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Welcome to EdCETInfo.com's EdCET 2003 Key :: Mathematics



PART - C

MATHEMATICS

(Marks : 100)
51 Suppose A and B are two sets with m and n elements respectively. Let the power sets of A and B contain M and N elements respectively. If M-N = 56 then the ordered pair (m,n) =   [      2      ]
(1) (7,6) (2) (6,3)
(3) (5,1) (4) (8,7)
52 If denotes the symmetric difference of the sets A,B then  = ( Here and respectively denote the complements of A and B)  [      4      ]
(1) (2)
(3) (4)
53 For a, b N, the relation R is defined by " a R b a divides b". Then R is  [      3      ]
(1) symmetric (2) an equivalence relation
(3) anti symmetric (4) reflexive and symmetric
54 The number of elements in the power set of {1,{1,2}, 3, {3,4}} is  [       2     ]
(1) 8 (2) 16
(3) 64 (4) 128
55 If f : Z N is defined by for each x Z then f _1 (201) =  [       2     ]
(1) 100 (2) _ 100
(3) 399 (4) _ 401
56 Suppose f : RR is defined by f (x) = 2 + x2 for each xR. Then the number of functions g : RR satisfying f (g(x)) = 2 + x2 _ 2x3 + x4 is  [       2     ]
(1) (2) 2
(3) 1 (4) 0
57 If f (x) = cos (logx) , x > 0 then  [      1      ]
(1) 0 (2) 1
(3) (4) cos ( log (x y) )
58 If a2 + a + 1 = 0, b2 + b + 1 = 0 and a b then the quadratic equation whose roots are b + a and ba is  [      3      ]
(1) x2 _ (a + b) x + ab = 0 (2) x2 + (a + b) x + ab = 0
(3) x2 _ 1 = 0 (4) x2 + 1 = 0
59 If are the roots of x2 + x + 1 = 0 then the quadratic equation whose roots are is  [      4      ]
(1) x2 _ x _ 1 = 0 (2) x2 _ x + 1 = 0
(3) x2 + x _ 1 = 0 (4) x2 + x + 1 = 0
60 If p,q are the roots of x2 + 2px + 3q = 0 then  [      2      ]
(1) p {1,_3} (2) p {0,3}
(3) p{_1,_3} (4) p {_1,_3}
61 If (x_2) is a factor of the polynomial f (x), then which of the following has x as a factor ?  [      3      ]
(1) f (x2_1) (2) f (x2+1)
(3) f (x2+2) (4) f (x2_2)
62 If the sum of coefficients in the expansion of (1 + 3x + 5x3)n is a and the sum of coefficients in the expansion of (1 + 2x2)n is b then  [      2      ]
(1) a = b3 (2) a = b2
(3) a3 = b (4) a2 = b
63 If x + y = 1 then =  [      3      ]
(1) nxnyn (2) nxy
(3) n (4) 1
64 If (1 _ x + x2)n = a0 + a1x + ... + a2n x2n then a0 + a2 + ... + a2n =  [      1      ]
(1) (2)
(3) (4)
65  [      4      ]
(1) (2)
(3) (4)
66 The term independent of x in the expansion of is  [      1      ]
(1) 9C2 (2) _9C2
(3) 9C3 (4) _9C3
67 If m and n denote the ranks of  and  , respectively, then  [      3      ]
(1) n = m + 1 (2) n = m _1
(3) n = m _1 (4) n = m _2
68 =  [       1     ]
(1) 0 (2) 40200
(3) 40602 (4) 40602
69 If A = then A4 _ A3 _ A2 =  [      2      ]
(1) A (2) _ A
(3) 2 A (4) _ 2 A
70 If A is a square matrix of order K and det (KA) = 81 det (A) then K =  [  none  ]
(1) 1 (2) 2
(3) 3 (4) 9
71 If A = then a characteristic root of A is  [      1      ]
(1) 0 (2) 1
(3) 2 (4) 3
72 The rank of the matrix  is  [      3      ]
(1) 1 (2) 2
(3) 3 (4) 4
73 If and  then the quadrant in which lies is  [      1      ]
(1) first quadrant (2) second quadrant
(3) third quadrant (4) fourth quadrant
74 The amplitude of  where is  [      2      ]
(1) (2)
(3) (4)
75 If in a , ( Sin A + Sin B + Sin C ) ( Sin A + Sin B _ Sin C ) = 3 Sin A Sin B then C =  [      1      ]
(1) 600 (2) 450
(3) 300 (4) 900
76  =  [      2      ]
(1) (2)
(3) (4)
77 A, B, O are collinear points in the same order on a level ground. A and B are d units apart and the angles of elevation of the top of a vertical tower OT from A and B are, respectively, and . Then the height of the tower is  [      4      ]
(1) (2)
(3) (4)
78 Tan 810 _ Tan 270 _ Tan 630 + Tan 90 =  [      4      ]
(1) 1 (2) 2
(3) 3 (4) 4
79 The set of solutions of  is  [     1      ]
(1) (2)
(3) (4)
80 The number of diagonals in a polygon with 14 sides is  [      2     ]
(1) 66 (2) 77
(3) 88 (4) 90
81 If then r =  [       1      ]
(1) 5 (2) 2
(3) 3 (4) 4
82 The number of integers greater than a million that can be formed with the cards labelled 0,2,3,3,4,4,4 is  [      1      ]
(1) 360 (2) 400
(3) 440 (4) 480
83 If a set A contains 10 elements, B contains 12 elements then the number of one-one functions from A into B is  [      2      ]
(1) 11! (2) 11! 6
(3) 132 (4) 10!
