is A.M between ๐ and ๐ then ๐ is equal to: (a) โ0 (b) -1 (c) 1 (d) 1 2 35. If ๐ ๐+๐๐ ๐๐−๐+๐๐−๐ is G.M between ๐ and ๐ then ๐ is equal to: (a) 0 (b) -1 (c) 1 (d) โ 1 2 36. If ๐ ๐+๐+๐๐+๐ ๐๐+๐๐ is H.M between ๐ and ๐ then ๐ is equal to: (a) 0 (b) โ -1 (c) 1 (d) 1 2 37. If ๐บ๐ = (๐ + ๐) , then ๐บ๐๐ is equal to: (a) 2๐ + 1 (b) โ 4๐2 + 4๐ + 1 (c) (2๐ − 1) 2 (d) cannot be determined 38. ∑ ๐ ๐ = (a) (๐+1)2 (b) (๐+1)(๐+2) 6 (c) โ ๐ 2(๐+1) 2 4 (d) (๐+1) 2 1. ๐๐๐ท๐= (a) 6890 (b) 6810 (c) โ6840 (d) 6880 2. If ๐๐ท๐=30 then ๐ = (a) 4 (b) 5 (c) โ6 (d) 10 3. The number of diagonals in 10-sided figure is (a) 10 (b) 10๐ถ2 (c) โ10๐ถ2 – 10 (d) 45 4. ๐๐ช๐= (a) 0 (b) โ 1 (c) ๐ (d) ๐! 5. How many arrangement of the word “MATHEMATICS” can be made (a) 11! (b) ( 11 3,2,1,1,1,1,1) (c) โ ( 11 2,2,2,1,1,1,1,1) (d) None 6. If ๐ is negative then ๐! Is (a) 1 (b) 0 (c) unique (d) โNot defined 7. ๐ − ๐๐ช๐ + ๐ − ๐๐ช๐−๐equals (a) โ๐๐ถ๐ (b) ๐๐ถ๐−1 (c) ๐ − 1๐ถ๐ (d) ๐ + 1๐ถ๐ 8. How many signals can be given by 5 flags of different colors , using 3 at a time (a) 120 (b) โ60 (c) 24 (d) 15 9. ๐๐ท๐= (a) 1 (b) ๐ (c) โ ๐! (d) None 10. ๐! ๐! = (a) โ8 (b) 7 (c) 56 (d) 8 7 11. If an event ๐จ can occur in ๐ ways and ๐ฉ can occur ๐ ways , then number of ways that both events occur is: (a) ๐ + ๐ (b) โ ๐. ๐ (c) (๐๐)! (d) (๐ + ๐)! 12. If ( ๐๐) = ( ๐ ๐ ) then the value of ๐, (a) 15 (b) 16 (c) 18 (d) โ20 13. Probability of non-occurrence of an event E is equal to : (a) โ1 − (๐ธ) (b) (๐ธ) + ๐(๐) ๐(๐ธ) (c) (๐) ๐(๐ธ) (d) 1 + (๐ธ) 14. For independent events (๐จ ∩ ๐ฉ) = (a) (๐ด) + ๐(๐ต) (b) (๐ด) − ๐(๐ต) (c) โ (๐ด). ๐(๐ต) (d) (๐ด) ๐(๐ต) 15. A card is drawn from a deck of 52 playing cards. The probability of card that it is an ace card is: (a) 2 13 (b) 4 13 (c) โ 1 13 (d) 17 13 16. Four persons wants to sit in a circular sofa, the total ways are: (a) 24 (b) โ6 (c) 4 (d) None of these 17. Two teams ๐จ and ๐ฉ are playing a match, the probability that team ๐จ does not lose is: (a) 1 3 (b) 2 3 (c) 1 (d) 0 18. Let ๐บ = {๐, ๐, ๐, … , ๐๐} the probability that a number is divided by 4 is : (a) 2 5 (b) โ 1 5 (c) 1 10 (d) 1 2 19. A die is rolled , the probability of getting 3 or 5 is: (a) 2 3 (b) โ 15 36 (c) 15 36 (d) 1 36 20. A coin is tossed 5 times , then ๐(๐บ) is equal to: (a) โ32 (b) 25 (c) 10 (d) 20 21. The number of ways for sitting 4 persons in a train on a straight sofa is: (a) โ24 (b) 6 (c) 4 (d) None of these 22. Sample space for tossing a coin is: (a) {๐ป} (b) {๐} (c) {๐ป, ๐ป} (d) โ {๐ป, ๐} 23. If (๐ฌ) = ๐ ๐๐ , ๐(๐บ) = ๐๐๐๐ , ๐(๐ฌ) = (a) 108 (b) โ4900 (c) 144 (d) 14400 24. In a permutation ๐๐ท๐ ๐๐ (๐, ๐) , it is always true that (a) โ๐ ≥ ๐ (b) ๐ < ๐ (c) ๐ ≤ ๐ (d) ๐ < 0, ๐ < 0 25. If an event always occurs , then it is called: (a) Null Event (b) Possible Event (c) โCertain event (d) Independent Event 26. If ๐ฌ is a certain event , then (a) (๐ธ) = 0 (b) โ(๐ธ) = 1 (c) 0 < (๐ธ) < 1 (d) (๐ธ) > 1 27. If ๐ฌ is an impossible event ,then (a) โ(๐ธ) = 0 (b) (๐ธ) = 1 (c) (๐ธ) ≠ 0 (d) 0 < (๐ธ) < 1 28. Non occurrence of an event E is denoted by: (a) ∼ ๐ธ (b) โ ๐ธ (c) ๐ธ ๐ (d) All of these 1. The statement ๐ ๐ + ๐๐ + ๐ is true when : (a) ๐ = 0 (b) ๐ = 1 (c) โ ๐ ≥ 2 (d) ๐ is any +iv integer 2. The number of terms in the expansion of (๐ + ๐) ๐ are: (a) ๐ (b) โ ๐ + 1 (c) 2 ๐ (d) 2 ๐−1 3. Middle term/s in the expansion of (๐ − ๐๐) ๐๐ is/are : (a) ๐7 (b) โ ๐8 (c) ๐6&๐7 (d) ๐7&๐8 4. The coefficient of the last term in the expansion of (๐ − ๐) ๐ is : (a) 1 (b) โ −1 (c) 7 (d) −7 5. ( ๐ ๐ ) + ( ๐๐ ๐ ) + ( ๐๐ ๐ ) + โฏ + ( ๐๐ ๐๐) is equal to: (a) 2 ๐ (b) โ2 2๐ (c) 2 2๐−1 (d) 2 2๐+1 6. ๐ + ๐ + ๐๐ + ๐๐ + โฏ (a) (1 + ๐ฅ) −1 (b) โ(1 − ๐ฅ) −1 (c) (1 + ๐ฅ) −2 (d) (1 − ๐ฅ) −2 7. The middle term in the expansion of (๐ + ๐) ๐ is ( ๐ + ๐) ; then ๐ is (a) Odd (b) โ even (c) prime (d) none of these 8. The number of terms in the expansion of (๐ + ๐) ๐๐ is: (a) 18 (b) 20 (c) โ 21 (d) 19 9. The expansion (๐ − ๐๐) −๐ is valid if: (a) โ|๐ฅ| < 1 4 (b) |๐ฅ| > 1 4 (c) −1 < ๐ฅ < 1 (d) |๐ฅ| < −1 10. The statement ๐ ๐ < ๐! is true, when (a) ๐ = 2 (b) ๐ = 4 (c) ๐ = 6 (d) โ๐ > 6 11. General term in the expansion of (๐ + ๐) ๐ is: (a) ( +1 ๐ )๐ ๐−๐๐ฅ^๐ (b)โ( ๐ ๐−1)๐ ๐−๐๐ฅ ๐ (c) ( ๐+1)๐ ๐−๐๐ฅ ๐ (d) ( ๐ )๐ ๐−๐๐ฅ ๐ 12. The method of induction was given by Francesco