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UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATTON ,ts"A, ( ECONOMICS 201J Ad mi ssion o nwo rd s ) l\,/ Semester Core Course OUANTTTATWE NIETHODS FOR ECONOMIC ANAIYS$ Choose the correct Answer from the bracket. E)(PONENTS 1. Find the Value (a) 2. of (b) 16 8 (c) 32 (d) 64 Find thevalueof (27)-aA ,.1 (a); 3; 23 x 21 @); t.) * (d) i Find the nalue of (.001)% (u) (b).1 .001 (c) .01 (d) .0001 1a563/+s\-2/z @16-r, c-fr (u) o/o, 5. (b), /o, The value of (-Z1s/z (a) Quontitotive Methods for e*iii "/o-, (d) b/ i" @ ,li. 'l-sz G) a*ty"ii (c) y'ro (d) J= o, U School of Distance Educotion 6. 36x7 ya + 4x6y is (a)9x2y3 7. (b) 9xy3 (c) 9y3x2 (d\ 9x1/eyt (b) 6' (c) 3' (d) (b) 2' (c) 2' (d) 4' 3 x 35 is equal to es (u) 3u "t'' a, 'gl (u) /zis equal to 8, 9. 100 is equal to (a) 70. If 10 x2= 1, (a) (b) 2 (b) (a) 0 (d) 100 -2 (c) 0 (d) 1 is x- 12. am x (c) x-2 isequal to 11. x^ x rtr (a) 1 (b) x- * " (.) r-" (d) x" (d) ao ao is equal to o' (b) 0 (c) m 13.2-3isequalto (u)8 16)% (.)2 (d)3 74. 3t27t -g.-+4valueof ris (a)7 Quonti.ative Mehods [or Economic O)3 Ahd',js I I (c)e (d)s (rt x xrs/z) 15. ts ls (a) x6 ,' (c) xs/z (b) r/,, (c) r' (d) (b) 4aa?b7 (c) 48a3b2 (d) +8arbs (b) qn-" (c) a-n 1u) ro% (c) ro% (c) 1 (d) xa/s /,, ,)' (.' lxe )'o 1.6. r7 L/." (a) lxe '/*" ) r' ? (6a3b (6a3 b2))(8 b2 (8a4,bt) ls 17. (a) ga72b1 14721bro r1o 18. am = an rn is mt (a) 7e. (a) (b) (d) a-+" ($"'o 10 lay ro% (d) 4 n. #isequarto (a)2 (b)3 LOGARITI{MS 21. logr 3 = (a) 22. 3 ax log6 (a) gu o n d to ti u " u (b) logo b 1 * o* 1* iiiiffi 9 (c) 1 (d) 0 a (c) b (d) 0 is equal to (b) 23. log2 1 is (a) (b) 2 (.) 1 o (d) 3 24. toe"(lt)= (a) log" b logJz I (a) 6 D (b) 4 (a) (d) -lo96 a is (c) I (d) 2 (b) 1 2 (c) 3 (d) 0 The characteristic of the logarithm of '0032 is (a) (b) -1 1 28. Antilogarithm of 2.4678 is (b) (a) 2e36 2e31 (c) -2 (d) -3 G) (d) 2e3s 2e3o Find the number of zeros in 3-2s immediately after the decimal point' 29. (a) 30. (b) 12 11 (c) 10 (d) e (c) 2 (d) s Find the logarithms of 125 to the base 5 (a) (b) 3 1 31. Change into the logarithm lotm (a) log5 216 = 32. (u) (c) lo96 a The characteristic of the logarithm of 83.2 is 26. 27. (b) -log. logr5 2lz 64 3 63 = 21'6 (b) log3 6 = 216 (c) lo963 = 216 (d) G) r/z (d) log3 216 is equal to b) 3lz QEntitoaivc ethoits lor Economic Anolysis I I 2 = 6 EOUATION 33. Find the value of rlr = 8 (b) @)a 34. 7x - 27 - 3x +13 = (a) 7+ If in the equation ar2 36. simple linear @) r/z 2 6x -19 isequal to o)1 2 (a) (c) 8 f (c) bx + c = (b) 0, (d) 3 .s b is zero, then the equation is called pure quadratic (c) generat quadratic (d) The ss and dd curves for a commodity are known to be gs = p _ I and qd =12/p. Find the equation price. (a) 37. (b) 4 The quanti ty b2- 4ac is called (a) roots U. b2- kc = O, (c) 2 _ (d) 6 s of the quadratic equation. (b) discriminmt (c) power (d) none the roots are (a) real and. equal (c) irrational and unequal o) rational (d) and unequal unreal 39. Find thevalue of K for which x2_ 2 kx + gk _ 15 = 0 has equal roots. (a) o) 3,s 3,6 40. (x + 2)2 = x2+ 4x + 4 is known (a) 41. Sum of the roots of quadratic equation. (^) /, b q u o, ti a ti v b) -b/o " u *h ods piiifr ffi s,3 (d) (c) both (d) 5,6 as. @) id.entity equation (c) (r) a/t (d) -a/r are' 42. Product of the roots of quadratic equations (a) ct lo @') (d) -c/a (c) a/c -'/" PROGRISSIONS