84 The number of parabolae y = ax2 + bx + c where a, b, c are three distinct elements drawn from the set {1,3,5,7} is  [      3      ]
(1) 720 (2) 120
(3) 24 (4) 12
85 The vertices of a triangle are (2,4), (4,_2) and (_3,_6). Then the origin  [      3      ]
(1) lies inside the triangle (2) lies outside the triangle
(3) lies on one of the sides (4) coincides with its incentre
86 The foot of the perpendicular from ( _ 4,8) to the line 5x _ 6y + 7 = 0 is  [      4      ]
(1) (2)
(3) (4)
87 The radical centre of the circles  x2 + y2 _ 2x + 6y = 0, x2 + y2 _ 4x _ 2y + 6 = 0 and x2 + y2 _12x + 2y +3 = 0 is  [      3      ]
(1) ( _3 , 0) (2) (3,0)
(3) (4)
88 If the acute angle between the pair of straight lines 6x2 _ 5xy + y2 = 0 is tan_1 ( p ) then p =  [      4      ]
(1) 2 (2) _2
(3) (4)
89 The line 2x _ y _ 6 = 0 meets the circle x2 + y2 _ 2y _ 9 = 0 in A and B. Then the equation of the circle with diameter AB is  [      1      ]
(1) x2 + y2 + 4x _ 4y + 3 = 0 (2) x2 + y2 + 4x + 4y + 3 = 0
(3) x2 + y2 _ 4x _ 4y + 3 = 0 (4) x2 + y2 + 4x + 4y _ 3 = 0
90 A line l passes through a fixed point (a,b). Then the locus of the foot of the perpendicular drawn from the origin to the line l is  [     4       ]
(1) 2xy = ab (2) b2x2 _ a2y2 = a2b2
(3) b2x2 + a2x2 = a2b2 (4) x2 + y2 = ax + by
91 Find the area (in square units) of the ellipse inscribed in the rectangle formed by the lines x2 _ 2x = 0, y2 _ y = 0 is  [      2      ]
(1) (2) 2
(3) 3 (4) 4
92 The point p which is equidistant from the vertices of the triangle formed by the lines xy = 0, x + y = 1 is  [      2      ]
(1) (1,1) (2)
(3) (4)
93 If (1,0) and (1,3) are the limiting points of a coaxial system of circles, then the radical axis of the system is  [      2      ]
(1) y = 3 (2) 2y = 3
(3) y = 4 (4) 3y = 4
94 The centre of the circle x2 + y2 _ 6x +16y _7 = 0 is  [      4      ]
(1) (_1,2) (2) (3,8)
(3) (_1,_2) (4) (3,_8)
95 If f (x + 3y, x _ 3y) = xy for all real values of x and y then f (x,y) =  [      3      ]
(1) (2)
(3) (4)
96  [      2      ]
(1) (2)
(3) (4) 0
97 If f : [0,1] [0,1] is continuous then  [      4      ]
(1) f is onto (2) f is one _ one
(3) f is monotonic (4) f (a) = a for some a[0,1]
98 If f : RR is such that and  is with then  [      2      ]
(1) 7 (2) 10
(3) 13 (4) 14
99 If f (a) = 3, (a) = 1, g (a) = _2 and (a) = _ 4 then  [      1      ]
(1) 10 (2) _10
(3) (4)
100 If f : RR is defined by then the set of all points where f is not differentiable is  [      3      ]
(1) {0,4} (2) {0, _ 4}
(3) {4, _ 4} (4) {0,4, _ 4}
101 If then = then  =  [      2      ]
(1) (2)
(3) (4)
102 If for every integer n then ...  [      3      ]
(1) 16 (2) 14
(3) 19 (4) 20
103 The least value of  is  [      2      ]
(1) 0 (2) 1
(3) 2 (4) 227
104 If y = 4x _ 5 is a tangent to the curve y 2 = ax3 + b at (2,3) then the ordered pair (a, b) =  [      1      ]
(1) (2,_7) (2) (_2,7)
(3) (_2,_7) (4) (2,7)
105 The differential equation formed by eliminating a and b from y = a cos (nx+b)  [      2      ]
(1) (2)
(3) (4)
106 The degree of the differential equation is  [      3      ]