who lived from: (a) โ1494-1575 (b) 1500-1575 (c) 1498-1575 (d) 1494-1570 1. Two rays with a common starting point form: (a) Triangle (b) โ Angle (c) Radian (d) Minute 2. The common starting point of two rays is called: (a) Origin (b) Initial Point (c) โ Vertex (d)All of these 3. If the rotation of the angle is counter clock wise, then angle is: (a) Negative (b) โ Positive (c) Non-Negative (d) None of these 4. If the initial ray โ๐ถ๐จโโโโโ rates in anti-clockwise direction in such a way that it coincides with itself, the angle then formed is: (a) 180° (b) 270° (c) 300° (d) โ 360° 5. One rotation in anti-clock wise direction is equal to: (a) 180° (b) 270° (c) โ360° (d) 90° 6. Straight line angle is equal to (a) 1 2 ๐๐๐ก๐๐ก๐๐๐ (b) ๐ radian (c) 180° (d) โ All of these 7. One right angle is equal to (a) ๐ 2 ๐๐๐๐๐๐ (b) 90° (c) 1 4 ๐๐๐ก๐๐ก๐๐๐ (d) โ All of these 8. ๐° is equal to (a) 30 minutes (b) โ 60 minutes (c) 1 60 minutes (d) 1 2 minutes 60th part of ๐° is equal to (a) One second (b) โ One minute (c) 1 Radian (d) ๐ radian 14. ๐๐°๐๐′ equal to (a) โ16.5° (b) 32° 2 (c) 16.05° (d) 16.2° 15. Conversion of ๐๐. ๐๐๐° to ๐ซ°๐ด′๐บ ′ ′ form is: (a) 21°25’6’’ (b) 21°40′27′′ (c) โ 21°15′22′′ (d) 21°30′2′′ 16. The angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle is called: (a) 1 Degree (b) 1’ (c) โ 1 Radian (d) 1’’ 17. The system of angular measurement in which the angle is measured in radian is called: (a) Sexagesimal System (b) โ Circular System (c) English System (d) Gradient System 18. Relation between the length of arc of a circle and the circular measure of it central angle is: (a) ๐ = ๐ ๐ (b) ๐ = ๐๐ (c) โ ๐ = ๐ ๐ (d) ๐ = 1 2 ๐ 2๐ 19. With usual notation , if ๐ = ๐๐๐, ๐ = ๐๐๐, then unit of ๐ฝ is: (a) ๐๐ (b) ๐๐2 (c) โ No unit (d) ๐๐3 20. ๐° is equal to: (a) ( 180) ° (b) 180 ๐ ๐๐๐ (c) ( 180 ๐ ) ๐๐๐ (d) โ ๐ 180 ๐๐๐ 21 . ๐° is equal to: (a) 0.175 ๐๐๐ (b) โ0.0175๐๐๐ (c) 1.75 ๐๐๐ (d) 0.00175๐๐๐ 22. 1 radian is equal to (a) ( 180) ° (b) 180 ๐ ๐๐๐ (c) โ ( 180 ๐ ) ° (d) ๐ 180 ๐๐๐ 23. 1 radian is equal to: (a) โ57.296° (b) 5.7296° (c) 175.27° (d) 17.5276 24. 3 radian is: (a) โ171.888° (b) 120° (c) 300° (d) 270° 25. ๐๐๐° = __________๐๐๐ ๐๐๐ (a) โ 7๐ 12 (b) 2๐ 3 (c) 5๐ 12 (d) 5๐ 6 26. 3’’= ___________ ๐๐๐ ๐๐๐ (a) 53๐ 270 (b) โ ๐ 216000 (c) 41๐ 720 (d) 27721๐ 32400 27. ๐ ๐ ๐๐๐ ๐๐๐ = ________๐ ๐๐๐๐๐ (a) โ45° (b) 30° (c) 60° (d) 75° 28. Circular measure of angle between the hands of a watch at ๐ ′๐ถ ๐๐๐๐๐ is (a) 45° (b) โ 120° (c) 3๐ 2 (d) 270° 29. If ๐ = ๐. ๐ ๐๐ & ๐ = ๐. ๐ ๐๐ then ๐ฝ is equal to: (a) โ 3 5 (b) 5 3 (c) 3.75 (d) ๐๐๐๐ 30. If ๐ฝ = ๐๐° , ๐ = ๐๐๐๐ , then ๐ = (a) โ 9 2 ๐ (b) 2 9 ๐ (c) 812mm (d) 810mm 31. Area of sector of circle of radius ๐ is: (a) โ 1 2 ๐ 2๐ (b) 1 2 ๐๐2 (c) 1 2 (๐๐) 2 (d) 1 2๐2๐ 32. Angles with same initial and terminal sides are called: (a) Acute angles (b) Allied Angles (c) โCoterminal angles (d) Quadrentel angles 1. Distance between the points (๐, ๐) & ๐ต(5,6) is: (a) โ2√2 (b) 3 (c) 4 (d) √2 2. Fundamental law of trigonometry is , ๐๐๐(๐ถ − ๐ท) (a) โ๐๐๐ ๐ผ๐๐๐ ๐ฝ + ๐ ๐๐๐ผ๐ ๐๐๐ฝ (b) ๐๐๐ ๐ผ๐๐๐ ๐ฝ – ๐ ๐๐๐ผ๐ ๐๐๐ฝ (c) ๐ ๐๐๐ผ๐๐๐ ๐ฝ + ๐๐๐ ๐ผ๐ ๐๐๐ฝ (d) ๐ ๐๐๐ผ๐๐๐ ๐ฝ − ๐๐๐ ๐ผ๐ ๐๐๐ฝ 3. ๐๐(๐ถ + ๐ท) is equal to: (a) ๐๐๐ ๐ผ๐๐๐ ๐ฝ + ๐ ๐๐๐ผ๐ ๐๐๐ฝ (b) โ ๐๐๐ ๐ผ๐๐๐ ๐ฝ – ๐ ๐๐๐ผ๐ ๐๐๐ฝ (c) ๐ ๐๐๐ผ๐๐๐ ๐ฝ + ๐๐๐ ๐ผ๐ ๐๐๐ฝ (d) ๐ ๐๐๐ผ๐๐๐ ๐ฝ – ๐๐๐ ๐ผ๐ ๐๐๐ฝ 4. ๐๐(๐ถ + ๐ท) is equal to: (a) ๐๐๐ ๐ผ๐๐๐ ๐ฝ + ๐ ๐๐๐ผ๐ ๐๐๐ฝ (b) ๐๐๐ ๐ผ๐๐๐ ๐ฝ – ๐ ๐๐๐ผ๐ ๐๐๐ฝ (c) โ ๐ ๐๐๐ผ๐๐๐ ๐ฝ + ๐๐๐ ๐ผ๐ ๐๐๐ฝ (d) ๐ ๐๐๐ผ๐๐๐ ๐ฝ – ๐๐๐ ๐ผ๐ ๐๐๐ฝ 5. ๐๐(๐ถ − ๐ท) is equal to: (a) ๐๐๐ ๐ผ๐๐๐ ๐ฝ + ๐ ๐๐๐ผ๐ ๐๐๐ฝ (b) ๐๐๐ ๐ผ๐๐๐ ๐ฝ – ๐ ๐๐๐ผ๐ ๐๐๐ฝ (c) ๐ ๐๐๐ผ๐๐๐ ๐ฝ + ๐๐๐ ๐ผ๐ ๐๐๐ฝ (d) โ ๐ ๐๐๐ผ๐๐๐ ๐ฝ – ๐๐๐ ๐ผ๐ ๐๐๐ฝ 6. ๐๐๐ (๐ ๐ − ๐ท) = (a) ๐๐๐ ๐ฝ (b) – ๐๐๐ ๐ฝ (c) โ ๐ ๐๐๐ฝ (d) – ๐ ๐๐๐ฝ 7. ๐๐๐ (๐ท + ๐ ) = (a) ๐๐๐ ๐ฝ (b) – ๐๐๐ ๐ฝ (c) ๐ ๐๐๐ฝ (d) โ – ๐ ๐๐๐ฝ 8. ๐๐๐ (๐ท − ๐ ) = (a) ๐๐๐ ๐ฝ (b) โ – ๐๐๐ ๐ฝ (c) ๐ ๐๐๐ฝ (d) โ – ๐ ๐๐๐ฝ 9. ๐๐(๐๐ − ๐ฝ) = (a) โ๐๐๐ ๐ (b) – ๐๐๐ ๐ (c) ๐ ๐๐๐ (d) – ๐ ๐๐๐ 10. ๐๐(๐๐ − ๐ฝ) = (a) ๐๐๐ ๐ (b) – ๐๐๐ ๐ (c) ๐ ๐๐๐ (d) โ – ๐ ๐๐๐ 11. ๐๐๐(๐ถ + ๐ท) = (a) ๐ก๐๐๐ผ−๐ก๐๐๐ฝ 1+๐ก๐๐๐ผ๐ก๐๐๐ฝ (b) โ ๐ก๐๐๐ผ+๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ (c) ๐ก๐๐๐ผ−๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ (d) ๐ก๐๐๐ผ+๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ 12. ๐๐๐(๐ถ − ๐ท) = (a) โ ๐ก๐๐๐ผ−๐ก๐๐๐ฝ 1+๐ก๐๐๐ผ๐ก๐๐๐ฝ (b) ๐ก๐๐๐ผ+๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ (c) ๐ก๐๐๐ผ−๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ (d) ๐ก๐๐๐ผ+๐ก๐๐๐ฝ 1−๐ก๐๐๐ผ๐ก๐๐๐ฝ 13. Angles associated with basic angles of measure ๐ฝ to a right angle or its multiple are called: (a) Coterminal angle (b) angle in standard position (c) โ Allied angle (d) obtuse angle 14. ๐๐๐ (๐ ๐ − ๐ฝ) = (a) โ๐๐๐ก๐ (b) ๐ก๐๐๐ (c) – ๐๐๐ก๐ (d) – ๐ก๐๐๐ 15. ๐๐๐ (๐ ๐ + ๐ฝ) = (a) ๐๐๐ก๐ (b) ๐ก๐๐๐ (c) โ– ๐๐๐ก๐ (d) – ๐ก๐๐๐ 16. ๐๐๐ ( ๐ ๐ + ๐ฝ) = (a) ๐ ๐๐๐ (b) ๐๐๐ ๐ (c) –๐ ๐๐๐ (d) โ – ๐๐๐ ๐ 17. ๐๐๐ ๐๐๐° is equal to: (a) 1 (b) 0 (c) โ 1 √2 (d) √3 2 18. ๐๐(−๐๐๐°) is equal to: (a) โ 1 (b) 0 (c) 1 √3 (d) -1 19 . ๐๐๐(−๐๐๐°) = (a) 1 (b) โ 0 (c) 2 (d) -1 20. ๐๐(๐๐๐° + ๐ถ)๐๐๐(๐๐° − ๐ถ) = (a) โ ๐ ๐๐๐ผ๐๐๐ ๐ผ (b) – ๐ ๐๐๐ผ๐๐๐ ๐ผ (c) ๐๐๐ ๐พ (d) – ๐๐๐ ๐พ 21. If ๐ถ, ๐ท and ๐ธ are the angles of a triangle ABC then ๐๐(๐ถ + ๐ท) = (a) โ ๐ ๐๐๐พ (b) – ๐ ๐๐๐พ (c) ๐๐๐ ๐พ (d) – ๐๐๐ ๐พ . If ๐ถ, ๐ท and ๐ธ are the angles of a triangle ABC then ๐๐๐ (๐ถ+๐ท ) = (a) โ sin ๐พ 2 (b) – sin ๐พ 2 (c) cos ๐พ 2 (d) – cos ๐พ 2 23. If ๐ถ, ๐ท and ๐ธ are the angles of a triangle ABC then ๐๐(๐ถ + ๐ท) = (a) ๐ ๐๐๐พ (b) – ๐ ๐๐๐พ (c) ๐๐๐ ๐พ (d) โ – ๐๐๐ ๐พ 24. ๐๐๐๐๐°+๐๐๐๐๐° ๐๐๐๐๐°−๐๐๐๐๐° = (a) โ ๐ก๐๐56° (b) ๐ก๐๐34° (c) ๐๐๐ก56° (d) ๐๐๐ก34° 25. ๐๐๐๐๐ถ is equal to: (a) cos2 ๐ผ − sin2 ๐ผ (b) 1 + ๐๐๐ 2๐ผ (c) โ 2๐ ๐๐๐ผ๐๐๐ ๐ผ (d) 2๐ ๐๐2๐ผ๐๐๐ 2๐ผ 26. ๐๐๐๐๐ถ = (a) cos2 ๐ผ − sin2 ๐ผ (b) 1 − 2 sin2 ๐ผ (c) 2 cos2 ๐ผ – 1 (d) โ All of these 27. ๐๐๐๐๐ถ = (a) 2๐ก๐๐๐ผ 1+๐ก๐๐2 ๐ผ (b) โ 2๐ก๐๐๐ผ 1−tan2 ๐ผ (c) 2 tan2 ๐ผ 1−tan2 ๐ผ (d) tan2 ๐ผ 1−tan2 ๐ผ 28. ๐๐๐๐ถ + ๐๐๐๐ท is equal to: (a) โ 2 sin ( +๐ฝ 2 ) cos ( ๐ผ−๐ฝ 2 ) (b) 2 cos (๐ผ+๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (c) −2 sin (๐ผ+๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (d) 2 cos (๐ผ+๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) 29. ๐๐๐๐ถ − ๐๐๐๐ท is equal to: (a) 2 sin ( +๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) (b) โ 2 cos ( +๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (c) −2 sin (๐ผ+๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (d) 2 cos (๐ผ+๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) 30. ๐๐๐๐ถ + ๐๐๐๐ท is equal to: (a) 2 sin ( +๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) (b) 2 cos (๐ผ+๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (c) -2 sin ( +๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (d) โ 2 cos ( +๐ฝ 2 ) cos ( ๐ผ−๐ฝ 2 ) 31. ๐๐๐๐ถ − ๐๐๐๐ท is equal to: (a) 2 sin ( +๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) (b) 2 cos (๐ผ+๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (c) โ − 2 sin ( +๐ฝ 2 ) sin ( ๐ผ−๐ฝ 2 ) (d) 2 cos (๐ผ+๐ฝ 2 ) cos (๐ผ−๐ฝ 2 ) 32. Which is the allied angle (a) โ 90° + ๐ (b) 60° + ๐ (c) 45° + ๐ (d) 30° + ๐ 33. ๐๐๐๐๐๐ฝ๐๐๐๐๐ฝ = (a) โ ๐ ๐๐10๐ + ๐ ๐๐4๐ (b) ๐ ๐๐5๐ − ๐ ๐๐2๐ (c) ๐๐๐ 10๐ + ๐๐๐ 4๐ (d) ๐๐๐ 5๐ − ๐๐๐ 2๐ 34. ๐๐๐๐๐๐ฝ๐๐๐๐๐ฝ = (b) โ ๐ ๐๐8๐ − ๐ ๐๐2๐ (b) ๐ ๐๐8๐ + ๐ ๐๐2๐ (c) ๐๐๐ 8๐ + ๐๐๐ 2๐ (d) ๐๐๐ 8๐ − ๐๐๐ 2๐ 1. Domain of ๐ = ๐๐๐๐ is (a) โ−∞ < ๐ฅ < ∞ (b) −1 ≤ ๐ฅ ≤ 1 (c) −∞ < ๐ฅ < ∞ , ๐ฅ ≠ ๐๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 2. Domain of ๐ = ๐๐๐๐ is (a) โ−∞ < ๐ฅ < ∞ (b) −1 ≤ ๐ฅ ≤ 1 (c) −∞ < ๐ฅ < ∞ , ๐ฅ ≠ ๐๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 3. Domain of ๐ = ๐๐๐๐ is (a) −∞ < ๐ฅ < ∞ (b) −1 ≤ ๐ฅ ≤ 1 (c) โ −∞ < ๐ฅ < ∞ , ๐ฅ ≠ 2๐+1 2 ๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 4. Domain of ๐ = ๐๐๐๐ is (a) −∞ < ๐ฅ < ∞ (b) −1 ≤ ๐ฅ ≤ 1 (c) โ −∞ < ๐ฅ < ∞ , ๐ฅ ≠ 2๐+1 2 ๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 5. Domain of ๐ = ๐๐๐๐ is (a) −∞ < ๐ฅ < ∞ (b)โ −1 ≤ ๐ฅ ≤ 1 (c) −∞ < ๐ฅ < ∞ , ๐ฅ ≠ 2๐+1 2 ๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 6. Domain of ๐ = ๐๐๐๐ is (a) −∞ < ๐ฅ < ∞ (b)โ −1 ≤ ๐ฅ ≤ 1 (c) −∞ < ๐ฅ < ∞ , ๐ฅ ≠ 2๐+1 2 ๐ , ๐ ∈ ๐ (d) ๐ฅ ≥ 1, ๐ฅ ≤ −1 1. A “Triangle” has : (a) Two elements (b) 3 elements (c) 4 elements (d) โ 6 elmen 2. When we look an object above the horizontal ray, the angle formed is called angle of: (a) โElevation (b) depression (c) incidence (d) reflects 3. When we look an object below the horizontal ray, the angle formed is called angle of: (a) Elevation (b) โ depression (c) incidence 4. A triangle which is not right is called: (a) โOblique