Arithmetic ProEression 43.AseriesissaidtobeinArithmeticProgression,ifanytermofitisobtainedby adding a constant number to its term' (c\ preceeding (a) succeeding p) preceeding - and succeeding (d) none The ntn term of an Arithmetic Progression' (b) a+n(n-1)d (d) a+(n-t)-d (a) a+ (n-r)d (c) o+(n-1)+d 45. l2thterm of the series 9 + 13 + 77 + 27 + ... ... .... (a) (b) s2 s3 (c) (d) sa ss ,16. The sum of first n natural numbers' (")ry M. (a) (b) i6 13 (c) 5, (d) none the last term is 45, Sn= 18 (d) e s,3 (d) s,6 The arithmetic mean between 8 and 14 is equal to (a) 49. +rl (c) n(n + 1)2 The first term of an Arithmetic Progression is n is equal to (a) 48. tu) 3,6 (b) (c) 3,s The nrh term of G.P. is Tn-l (b) -n-t = qrordur;* U"*o* 1", Economic Anatvsis ll (c) arr-r (d); 400, 50. when r < 1, the sum of n terms of G.p. is a(rn-l) r-l ,r', 51. (b) ++ The sum of infinite G.p. (a) 52. C.M. between (a) none 8 (c) 16 (d) 2 120 (c) e0 (d) s4 18 and 162 (b) 22 SET 53. (d) 16,&4,........ (b) 32 (c) both TTilORY Ina set theory, the set of numberc1.,3, S,Z 9..... can be represented by A-{X: X is an odd integer} is a method. _ 54. 55. 56. (a) Tabular Method (b) Rule method. (c) Roster method (d) Enumeration Method Two sets A ={7,3,4,7) and B = {7,3,1, 4} are said to be (a) Equality (c) Null set of sets s8. (d) Singleton (d) none The subset of every set O) Equal Set The set 0 is represented by (a) singleton (b) NuLl (c) Null set (d) none (c) Both (d) none (c) a (d) -4 *\24i" x-2 (a) Qu a n Equiualent sets A set which contains only one element is called (a) Null set (c) Singleton @) Equal set . (a) Singleton 57. @) (b) o titatiye M e th o d s Io r Econ o- ic i o tyJlii " ,\z (a) 60. ,r*z i" (b) 32 A function is continuous Lt (a) x -.t a d 4x4+ 3x3 (u) 4/s 62. (u) 'b' (r) a/t (d)3/+ The derivative of e:2 is (b) e2' The minimum of the function y Derivative of If 7f,, = 10 + -2' " @) 2x lteddtlo 4x2 * g is at (c) x=4 (d) None of these (c) 2x-3 (d) N one of these 2r + 3r2 be the cost function then the srope of the average cost be (a) 2+6x Quantihdve -- (d) 2x e'2 is (b) r (c) Zex (b) r=8 (d -x2 65. of the above ts (a) x=0 64. None (d) None of the above (b)a/z e" 63. (c) Both 'a' and f inite quantity bl. ,-+ _r ------;-:-:--1 (d) if f(x) = f(a) exist (b) /(a)is tt (c) I 3e Economtc Ano,'l. tt + 3x2 (.)4+ a (d) zxz + 4x3 66. The derivative of (a) (x2 + r2e' 2)e, is (b) (x, rfy=li?,o (a) 3x ! 2x)e, (c) x2e, (d) (2x + L)ex 67. 68. 69. (a) (b) !x-3 dx ft y = *the (u) (c) logex (d) t/", (b) log x2 (c) , (d)r/* (b) (c) 3x-a (d) 3x-2 (c) 2x2 (d) N one of these N one of these -ax-z derivative is (a) o 72. e' is (a) 3 x-a 7't. (d)r/* The derivative of Jogx r log r 70. 612frxL/z Derivative of ex is xe'-L (a) r/rru/, b) b)1/z lxbsxis dx r/* 73. xy=c2 @) t + logx (c) llogx (d) G) -'/y (d)-Y/x the derivative is (u)Y/, Quantiutive tlethods fot Econonic (b)'/y Anctysis I ! School of Distonce Education 74. A function is said to be maximum at r - a if (a) /(a) is negative andf"(a) zero (b) f(a) is zero andf "(a) is negative (c) f(a) is zero and f " (a) is zerc (d) 75. /(a) is negative andf "(a) is negative A function is said to be minimum (u) f '=0 and f ">0 (b) f'=0 and f"<0 (c) f '>0 and f"=0 (d) f '<0andf "=0 76. The function 2x2 (a) 77. At - 8x t 2 the function -3xz (a) maximum 78. (c) ' is equal to (c) 2x (b) e -e (u) (b) (c) (d) + 2 - (3 - r), (c) (b) (d) Negative Non-positive The function 3x3 (d) p) minimum (c) Point of Inf lection (d) N one of the above -3 Increasing function if and only if its derivatives on (a, b) is (a) 80. at'r' + lZ + 5 is When Revenue is maximum if R = 3000 (u) 79. minimum (b) -8 4 t= 10 is 3x2 * x - 10 is An increasing function Decreasing function Standard function None of the above Quanti.ative Methods lot Econonic Anolysis ll Non - N e gatioe None ofthe above (d) 3 81' If the second derivative of a function/r) is positive then in the given interval the function is said to be (a) Ino.easing @) Dec,reasing (c) 82. (d) Convex Concave The differential Coefficient of the dependent variabre with respect to one of the independent variabres keeping the other independent variabre is constant is called (a) (c) Simple derivotive Partial derivative (b) (d) Total derivative Cross derivative BASIC MATRD( AIGEBRA A triangular matrix is the one in which a. All the diagonal elements are zero b. All the elements above or below the diagonal are zero c. All diagonal elements are non-zero d. All the elements are unity 84. If A = AT, the A is called a. Square matrix b. Skew symmetric 85. c. Orthogonal matrix d. Symmetric Matrix matrix When the determinant of a matrix is zero, the matrix is called a. Singular c. Null b. Non singular 85. Given A d. Identity is 2x2 matrix and B is 2x3, the matrix AB a.2x2 b.2x3 will be c.3x3 d.3x2 87. If the two rows or columns are identical or proportional , the determinant is a. One b. Infinity 88. The transpose of a matrix of minors a. Adjoint b. Cofactor Quontitative Me,hodslor Econonic Anatysis c. Undefined d. Zero Determinat d. Inverse is called c. 89. tu{-l= a.A -. 90. =A-1A b. A-1 c. I d. None of the above For a matrix minor M12=-34, then the cofactor C12 a. 34 b. will be '17 c. -34 d.0 91.. The linear form AX= B implies that a. X= A-1B b. c. X=B-1A X=AB d. X=BA-1 92. The determinant is defined only for a. Row matrix b. Column matrix c. Square matrix d. Null matrix . 93. Matrix B is called Skew symmetric a. b. if B=BT c. B=-BT B=B2 d. None of the above 94. If the turo matrices are of the order mm and nxp, then AB will of the dimension a. b. c. Pxn mxP 95. If A=AZ the matrix A is known a. Symmetric b. Skew SYmmetric d. nxp mxn as . c. IdemPotent d. Triangular 95. If AxA = A, then the matrix A is a. Nil potent b. Symmetric 97' c. d. Triangular Identity If the determinant of a matrix is found out to be -65, the determinant of its transpose is a. -65 b. 65 c. 32.5 d. Cannot say 98. A square matrix in which all the diagonal elements are equal and non_diagonal elements are zero is called a. Diagonal matrix b. Scalar matrix 99. The determinant of 3x3 matrix is called a. First order determinant b. Second order determinant c. d. c. d. Triangular matrix Unit matrix Third order determinant Fourth order determinant 100. A matrix with equal number of rows and column is called a. Square matrix c. Column matrix b. Row matrix d. Null matrix 101. A diagonal matrix with each of the diagonal elements is unity is a. Vector c. Diagonal matrix b. Square rirahix d. Identity matrix -102. If in it a square matrix, all the elements below the leading diagonal is zero, is a. Lower triangular matrix b. Upper triangular matrix c. d. Identity metrix Null matrix 103. The maximum number of linearly independent rows or columns matrix is called a. Determinant