(1) 1 (2) 2
(3) 3 (4) 4
107 The solution of the differential equation (1 + x2) dy= (1 + y2 ) dx is  [      2      ]
(1) y + x = c (1 _ xy) (2) y _ x = c (1 + xy)
(3) y _ x = c (1 _ xy) (4) y + x = c (1 + xy)
108 The general solution of the differential equation ( D 2 _1 ) y = ex is  [ none ]
(1) (2)
(3) (4)
109 The particular integral of ( D3 _ D2 _ D +1) ( y) = 1 + x2 is  [      1     ]
(1) 5 + 2x + x 2 (2) 1 + x + x2 + x 3
(3) 2x + x 2 (4) 5 + 2x
110 The general solution of the differential equation ( D3 _ 3D + 2) y = 0 is  [      4      ]
(1) y = (c1 + c2 x) ex + c3e2x (2) y = (c1 + c2 x) e_x + 3 e_2x
(3) y = (c1+c2 x) e_x + 3e2x (4) y = (c1+c2 x) ex + c3 e_2x
111 If a sequence is defined by an = 4k, where n k (mod 4) with 0 k < 4, then a 2003 =  [     1      ]
(1) a 203 (2) a 302
(3) a 401 (4) a 104
112 A sequenceis defined by and . Then the sequence { bn }  [      3      ]
(1) diverges (2) converges to
(3) converges to 5 (4) converges to
113 If for n = 1, 2, 3, .... then =  [      3      ]
(1) does not exist (2) 0
(3) _1 (4) 1
114 If for, dn = 0, 1 or 2 according as n0, 1 or 2 (mod 3) then the sequence  [      2      ]
(1) converges (2) is bounded but does not converge
(3) has no subsequence that converges (4) diverges to infinity
115 A convergent series, among the following is  [      2      ]
(1) (2)
(3) (4)
116 The series is  [      2      ]
(1) absolutely convergent (2) conditionally convergent
(3) diverges to _ (4) diverges to +
117 The series converges to  [     1      ]
(1) e (2) e _ 1
(3) e (4) e2
118 If 0 < x <1 then the series converges to  [      2      ]
(1) 1 _ x (2) (1 _ x)_1
(3) 1 (4) 0
119 converges if  [     4      ]
(1) _ 1 < x < 1 (2) 0 < x < 1
(3) _ 1 < x < 0 (4) x < _1 and x > 1
120 converges if  [      3     ]
(1) (2)
(3) (4)
121 Let f : [a,b] R be a continuous function. Then  [      3      ]
(1) f is differentiable on [a,b] (2) f is an increasing function on [a,b]
(3) f is Riemann integrable function on [a,b] (4) f is a decreasing function on [a,b]
122 Which of the following sets is not closed in R?  [      4      ]
(1) [0,1] (2) R
(3) (4) Q
123 If f : [0,2] R is a continious function, f (2) = 2, f (x) Q x [0,2] and if xn1 as n ( xn[0,2] ) then as n, f (xn)  [      2      ]
(1) 1 (2) 2
(3) 3 (4) 8
124 If f : [a,b]R is a continuous function and is differentiable on (a,b) then a possible value of c (a,b) such that is  [      3      ]
(1) (2)
(3) (4)
125 If f: [a,b]R (a < b), is a continuous function then which of the following sets can not be the range of f ?  [      1      ]
(1) {0,1} (2) {0}
(3) {1} (4) [0,1]
126 . If f: [1,5]R is defined by then which of the following is not true?  [      3      ]
(1) f is continuous on [1,5] (2) f is bounded on [1,5]
(3) f is not continuous at 3 (4) f is increasing on [1,5]
127 The set of limit points of in R is  [      2      ]
(1) {0} (2) The empty set
(3) {1} (4) A
128 An example of a set S having the following property is "Every set in S which is bounded above has a supremum in S"  [      3      ]
(1) (0,1) (2) Q
(3) R (4) [0,1]
