ECAT Mathematics Online Test With Answers

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ECAT Mathematics Online Test

Sr. # Questions Answers Choice
1 If A and B are two matrices such that AB = B and BA =A, then A2+ B2= 2 AB 2 BA A + B AB
2
3 3, -3, 11 3, 3, 11 -3, 3, -11 -3, -3, 11
4
5 a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> 4a<sup>2</sup>b<sup>2</sup>c<sup>2</sup> 4abc None
6
7 1 -1 0 I
8 Let A be a square matrix. Then, 1/2 (A-A') is Skew-symmetric Symmetric Null None of the above
9 If A is a skew-symmetric matrix of order n and P, any square matrix of order n, prove that P' AP is Skew-symmetric Symmetric Null Diagonal
10 (ABC)' = CBA' CBA C' B' A' None of these
11 1 0 -1 2
12 1 0 3 -1
13 -3 -7 1 0
14 A<sup>2</sup>- 5A + 7I = 1 2A<sup>2</sup>- 3A + 7I = 0 A<sup>2</sup>- 5A + I = 0 A<sup>2</sup>- 5A + 7I = 0
15
16
17 a = 2, b = 3 a = 3, b = 2 a = 2, b = 1, 2 a = 3, b = 3
18 Power set of X i.e P(X) _______ under the binary operation of union U Forms a group Does not form a group Has no identity element Infinite set although X is infinite
19 The statement that a group can have more than one identity elements is True False Ambiguous Some times true
20 The set {Z\{0}} is group w.r.t Addition Multiplication Division Subtraction
21 The set R is ______ w.r.t subtraction Not a group A group No conclusion drawn Non commutative group
22 The set {1, -1, i, -i} Form a group w.r.t addition Form a group w.r.t multiplication Does not form a group w.r.t multiplication Not closed under multiplication
23 The set of complex numbers forms Commutative group w.r.t addition Commutative group w.r.t multiplication Commutative group w.r.t division Non commutative group w.r.t addition
24 The multiplicative inverse of -1 in the set {1-, 1} is 1 -1 +-1 0
25 The set {-1, 1} is Group under the multiplication Group under addition Does not form a group Contains no identity element
26 Addition Multiplication Division Both addition and multiplication
27 The set of integer is Finite group A group w.r.t addition A group w.r.t multiplication Not a group
28 To each element of a group there corresponds ______ inverse element Two One No Three
29 The function f{(x, y) | y = ax2+ bx + c} is One-one function Constant function Onto function Quadratic function
30 The graph of a quadratic function is Circle Straight line Parabola Triangle
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