b. Trace Quontitative Methods lot Econonic Anolysis c. d. It Rank Minor in the 104. The determinant of the triangular matrix is the product of a. b. c. Rows Columns d. Rows and columns Diagonals 105. Minor with the prescribed sign is called c. a. Inverse b. Cofactor 106. d. Determinant Adjoint The transpose of the cofactor matrix is a. b. c. Cofactor Rank Inverse d. Adjoint 1.07. For a square matrix, inverse exists if and only if it is a. b. Non-singular Singular c. Null d. Cannot say FI'NCTIONS AND GRAPHS 108. A is a value that may change set of operations within the scope of a given problem or - (a) constant (b) variable function (d) exponent (c) 109. Given y = f (x) 'y' is called a variable and variable. (a) independent, dependent (b) variable, constant - variable (d) dependent, independent (c) constant, 110. In u = f (xl.'r/ (a) is called output, input (b) variable, constant (c) input, output (d) constant variable Quand&,dvc N.ahodshr E..,,,onb Arfrod/l lt and 'r' is called 'x' is called an 111. . represents a response, behaviour, wishes to predict or explain. or outcome that the researcher (a) independent variable (b) function (c) equation (d) dependent variable 1-12. variable is a factor that is not itself under study but affects the measurement of the study variables or the examination of thJir relaU."rf,ipr. (a) Exogenous (b) Endogenous -(c) Extraneous (d) Dependent 113. If a term cohsists of only variables, its coefficient is (a) 1 (b) does not exist (.) o (d) unknown 114. Expressions consisting of a real number or of a coefficient times one or more variables raised to the power of a positive integer are called ..... (a) polynomials (b) monomials (c) functions (d) equations 115. In a variable expressions 5a + 3b, ,a, and ,b, are_ 5 and 3 are and+ is an (a) variables, constants, operator (b) constants, variables, operator (c) operator, variables, constants (d) variables, operator, constants 116' A is an equation for which any x that can will- yield exactly one y out of the equation (a) monomial (b) polynomial (c) function (d) operator Quantitotive Methods lor t"ono-i, l,nAyri" t 1 be prugged into the equation plot a graph of a function, as independent variable on the _ variable on the _ axis. 117. Tci a matter axis of of convention, we plot the a graph, and the dependent (a) horizontal, vertical (b) vertical, horizontal (c) vertical or horizontal (d) vertical and horizontal 118. take the form y = a + qr (a) Power (b) Quadratic (c) Linear -functions (d) Exponential "179. functions take the form y = a + kxp -(a) Power (b) Quadratic (c) Linear (d) Exponential -120. If the relation between two variables x and y is expressed in the form t(x,y)=O, ' where x cannot be expressed as a function of y, oiy .unoot be expressed as a function of x, is called _ function. (a) Quadratic (b) function implicit explicit (d) Linear function (c) The graph of is such that the two ends of the graph will be directed towards the same side. (a) odd (b) implicit (c) -function power (d) even 122. A function/x) has an inverse function if and only if f(x) is (a) one-to-one (b) one-to-many (c) many-to-one (d) one-to-two Quantitative Methods lor Econonic Atlotysis II 123. In the rectangular coordinate system This notation is called (a) cartesian the coordinates of the origin are (e0). product (b) ordered pair (c) Determinant (d) None of these 