Pure Mathematics Mcqs Test

Pure Mathematics Mcqs Test

(1) The additive group of integers has:
(a) 3 quotient groups of order 2 each
(b) 5 quotient groups of order 5 each
(c) one quotient groups of order 5
(d) None of these

(2) Let Q and Z be the additive groups of rationals and integers respectively. Then the
group Q/Z:
(a) is cyclic (b) is a finite group
(c) has no element of order 6 (d) None of these

(3) Every field contains more than:
(a) one element (b) three element
(c) two element (d) None of these

(4) Suppose A,B are matrices such that AB exists and is zero matrix. Then:
(a) a must be zero matrix (b) B must be zero matrix
(c) Neither A nor B needs be zero matrix
(d) None of these

(5) The unit matrix of order n has rank:
(a) zero (b) n
(c) 1 (d) None of these

(6) Let V be the real vector space of all functions on R to R, and let A = {x2, Sin x}.
(a) A spans V (b) A is linearly independent
(c) A is linearly dependent (d) None of these

(7) If the matrix equation AX = 0, where A is an n´ n matrix, has a non-trivial solution,
(a) determinant A is zero (b) Matrix A is non-singular
(c) determinant A is non zero (d) None of these

(8) Let Jn denote the ring of integers mod n. Then:
(a) J6 is a field (b) J5 is a field
(c) J8 is an integral domain (d) None of these

(11) The rectangular coordinates of the point with spherical coordinates (6,
6P, 6P) are:
(a) (6,0,0) (b) (0,6,0)
(c) (0,0,6) (d) None of these

(12) The only space curve whose curvature and torsion are both constant is:
(a) parabola (b) a circular helix
(c) a circle (d) None of these

(13) If the torsion at all points of a curve is zero, then the curve is:
(a) a helix (b) a straight line
(c) all in one plane (d) None of these

(14) Let G be a group of order 17. Then:
(a) G is no cyclic (b) G is non abelian
(c) G is commutative (d) None of these
(16) If V is n-dimensional vector spaces, then any set of n+1 vectors in V is:
(a) linearly dependent (b) linearly independent
(c) a basis of V (d) None of these

(17) If f :V — W is a linear map of an n-dimensional vector space V onto W, then:
(a) dim W = dim Ker f + dim V
(b) dim Ker f + dim W = dim V
(c) Dim Ker f = dim W
(d) None of these

(18) If determinant | A | = 2, then:
(a) | A4 | = 12 (b) | A5 | = 32
(c) | A6 | = 60 (d) None of these

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