129 If [x] denotes the greatest integer not exceeding x, then =  [      2      ]
(1) 1 (2) 0
(3) _1 (4) _2
130 If then the lower Riemann integral of f over [1,4] is  [     3      ]
(1) 4 (2) 5
(3) 6 (4) 7
131 If G is a cyclic group of order 125 then the number of generators of G is  [      1      ]
(1) 100 (2) 75
(3) 50 (4) 2
132 The number of idempotent elements in an integral domain with identity is  [      3      ]
(1) 0 (2) 1
(3) 2 (4) 3
133 If is a group under matrix multiplication with the identity , then the inverse of is  [      4      ]
(1) (2)
(3) (4)
134 If mZ is the ring of integral multiples of m then which of the following is a field?  [      4       ]
(1) (2)
(3) (4)
135 If m Z = {mx : xZ} is the ring of integral multiples of m then the number of units in the quotient ring is  [      3       ]
(1) 4 (2) 5
(3) 6 (4) 7
136 If * is a binary operation on Z defined by a * b = a + b _10 then the solution of the equation 1 * 2 * x * 3 = 20 is  [      4       ]
(1) 41 (2) 42
(3) 43 (4) 44
137 The linear factors of x2 + 4 in Z5 [x], the polynomial ring over the ring of integers modulo 5 are  [       3      ]
(1) (x_1) , (x_2) (2) (x_1) , (x_3)
(3) (x_1) , (x_4) (4) (x_2) , (x_3)
138 If M is a maximal ideal in R then the number of ideals in the quotient ring is ( Here R is a commutative ring with unity.)  [      3       ]
(1) 0 (2) 1
(3) 2 (4) 3
139 If H {e} is a proper subgroup of a group G and 0(G) = 121 then index of H in G is  [      1      ]
(1) 11 (2) 121
(3) 1 (4) 12
140 If : G is a group homomorphism, a, b K , K the Kernel of then (ab) =  [      2      ]
(1) e, the identity in G (2) , the identity in, 
(3) a (4) b
141 Which of the following is a linearly independent set in R3 (R) ?  [      4      ]
(1) (2)
(3) (4)
142 Suppose A,B are subspaces of a vector space V over a field F. Then which of the following is not a subspace of V in general?  [      1      ]
(1) (2)
(3) (4)
143 Suppose S,T are two subspaces of a vector space V over a field F. Then S + T = S  [      2      ]
(1) (2)
(3) (4)
144 If u, v, w are linearly independent vectors in a vector space V over a field F then which of the following sets is linearly dependent?  [      4      ]
(1) (2)
(3) (4)
145 Suppose U,V are two subspaces of a vector space W over a field F. Let dim (U+V ) = dim V = 5 and dim U = 3. Then dim (UV ) =  [     3      ]
(1) 1 (2) 2
(3) 3 (4) 4
146 If T : R3 R3 is defined by T(x,y,z) = (2x, 3y, 4z) for (x,y,z)R3 then T _1 (x,y,z) =  [      2      ]
(1) (2)
(3) (4)
147 If T : R4 R3 is defined by T (x,y,z,w) = (x _ y, y _ z, z _ w) for (x,y,z,w)R4 then the dimension of the Kernel of T is  [      2      ]
(1) 0 (2) 1
(3) 2 (4) 3
148 If dim FV = m and dim FU = n then  [      3      ]
(1) mn (2) nm
(3) nm (4) n + m
149 If T: U U is a linear transformation on a vector space U such that the range of T is equal to the Kernel of T then  [      2      ]
(1) (2)
(3) (4)
150 If T : R3R3 is defined by T (x,y,z) = (x-y, y-z, z-x) for (x,y,z) R3 then the range of T is  [      1      ]
(1) (2)
(3) (4)




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