124. In the rectangular coordinate system, in quadrant IV, x is always. and y is always_ (a) negative, positive (b) negative, negative (c) positive, negative (d) positive, positive 125. The distance formula can be obtained by creating a triangle and using the Pythagorean Theorem to find the length of the " (a) arc (b) slope (c) graph (d) hypotenuse 125' The is an ordered pair formed by finding the average of the x-varues and the average of the y-values of thu gire., po"ints - (a) arc (b) slope (c) midpoint (d) hypotenuse -127. The _of a line measures the change in y (Ay) divided by change in x (Ax). (a) stope (b) arc (c) hypotenuse (d) midpoint 128. The _the absolute value of the slope, the (a) steeper, greater (b) $eater, steeper (c) greater, flatter (d) lesser, steeper Qu o n ti to ti v e M e th o ds Fo r e, o" oiiirr,fi ii _the line. 129. The slope of a vertical line (for example for which Ax = 0, is a perfectly inelastic demand curve), (a) o (b) 1 (c) -1 (d) undefined 130. The (a) x is the point where your line crosses the x-axis. ihtercept - (b) slope (c) arc (d) quadrant A is a relation (usually an equation) in which no two ordered pairs have same x<oordinate when graphed. the - (a) graph @) quadratic (c) function equation (d) linear equation Point-slope refers to a method for (a) a graphing equation on an x-y axis. linear (b) a quadratic linear (d) a cubic (c) a non - School oI Dtstance Edu ANSWERKEY 1. (a) 16 n. (a) maximum 78. (d) 3 79. (b) Non-Negative 80. (a) An increasing function 81. (c) convex 82. (c) Partial derivative 83 (b) All the elements above or 2. G)r/u 3. 4' 5. 6. ' 7. .7 @)"/o, (a).\E3Z p) 9xy3 (d) 3u (b) below the diagonal are zero 8. 9. 10. 11. 12. 28 (b) 1 (d) 1 (b) :-*" (a) a- &1 85 86 8Z 88 (b) 2x3 13. 1u) 8e (") I -t4. % (a) (c) 7 15. (u) ,u 76. @) 1/r" 77. @) 48a?b7 18. (b) a--" 19. (a) 10 20. (a) 2 21.. (c) 1 22. (a) 1 23. (c) 0 24. (b) log" D 25. (a)6 26. (a)1 27. (d)3 Quontitotive l,lethodsfor Econonic Ahab,sis L 90 91 92 93 94 95 96 97 98 99 (d) symmetric Mahix (a) Singular (d) Zero (b) cofactor (a) 34 (a) X= A-1B (c) Square Matrix (c) B=-BT (b) Mxp (c) Idempotent (d) Identity (a) -6s (a) Diagonal matrix (c) Third order determinant 100 (a) Square matrix 101 (d) Identity matrix 102 (b) Upper triangular 103 (c) Rank t t matrix 22 28. (a)2936 1& (d) Diagonals 29. (b) 11 (b) Cofactor 30. (a) 3 31- (a) logu2l6=3 32. (b)3/z 105 106 107 108 JJ. (c) 2 109 (d) dependent, independent 34. (a) 2 110. (a) output, 35. (b) Pure Quadratic 111. (d) dependent variable 36. (a) 4 112. (c) Extraneous J/. (b) discriminant 113 (u) 38. (a) real and equal 114. (b) monomials 39. (c) s,3 (a) variables, constants, operator 40. (b) identity 41.. (b) b/" 115 776 777 42. (u) 118 43. (b) preceeding 119 (a) Power u. (a) a+ (n-1)d 120. (b) 45. (b) s3 nfn+1) - ---:------(al 121. (d) even 46. '/a (b) 49. (c) s0. s1. 52. 53. 54. 55. 56. (a) Non-singular (b) variable input 1 (c) function (a) horizontal, vertical (d) Exponential implicit -122. (a) one-to-one 2 47. 48. (d) Adioint "123 (b) ordered pair Da. @) 125. (d) hypotenuse 126. (c) (a) 32 127. (a) slope (d) s4 128. (b) greater, steeper (b) Rule Method 129. (d) undefined (a) Equality of sets 130. (a) intercept (c) Singleton 131. (c) function 132. (a) a linear 16 (a) 11 1u) ar"-1 g!# (c) Null set Quontitotive Mehods lor Economic Anollsis ll positive, negative midpoint