TRB Tripura STPGT Mathematics Paper 2016

STPGT TRB Tripura  Mathematics  2016 Paper

Two finite sets A and B have m and n elements respectively. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m is
(a) 7
(b) 9
(c) 10
(d) None of the above

The relation R={(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)} on the set A = {1,2,3} is
(a) reflexive but not symmetric
(b) reflexive but not transitive
(c) symmetric and transitive
(d) neither symmetric nor transitive

The identity element for the binary operation * defiend by a*b=ab/2, where a and b are the elements of a set of non-zero rational numbers, is
(a) 1
(b) 2
(c) 0
(d) None of the above

Which one of the following is NOT a group ?
(a) (N,+); N=Set of natural nubmers
(b) (Q,+); Q=Set of rational numbers
(c) (R,+); R=Set of real numbers
(d) None of the above

If a polygon has 44 diagonals, then the number of its sides is
(a) 10
(b) 7
(c) 8
(d) 11

The value of the determinant of an orthononal matrix is
(a) 1
(b) -1
(c) 1 or -1
(d) None of the above

If a line passes through the point (2,2) and is perpendicular to the line 3x+y=3, then its y intercept is
(a) 1/3
(b) 2/3
(c) 1
(d) 4/3

The angle between the planes 2x-y+z=6 and x+y+2z=7 is
(a) Pie/3
(b) pie/2
(c) pie/4
(d) None of the above

The two lines
(x-1)/-3 = y-2/2k = z-3/2
and x-1/3k = y-5/1 = z-6/-5
will be perpendicular to each other, if the value of k is
(a) 10/7
(b) -10/7
(c) 20/7
(d) None of the above