triangle (b) Isosceles triangle (c) Scalene triangle (d) Right isosceles triangle 5. To solve an oblique triangle we use: (a) โLaw of Sine (b) Law of Cosine (c) Law of Tangents (d) All of these 6. In any triangle ๐จ๐ฉ๐ช, ๐ ๐+๐๐−๐๐ ๐๐๐ = (a) โ๐๐๐ ๐ผ (b) ๐ ๐๐๐ผ (c) ๐๐๐ ๐ฝ (d) ๐๐๐ ๐พ 7. Which can be reduced to Pythagoras theorem, (a) Law of sine (b) โ law of cosine (c) law of tangents (d) Half angle formulas 8. In any triangle ๐จ๐ฉ๐ช, if ๐ท = ๐๐° , then ๐ ๐ = ๐๐ + ๐๐ − ๐๐๐๐๐๐๐ท becomes: (a) Law of sine (b) Law of tangents (c) โLaw of cosine (d) None of these 9. In any triangle ๐จ๐ฉ๐ช, law of tangent is : (a) ๐−๐ ๐+๐ = tan (๐ผ−๐ฝ) tan (๐ผ+๐ฝ) (b) ๐+๐ ๐−๐ = tan (๐ผ+๐ฝ) tan (๐ผ−๐ฝ) (c) โ ๐−๐ ๐+๐ = tan๐ผ−๐ฝ 2 tan๐ผ+๐ฝ 2 (d) ๐−๐ ๐+๐ = tan๐ผ+๐ฝ 2 tan๐ผ−๐ฝ 2 10. In any triangle ๐จ๐ฉ๐ช, √ (๐บ−๐)(๐−๐) ๐๐ = (a) sin ๐ผ 2 (b) sin ๐ฝ 2 (c) โ sin ๐พ 2 (d) cos ๐ผ 2 11. In any triangle ๐จ๐ฉ๐ช, √ (๐บ−๐)(๐−๐) ๐๐ = (a) โ sin ๐ผ 2 (b) sin ๐ฝ 2 (c) sin ๐พ 2 (d) cos ๐ผ 2 12. In any triangle ๐จ๐ฉ๐ช, √ (๐บ−๐)(๐−๐) ๐๐ = (a) sin ๐ผ 2 (b) โ sin ๐ฝ 2 (c) sin ๐พ 2 (d) cos ๐ผ 2 13. In any triangle ๐จ๐ฉ๐ช, ๐๐๐ ๐ถ ๐ = (a) √ (๐ −๐) ๐๐ (b) √ (๐ −๐) ๐๐ (c) โ √ (๐ −๐) ๐๐ (d) √ (๐ −๐) ๐๐ 14. In any triangle ๐จ๐ฉ๐ช, ๐๐๐ ๐ท ๐ = (a) √ (๐ −๐) ๐๐ (b) โ√ (๐ −๐) ๐๐ (c) √ (๐ −๐) ๐๐ (d) √ (๐ −๐) ๐๐ 15. In any triangle ๐จ๐ฉ๐ช, ๐๐๐ ๐ธ ๐ = (a) √ (๐ −๐) ๐๐ (b) √ (๐ −๐) ๐๐ (c) √ (๐ −๐) ๐๐ (d) โ √ (๐ −๐) ๐๐ 16. In any triangle ๐จ๐ฉ๐ช, with usual notations , ๐ is equal to (a) ๐ + ๐ + ๐ (b) ๐+๐+๐ 3 (c) โ ๐+๐+๐ 2 (d) ๐๐๐ 2 17. In any triangle ๐จ๐ฉ๐ช, √ (๐−๐) (๐−๐)(๐−๐) = (a) sin ๐พ 2 (b) cos ๐พ 2 (c) tan ๐พ 2 (d) โ cot ๐พ 2 18. In any triangle ๐จ๐ฉ๐ช, √ (๐−๐)(๐−๐) ๐(๐−๐) = (a) sin ๐พ 2 (b) cos ๐พ 2 (c) โ tan ๐พ 2 (d) cot ๐พ 2 19. To solve an oblique triangles when measure of three sides are given , we can use: (a) โHero’s formula (b) Law of cosine (c) Law of sine (d) Law of tangents 20. The smallest angle of โ๐จ๐ฉ๐ช, when ๐ = ๐๐. ๐๐ , ๐ = ๐. ๐๐ , ๐ = ๐๐. ๐๐ is (a) ๐ผ (b) โ๐ฝ (c) ๐พ (d) cannot be determined 21. In any triangle ๐จ๐ฉ๐ช Area if triangle is : (a) ๐๐ sin๐ผ (b) 1 2 ๐๐ ๐ ๐๐๐ผ (c) 1 2 ๐๐ ๐ ๐๐๐ฝ (d) โ 1 2 ๐๐๐ ๐๐๐พ 22. The circle passing through the thee vertices of a triangle is called: (a) โCircum circle (b) in-circle (c) ex-centre (d) escribed circle 23. The point of intersection of the right bisectors of the sides of the triangle is : (a) โCircum centre (b) In-centre (c) Escribed center (d) Diameter 24. In any triangle ๐จ๐ฉ๐ช, with usual notations, ๐ ๐๐๐๐๐ถ = (a) ๐ (b) ๐1 (c) โ ๐ (d) โ 25. In any triangle ๐จ๐ฉ๐ช, with usual notations, ๐ ๐๐๐๐ท = (a) 2๐ (b)2 ๐1 (c) โ2๐ (d) 2โ 26. In any triangle ๐จ๐ฉ๐ช, with usual notations, ๐๐๐ ๐ธ = (a) ๐ (b) โ ๐ 2๐ (c) 2๐ ๐ (d) ๐ 2 27. In any triangle ๐จ๐ฉ๐ช, with usual notations, ๐๐๐ = (a) ๐ (b) ๐ ๐ (c) โ4๐ โ (d) โ ๐ 28. In any triangle ๐จ๐ฉ๐ช, with usual notations, โ ๐−๐ = (a) ๐ (b) ๐ (c) โ ๐1 (d) ๐2 29. In any triangle ๐จ๐ฉ๐ช, with usual notations, โ ๐−๐ = (a) ๐ (b) ๐ (c) ๐1 (d) โ ๐2 30. In any triangle ๐จ๐ฉ๐ช, with usual notations, โ ๐−๐ = (a) โ๐3 (b) ๐ (c) ๐1 (d) ๐2 31. In any triangle ๐จ๐ฉ๐ช, with usual notation , ๐: ๐น: ๐๐ = (a) 3:2:1 (b) 1:2:2 (c) โ 1:2:3 (d) 1:1:1 32. In any triangle ๐จ๐ฉ๐ช, with usual notation , ๐: ๐น: ๐๐: ๐๐: ๐๐ = (a) 3:3:3:2:1 (b) 1:2:2:3:3 (c) โ 1:2:3:3:3 (d) 1:1:1:1:1 1. An equation containing at least one trigonometric function is called: (a) Trigonometric function (b) โTrigonometric equation (c) Trigonometric value (d) None 2. If ๐๐๐๐ = ๐ , then solution in the interval [๐, ๐๐ ] is: (a) โ{ ๐ 6 , 5๐ 6 } (b) { 6 , 7๐ 6 } (c) { 3 , 4๐ 6 } (d) { 3 , 2๐ 6 } 3. If ๐๐๐๐ = ๐ , then the reference angle is: (a) โ ๐ 3 (b) – ๐ 3 (c) ๐ 6 (d) – ๐ 6 4. If ๐๐๐๐ = ๐ , then the reference angle is: (a) ๐ 3 (b) – ๐ 3 (c) โ ๐ 6 (d) – ๐ 6 5. General solution of ๐๐๐๐ = ๐ is: (a) โ{ ๐ 4 + ๐๐, 5๐ 4 + ๐๐} (b){ 4 + 2๐๐, 5๐ 4 + 2๐๐} (c){ 4 + ๐๐, 3๐ 4 + ๐๐} (d){ 4 + 2๐๐, 3๐ 4 + 2๐๐} 6. If ๐๐๐๐๐ = −๐, then solution in the interval [๐, ๐ ]is: (a) โ ๐ 8 (b) ๐ 4 (c) 3๐ 8 (d) 3๐ 4 7. If ๐๐๐๐ + ๐๐๐๐ = ๐ then value of ๐ ∈ [๐, ๐๐ ] (a) { 4 , 3๐ 4 } (b) { 4 , 7๐ 4 } (c) โ { 3๐ 4 , 7๐ 4 } (d) { 4 , −๐ 4 } 8. General solution of ๐๐๐๐๐ − ๐ = ๐ is: (a) {๐ + 2๐๐} (b) {๐ + ๐๐} (c) {−๐ + ๐๐} (d) โnot possible 9. General solution of ๐ + ๐๐๐๐ = ๐ is: (a) โ{๐ + 2๐๐} (b) {๐ + ๐๐} (c) {−๐ + ๐๐} (d) not possible 10. For the general solution , we first find the solution in the interval whose length is equal to its: (a) Range (b) domain (c) co-domain (d) โ period 11. All trigonometric functions are ……………….. functions. (a) โPeriodic (b) continues (c) injective (d) bijective 12. General solution of every trigonometric equation consists of : (a) One solution only (b) two solutions (c) โ infinitely many solutions (d) no real solution 1. The function ๐ฐ(๐) = ๐ is called : (a) A linear function (b) โ An identity function (c) A quadratic function (d) A cubic function 2. If ๐ is expressed in terms of a variable ๐ as ๐ = ๐(๐), then ๐ is called : (a) โAn explicit function (b) An implicit function (c) A linear function (d) An identity function 3. ๐ช๐๐๐๐๐ − ๐บ๐๐๐ ๐๐ = (a) -1 (b) 0 (c) โ1 (d) None of these 4. ๐๐๐๐๐๐๐ is equal to (a) 2 ๐ ๐ฅ+๐−๐ฅ (b) 1 ๐ ๐ฅ−๐−๐ฅ (c) โ 2 ๐ ๐ฅ−๐−๐ฅ (d) 2 ๐−๐ฅ+๐๐ฅ 5. ๐ฅ๐ข๐ฆ๐→๐ ๐ ๐−๐๐ ๐−๐ = (a) Undefined (b) โ 3๐2 (c) ๐ 2 (d) 0 6. ๐ฅ๐ข๐ฆ๐→๐(๐ + ๐) ๐ ๐ = (a) 1 ๐ (b) โ ๐ (c) ๐ 2 (d) Undefined 7. The notation ๐ = ๐(๐) was invented by (a) Lebnitz (b) โ Euler (c) Newton (d) Lagrange 8. If ๐(๐) = ๐๐ − ๐๐ + ๐ , then ๐(๐) = (a) -1 (b) 0 (c) โ 1 (d) 2 9. When we say that ๐ is function from set ๐ฟ to set ๐, then ๐ฟ is called (a) โDomain of ๐ (b) Range of ๐ (c) Codomain of ๐ (d) None of these 10. The term “Function” was recognized by______ to describe the dependence of one quantity to another. (a) โLebnitz (b) Euler (c) Newton (d) Lagrange 11. If ๐(๐) = ๐๐ then the range of ๐ is (a) โ [0,∞) (b) (-∞, 0] (c) (0, ∞) (d) None of these 12. If ๐(๐) = ๐ ๐ ๐−๐ then domain of ๐ is (a) ๐ (b) ๐ − {0} (c) โ ๐ − {±2} (d) ๐ 13. If a graph express a function , then a vertical line must cut the graph at (a) โOne point only (b) Two points (c) More than one point (d) No point 14. If ๐(๐) = { ๐ , ๐๐๐๐๐ ≤ ๐ ≤ ๐ ๐ − ๐ , ๐๐๐๐ ๐ < ๐ฅ ≤ 2 , then domain of ๐ (a) โ [0,2] (b) (0,2) (c) [1,2] (d) all real numbers 15. The graph of linear equation is always a (a) โStraight line (b) parabola (c) circle (d) cube 16. The domain and range of identity function , ๐ฐ: ๐ฟ → ๐ฟ is (a) โ๐ (b) +iv real numbers (c) –iv real numbers (d) integers 17. The linear function ๐(๐) = ๐๐ + ๐ is identity function if (a) ๐ ≠ 0, ๐ = 1 (b) ๐ = 1, ๐ = 0 (c) ๐ = 1, ๐ = 1 (d) ๐ = 0 18. The linear function ๐(๐) = ๐๐ + ๐ is constant function if ๐ ≠ 0, (a) ๐ = 1 (b) ๐ = 1, ๐ = 0 (c) ๐ = 1, ๐ = 1 (d) โ ๐ = 0 19. If ๐ = ๐๐๐๐ , ๐ ๐๐๐๐๐ = ๐น then range is (a) -1,1 (b) โ [-1,1] (c) ๐ -[-1,1] (d) ๐ −]-1,1[ 20. If ๐ = ๐๐๐๐, ๐ ๐๐๐๐๐ = {๐|๐ ∈ ๐น, ๐ ≠ (๐๐ + ๐) ๐ ๐ , ๐ ๐๐๐๐๐๐๐๐} then range is (a) ]-1,1[ (b) [-1,1[ (c) ๐ -[-1,1] (d) โ all real numbers 21. If ๐ = ๐๐๐๐ , ๐ ๐๐๐๐๐ = {๐|๐ ∈ ๐น, ๐ ≠ (๐๐ + ๐) ๐ ๐ , ๐ ๐๐๐๐๐๐๐๐} then range is (a) ]-1,1[ (b) [-1,1[ (c) ๐ -[-1,1] (d) โ ๐ −]-1,1[ 22. If ๐ = ๐๐๐๐ , ๐ ๐๐๐๐๐ = {๐|๐ ∈ ๐น, ๐ = ๐๐ , ๐ ๐๐๐๐๐๐๐} then range is (a)๐ฆ ≥ 1, ๐ฆ ≤ −1 (b) ๐ฆ ≤ 1, ๐ฆ ≥ −1 (c) ๐ฆ < 1, ๐ฆ > −1 (d) โ all real numbers 23. If ๐ = ๐๐๐๐๐๐ , ๐ ๐๐๐๐๐ = {๐|๐ ∈ ๐น, ๐ = ๐๐ , ๐ ๐๐๐๐๐๐๐} then range is (a) โ๐ฆ ≥ 1, ๐ฆ ≤ −1 (b) ๐ฆ ≤ 1, ๐ฆ ≥ −1 (c) ๐ฆ < 1, ๐ฆ > −1 (d) all real numbers 24. If ๐ = ๐๐ , ๐๐๐๐ ๐ = ๐๐๐๐ ๐ is called logarithmic function if (a) ๐ < 0 (b) ๐ > 0 (c) ๐ = 0 (d) โ๐ > 0 , ๐ ≠ 1 25. If ๐๐๐๐๐ = ๐ ๐+๐−๐ ๐ , then its domain is set of real numbers and range is (a) Set of all real numbers (b) โ Set of +iv real numbers (c) [1,∞) (d) [-1,∞) 26. In logarithmic form ๐๐๐๐−๐๐ can be written as (a) โln (๐ฅ + √๐ฅ 2 + 1) (b) ln (๐ฅ + √๐ฅ2 − 1) (c) ln (๐ฅ − √๐ฅ 2 + 1) (d) ln (๐ฅ − √๐ฅ2 − 1) 27. In logarithmic function ๐๐๐๐−๐๐ is written as (a) ln (๐ฅ + √๐ฅ 2 + 1) (b) โ ln (๐ฅ + √๐ฅ2 − 1) (c) ln (๐ฅ − √๐ฅ 2 + 1) (d) ln (๐ฅ − √๐ฅ2 − 1) 28. In logarithmic form, ๐๐๐๐−๐๐ can be written as (a) โ 1 2 ln ( ๐ฅ+1 ๐ฅ−1) , |๐ฅ| < 1 (b) 1 2 ln ( 1+๐ฅ 1−๐ฅ) , |๐ฅ| < 1 (c) ln ( 1 ๐ฅ + √1−๐ฅ2 ๐ฅ ) , 0 ≤ ๐ฅ ≤ 1 (d) ln ( 1 ๐ฅ + √1−๐ฅ2 |๐ฅ| ) , ๐ฅ ≠ 0 29. In logarithmic form, ๐๐๐๐−๐ can be written as (a) 1 2 ln ( ๐ฅ+1 ๐ฅ−1) , |๐ฅ| < 1 (b) โ 1 2 ln ( 1+๐ฅ 1−๐ฅ) , |๐ฅ| < 1 (c) ln ( 1 ๐ฅ + √1−๐ฅ2 ๐ฅ ) , 0 ≤ ๐ฅ ≤ 1 (d) ln ( 1 ๐ฅ + √1−๐ฅ2 |๐ฅ| ) , ๐ฅ ≠ 0 30. In logarithmic form, ๐บ๐๐๐−๐ can be written as (a) 1 2 ln ( ๐ฅ+1 ๐ฅ−1) , |๐ฅ| < 1 (b) 1 2 ln ( 1+๐ฅ 1−๐ฅ) , |๐ฅ| < 1 (c) โ ln ( 1 ๐ฅ + √1−๐ฅ2 ๐ฅ ) , 0 ≤ ๐ฅ ≤ 1 (d) ln ( 1 ๐ฅ + √1−๐ฅ2 |๐ฅ| ) , ๐ฅ ≠ 0 1. ๐ ๐ ๐ ๐๐๐๐๐ = (a) โ3 sec2 3๐ฅ (b) 1 3 sec2 3๐ฅ (c) ๐๐๐ก3๐ฅ (d) sec2 ๐ฅ 2. ๐ ๐ ๐ ๐ ๐ = (a) 2 ๐ฅ ๐๐2 (b) ๐๐2 2 ๐ฅ (c) โ 2 ๐ฅ ๐๐2 (d) 2 ๐ฅ 3. If ๐ = ๐๐๐ , then ๐๐ = (a) ๐ 2๐ฅ (b) 2๐2๐ฅ (c) โ4 ๐2๐ฅ (d) 16 ๐ 2๐ฅ 4. ๐ ๐ ๐ (๐๐ + ๐) ๐ = (a) ๐(๐๐−1๐ฅ + ๐) (b) ๐(๐๐ฅ + ๐) ๐−1 (c) ๐(๐๐−1๐ฅ) (d) โ ๐๐(๐๐ฅ + ๐) ๐−1 5. The change in variable ๐ is called increment of ๐.It is denoted by ๐น๐ which is (a) +iv only (b) –iv only (c) โ +iv or –iv (d) none of these 6. The notation ๐ ๐ ๐ ๐ or ๐ ๐ ๐ ๐ is used by (a) โLeibnitz (b) Newton (c)Lagrange (d) Cauchy 7. The notation ๐ฬ(๐) is used by (a) Leibnitz (b) โ Newton (c) Lagrange (d) Cauchy 8. The notation ๐ ′ (๐) or ๐ ′ is used by (a) Leibnitz (b) Newton (c) โ Lagrange (d) Cauchy 9. The notation ๐ซ๐(๐) or ๐ซ๐ is used by (a) Leibnitz (b) Newton (c) Lagrange (d) โ Cauchy 1. If ๐ = ๐(๐), then differential of ๐ is (a) ๐๐ฆ = ๐′ (๐ฅ) (b) โ ๐๐ฆ = ๐′ (๐ฅ)๐๐ฅ (c) ๐๐ฆ = ๐(๐ฅ)๐๐ฅ (d) ๐๐ฆ ๐๐ฅ 2. If ∫ ๐(๐)๐ ๐ = ๐(๐) + ๐ ,then ๐(๐) is called (a) Integral (b) differential (c) derivative (d) โ integrand 3. If ๐ ≠ ๐, then ∫(๐๐ + ๐) ๐๐ ๐ = (a) ๐(๐๐ฅ+๐) ๐−1 ๐ + ๐ (b) ๐(๐๐ฅ+๐) ๐+1 ๐ + ๐ (c) (๐๐ฅ+๐) ๐−1 ๐+1 + ๐ (d) โ (๐๐ฅ+๐) ๐+1 ๐(๐+1) + ๐ 4. ∫ ๐ฌ๐ข๐ง(๐๐ + ๐) ๐ ๐= (a) โ −1 ๐ cos(๐๐ฅ + ๐) + ๐ (b) 1 ๐ cos(๐๐ฅ + ๐) + ๐ (c) ๐ cos(๐๐ฅ + ๐) + ๐ (d)−๐ cos(๐๐ฅ + ๐) + ๐ 5. ∫ ๐ −๐๐๐ ๐ = (a) ๐๐−๐๐ฅ + ๐ (b) – ๐๐−๐๐ฅ + ๐ (c) ๐ −๐๐ฅ ๐ + ๐ (d) โ ๐ −๐๐ฅ −๐ + ๐ 6. ∫ ๐ ๐๐๐ ๐ = (a) ๐ ๐๐ฅ ๐ (b) ๐ ๐๐ฅ ๐๐๐ (c) โ ๐ ๐๐ฅ ๐๐๐๐ (d) ๐ ๐๐ฅ๐. ๐๐๐ 7. ∫[๐(๐)] ๐๐ ′ (๐)๐ ๐ = (a) ๐ ๐(๐ฅ) ๐ + ๐ (b) ๐(๐ฅ) + ๐ (c) โ ๐ ๐+1(๐ฅ) ๐+1 + ๐ (d) ๐๐๐+1(๐ฅ) + ๐ 8. ∫ ๐ ′ (๐) ๐(๐) ๐ ๐ = (a) ๐(๐ฅ) + ๐ (b) ๐ ′ (๐ฅ) + ๐ (c) โln|๐ฅ| + ๐ (nd) ln|๐ ′ (๐ฅ)| + ๐ 9. ∫ ๐ ๐ √๐+๐+√๐ can be evaluated if (a) โ๐ฅ > 0, ๐ > 0 (b) ๐ฅ < 0, ๐ > 0 (c) ๐ฅ < 0, ๐ < 0 (d) ๐ฅ > 0, ๐ < 0 10. ∫ ๐ √๐ ๐+๐ ๐ ๐ = (a) โ√๐ฅ 2 + 3 + ๐ (b) −√๐ฅ 2 + 3 + ๐ (c) √๐ฅ2+3 2 + ๐ (d) − 1 2 √๐ฅ 2 + 3 + ๐ 11. ∫ ๐ ๐ ๐ . ๐๐ ๐ = (a) ๐ ๐ฅ 2 ๐๐๐ + ๐ (b) โ ๐ ๐ฅ 2 2๐๐๐ + ๐ (c) ๐ ๐ฅ 2 ๐๐๐ + ๐ (d) ๐ ๐ฅ 2 2 + ๐ 12. ∫ ๐ ๐๐[๐๐(๐) + ๐′ (๐)]๐ ๐ = (a) โ๐ ๐๐ฅ๐(๐ฅ) + ๐ (b) ๐ ๐๐ฅ๐ ′ (๐ฅ) + ๐ (c) ๐๐๐๐ฅ๐(๐ฅ) + ๐ (d) ๐๐๐๐ฅ๐ ′ (๐ฅ) + ๐ 13. ∫ ๐ ๐ [๐๐๐๐ + ๐๐๐]๐ ๐ = (a) โ๐ ๐ฅ ๐ ๐๐๐ฅ + ๐ (b) ๐ ๐ฅ ๐๐๐ + ๐ (c) – ๐๐ฅ ๐ ๐๐๐ฅ + ๐ (d) – ๐๐ฅ ๐๐๐ ๐ฅ + ๐ 14. To determine the area under the curve by the use of integration , the idea was given by (a) Newton (b) โ Archimedes (c) Leibnitz (d) Taylor 15. The order of the differential equation : ๐ ๐ ๐๐ ๐ ๐๐ + ๐ ๐ ๐ ๐ − ๐ = ๐ (a) 0 (b) 1 (c) โ 2 (d) more than 2 16. The equation ๐ = ๐๐ − ๐๐ + ๐ represents ( ๐ being a parameter ) (a) One parabola (b) family of parabolas (c) family of line (d) two parabolas 17. ∫ ๐ ๐๐๐๐. ๐๐๐๐๐ ๐ = (a) โ๐ ๐ ๐๐๐ฅ + ๐ (b) ๐ ๐๐๐ ๐ฅ + ๐ (c) ๐ ๐ ๐๐๐ฅ ๐๐๐ ๐ฅ (d) ๐ ๐๐๐ ๐ฅ ๐ ๐๐๐ฅ 18. ∫(๐๐ + ๐) ๐ ๐๐ ๐ = (a) 1 3 (2๐ฅ + 3) 3 2 (b) 1 3 (2๐ฅ + 3) − 1 2 (c) 1 3 (2๐ฅ + 3) (d) None 19. ∫ ๐ ๐๐ ๐ = ๐ +๐ ๐+๐ + ๐ is true for all values of ๐ except (a) ๐ = 0 (b) ๐ = 1 (c) โ๐ ≠ −1 (d) ๐ = ๐๐๐ฆ ๐๐๐๐๐ก๐๐๐๐๐ ๐ฃ๐๐๐ข๐ 20. ∫ ๐ ๐๐ ๐ = ๐ ๐ (a) (๐ 2 − ๐)๐๐๐ (b) โ (๐2−๐) ๐๐๐ (c) (๐2−๐) log ๐ (d) (๐ 2 − ๐)๐๐๏ฟฝ ๐ฐ๐ ๐ < 0, ๐ฆ < 0 then the point ๐ท(๐, ๐) lies in the quadrant (a) I (b) II (c) โ III (d) IV 2. The point P in the plane that corresponds to the ordered pair (๐, ๐) is called: (a) โ๐๐๐๐โ ๐๐ (๐ฅ, ๐ฆ) (b) mid-point of ๐ฅ, ๐ฆ (c) ๐๐๐ ๐๐๐ ๐ ๐ ๐๐ ๐ฅ, ๐ฆ (d) ordinate of ๐ฅ, ๐ฆ 3. If ๐ < 0 , ๐ฆ > 0 then the point ๐ท(−๐, −๐) lies in the quadrant (a) I (b) II (c) III (d) โ IV 4. The straight line which passes through one vertex and though the mid-point of the opposite side is called: (a) โMedian (b) altitude (c) perpendicular bisector (d) normal 5. The straight line which passes through one vertex and perpendicular to opposite side is called: (a) Median (b) โ altitude (c) perpendicular bisector (d) normal 6. The point where the medians of a triangle intersect is called_________ of the triangle . (a) โCentroid (b) centre (c) orthocenter (d) circumference 7. The point where the altitudes of a triangle intersect is called_________ of the triangle. (a) Centroid (b) centre (c) โ orthocenter (d) circumference 8. The centroid of a triangle divides each median in the ration of (a) โ2:1 (b) 1:2 (c) 1:1 (d) None of these 9. The point where the angle bisectors of a triangle intersect is called_________ of the triangle. (a) Centroid (b) โin centre (c) orthocenter (d) circumference 10. If ๐ and ๐ have opposite signs then the point ๐ท(๐, ๐) lies the quadrants (a) I & II (b) I & III (c) โ II & IV (d) I & IV 11. A line bisecting 2nd and 4th quadrants has inclination: (a) 0° (b) 45° (c) โ 135° (d) ∞ 12. ๐ = ๐ is the straight line (a) โBisecting I & III (b) parallel to ๐ฅ − ๐๐ฅ๐๐ฅ (c) bisecting II & IV (d) parallel to ๐ฆ – ๐๐ฅ๐๐ 13. If all the sides of four sided polygon are equal but the four angles are not equal to ๐๐° each then it is a (a) Kite (b) โ rhombus (c) ||gram (d) trapezoid 1. The solution of ๐๐ + ๐ < ๐ is (a) Closed half plane (b) โ open half plane (c) circle (d) parabola 2. A function which is to be maximized or minimized is called______ function (a) Subjective (b) โ objective (c) qualitative (d) quantitative 3. The number of variables in ๐๐ + ๐๐ ≤ ๐ are (a) 1 (b) โ 2 (c) 3 (d) 4 4. (0,0) is the solution of the inequality (a) 7๐ฅ + 2๐ฆ > 0 (b) 2๐ฅ − ๐ฆ > 0 (c) โ ๐ฅ + ๐ฆ ≥ 0 (d) 3๐ฅ + 5๐ฆ < 0 5. (0,0) is satisfied by (a) ๐ฅ − ๐ฆ < 10 (b) 2๐ฅ + 5๐ฆ > 10 (c) โ ๐ฅ − ๐ฆ ≥ 13 (d) None 6. The point where two boundary lines of a shaded region intersect is called _____ point. (a) Boundary (b) โ corner (c) stationary (d) feasible 7. If ๐ > ๐ then (a) – ๐ฅ > −๐ (b) – ๐ฅ < ๐ (c) ๐ฅ < ๐ (d) โ – ๐ฅ < −๐ 8. The symbols used for inequality are (a) 1 (b) 2 (c) 3 (d) โ4 9. A linear inequality contains at least _________ variables. (a) โOne (b) two (c) three (d) more than three 10. An inequality with one or two variables has ________ solutions. (a) One (b) two (c) three (d) โinfinitely many 11. ๐๐ + ๐๐ < ๐ is not a linear inequality if (a) โ๐ = 0, ๐ = 0 (b) ๐ ≠ 0 , ๐ ≠ 0 (c) ๐ = 0, ๐ ≠ 0 (d) ๐ ≠ 0, ๐ = 0, ๐ = 0 12. The graph of corresponding linear equation of the linear inequality is a line called________ (a) โBoundary line (b) horizontal line (c) vertical line (d) inclined line 13. The graph of a linear equation of the form ๐๐ + ๐๐ = ๐ is a line which divides the whole plane into ______ disjoints parts. (a) โTwo (b) four (c) more than four (d) infinitely many 14. The graph of the inequality ๐ ≤ ๐ is (a) Upper half plane (b) lower half plane (c) โ left half plane (d) right half plane 15. The graph of the inequality ๐ ≤ ๐ is (a) Upper half plane (b) โ lower half plane (c) left half plane (d) right half plane 16. The graph of the inequality ๐๐ + ๐๐ ≤ ๐ is _____ side of line ๐๐ + ๐๐ = ๐ (a) โOrigin side (b) non-origin side (c) upper (d) lower 17. The graph of the inequality ๐๐ + ๐๐ ≥ ๐ is _____ side of line ๐๐ + ๐๐ = ๐ (a) Origin side (b) โ non-origin side (c) upper (d) left 18. The feasible solution which maximizes or minimizes the objective function is called (a) Exact solution (b) โ optimal solution (c) final solution (d) objective function 19. Solution space consisting of all feasible solutions of system of linear in inequalities is called (a) Feasible solution (b) Optimal solution (c) โ Feasible region (d) General solution 20. Corner point is also called (a) Origin (b) Focus (c) โ Vertex (d) Test point 21. For feasible region: (a) โ๐ฅ ≥ 0, ๐ฆ ≥ 0 (b) ๐ฅ ≥ 0, ๐ฆ ≤ 0 (c) ๐ฅ ≤ 0, ๐ฆ ≥ 0 (d) ๐ฅ ≤ 0, ๐ฆ ≤ 0 22. ๐ = ๐ is in the solution of the inequality (a) ๐ฅ < 0 (b) ๐ฅ + 4 < 0 (c) โ2๐ฅ + 3 > 0 (d)2๐ฅ + 3 < 0 23. Linear inequality ๐๐ − ๐๐ > 3 is satisfied by the point (a) (5,1) (b) (-5,-1) (c) (0,0) (d) โ (1,-1) 24. The non-negative constraints are also called (a) โDecision variable (b) Convex variable (c) Decision constraints (d) concave variable 25. If the line segment obtained by joining any two points of a region lies entirely within the region , then the region is called (a) Feasible region (b) โ Convex region (c) Solution region (d) Concave region 1. The locus of a revolving line with one end fixed and other end on the circumference of a circle of a circle is called: (a) a sphere (b) a circle (c) โa cone (d) a conic 2. The set of points which are equal distance from a fixed point is called: (a) โCircle (b) Parabola (c) Ellipse (d) Hyperbola 3. The circle whose radius is zero is called: (a) Unit circle (b) โpoint circle (c) circumcircle (d) in-circle 4. The circle whose radius is 1 is called: (a) โUnit circle (b) point circle (c) circumcircle (d) in-circle 5. The equation ๐ ๐ + ๐๐ + ๐๐๐ + ๐๐๐ + ๐ = ๐ represents the circle with centre (a) (๐, ๐) (b) โ (−๐, −๐) (c) (−๐, −๐) (d) (๐, −๐) 6. The equation ๐ ๐ + ๐๐ + ๐๐๐ + ๐๐๐ + ๐ = ๐ represents the circle with centre (a) โ√๐2 + ๐2 − ๐ (b) √๐2 + ๐2 + ๐ (c) √๐2 + ๐2 – ๐ (d) √๐ + ๐ − ๐ 7. The angle inscribed in semi-circle is: (a) โ ๐ 2 (b) ๐ 3 (c) ๐ 4 (d) None of these 8. For any parabola in the standard form , if the directrix is ๐ = ๐ , then its equation is (a) ๐ฆ 2 = 4๐๐ฅ (b) โ ๐ฆ 2 = −4๐๐ฅ (c) ๐ฅ 2 = 4๐๐ฆ (d) ๐ฅ 2 = −4๐๐ฆ 9. For any parabola in the standard form , if the directrix is ๐ = −๐ , then its equation is (a) โ๐ฆ 2 = 4๐๐ฅ (b) ๐ฆ 2 = −4๐๐ฅ (c) ๐ฅ 2 = 4๐๐ฆ (d) ๐ฅ 2 = −4๐๐ฆ 10. For any parabola in the standard form , if the directrix is ๐ = ๐ , then its equation is (a) ๐ฆ 2 = 4๐๐ฅ (b) ๐ฆ 2 = −4๐๐ฅ (c) ๐ฅ 2 = 4๐๐ฆ (d) โ ๐ฅ 2 = −4๐๐ฆ 11. For any parabola in the standard form , if the directrix is ๐ = −๐ , then its equation is (a) ๐ฆ 2 = 4๐๐ฅ (b) ๐ฆ 2 = −4๐๐ฅ (c) โ ๐ฅ 2 = 4๐๐ฆ (d) ๐ฅ 2 = −4๐๐ฆ 12. All lines through vertex and points on circle generate a (a) โCircle (b) Ellipse (c) Circular cone (d) None of these 13. The equation ๐ ๐ + ๐๐ = ๐ then circle is (a) โPoint Circle (b) Unit Circle (c) Real circle (d) Imaginary Circle 14. The line perpendicular to the tangent at any point ๐ท(๐, ๐) is known as; (a) Tangent line (b) โ Normal at ๐ (c) Slope of tangent (d) None of these 15. The point ๐ท(−๐, ๐) lies __________ the circle ๐ ๐ + ๐๐ + ๐๐ − ๐๐ = ๐๐ (a) โInside (b) Outside (c) On (d) None of these 16. The chord containing the centre of the circle is (a) Radius of circle (b) โDiameter of circle (c) Area of circle (d) Tangent of circle 17. The ratio of the distance of a point from the focus to distance from the directrix is denoted by (a) โ๐ (b) ๐ (c) ๐ธ (d)e 18. Standard equation of Parabola is : (a) ๐ฆ 2 = 4๐ (b) ๐ฅ 2 + ๐ฆ2 = ๐2 (c) โ ๐ฆ 2 = 4๐๐ฅ (d) ๐ = ๐ฃ๐ก 19. The focal chord is a chord which is passing through (a) โVertex (b) Focus (c) Origin (d) None of these 20. The curve ๐ ๐ = ๐๐๐ is symmetric about (a) โ๐ฆ – ๐๐ฅ๐๐ (b) ๐ฅ – ๐๐ฅ๐๐ (c) Both (a) and (b) (d) None of these The vector whose magnitude is 1 is called (a) Null vector (b) โ unit vector (c) free vector (d) scalar 3. Two vectors are said to be negative of each other if they have the same magnitude and __________direction. (a) Same (b) โ opposite (c) negative (d) parallel 4. Parallelogram law of vector addition to describe the combined action of two forces, was used by (a) Cauchy (b) โ Aristotle (c) Alkhwarzmi (d) Leibnitz 5. The vector whose initial point is at the origin and terminal point is ๐ท , is called (a) Null vector (b) unit vector (c) โposition vector (d) normal vector 6. If ๐น be the set of real numbers, then the Cartesian plane is defined as (a) ๐ 2 = {(๐ฅ 2 , ๐ฆ2 ): ๐ฅ, ๐ฆ ∈ ๐ } (b) โ ๐ 2 = {(๐ฅ, ๐ฆ): ๐ฅ, ๐ฆ ∈ ๐ } (c) ๐ 2 = {(๐ฅ, ๐ฆ): ๐ฅ, ๐ฆ ∈ ๐ , ๐ฅ = −๐ฆ} (d) ๐ 2 = {(๐ฅ, ๐ฆ): ๐ฅ, ๐ฆ ∈ ๐ , ๐ฅ = ๐ฆ} 7. The element (๐, ๐) ∈ ๐น๐ represents a (a) Space (b) โ point (c) vector (d) line 8. If ๐ = [๐, ๐] in ๐น ๐ , then |๐| =? (a) ๐ฅ 2 + ๐ฆ2 (b) โ √๐ฅ 2 + ๐ฆ2 (c) ±√๐ฅ 2 + ๐ฆ2 (d) ๐ฅ 2 − ๐ฆ2 9. If |๐| = √๐๐ + ๐๐ = ๐, then it must be true that (a) ๐ฅ ≥ 0, ๐ฆ ≥ 0 (b) ๐ฅ ≤ 0, ๐ฆ ≤ 0 (c) ๐ฅ ≥ 0, ๐ฆ ≤ 0 (d) โ ๐ฅ = 0, ๐ฆ = 0 10. Each vector [๐, ๐]in ๐น ๐ can be uniquely represented as (a) ๐ฅ๐ – ๐ฆ๐ (b) โ ๐ฅ๐ + ๐ฆ๐ (c) ๐ฅ + ๐ฆ (d) √๐ฅ 2 + ๐ฆ2 11. The lines joining the mid-points of any two sides of a triangle is always _____to the third side. (a) Equal (b) โ Parallel (c) perpendicular (d) base 12. A point P in space has __________ coordinates. (a) 1 (b) 2 (c) โ 3 (d) infinitely many 13. In space the vector ๐ can be written as (a) โ (1,0,0) (b) (0,1,0) (c) (0,0,1) (d) (1,0) 14. In space the vector ๐ can be written as (a) (1,0,0) (b) โ (0,1,0) (c) (0,0,1) (d) (1,0) 15. In space the vector ๐ can be written as (a) (1,0,0) (b) (0,1,0) (c) โ (0,0,1) (d) (1,0) 16. ๐ = ๐๐ + ๐๐ + ๐,๐ = −๐๐ − ๐๐ − ๐๐ are _________vectors. (a) โParallel (b)perpendicular (c) reciprocal (d) negative 17. The angles ๐ถ, ๐ท, ๐๐๐ ๐ธ which a non-zero vector ๐ makes with ๐ − ๐๐๐๐, ๐ − ๐๐๐๐ and ๐ − ๐๐๐๐ respectively are called_____________ of ๐. (a) Direction cosines (b) direction ratios (c) โ direction angles (d) inclinations