ECAT Pre General Science Mathematics Online Test With Answers

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ECAT Pre General Science Mathematics Online Test

Sr. # Questions Answers Choice
1 Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then α = β αβ = 1 α = β α = 1
2 Only one of the root of ax2 + bx + c =0, a≠ 0 is zero if c = 0 c = 0,b≠ 0 b = 0,c = 0 b = 0,c≠ 0
3 The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is a > 0 a < 0 a≠ 0 a≠ 0,b ≠ 0
4 The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is 2 x 3 3 x 2 2 x 5 5 x 2
5 If for the matrix A,A5 = 1,then A-1= A2 A3 A None of above
6 For a square matrix A, if A = At, then A is called Matrix Transpose Symmetric Non-symmetric
7 If A = |aij| is (m x n) matrix then transpose of A is of the order m x m m x n n x n n x m
8 We solve the system of non-homogeneous linear equations by a and b b and c c and a a,b and c
9 Trival solution of homogeneous linear equation is (0, 0, 0) (1, 2, 3) (1, 3, 5) a.b and c
10 For non-trival solution |A| is non zero A = 0 |A| = 0 At = 0
11 For trival solution |A| is A |A| = 0 A = 0 |A|≠ 0
12 System of linear equation is inconsistent if System has no solution System has one solution System has two solution None of above
13 An equation of the form ax + by = k is homogeneous linear equation when b = 0, a = 0 a = 0,b ≠ 0 b = -0,a≠ 0 a≠ 0,b≠ 0, k = 0
14 The matrix A is Hermitian when (A)' = A -A A A'
15 The square matrix A is skew Hermitian when (A)'= A A' -A A
16 The square matrix A is skew-symmetric when At = -B -C -A -D
17 A square matrix A = [aij] is upper triangular when cij = 0 bij = 0 aij = 0 for all i > j dij = 0
18 A square matrix A = [aij] is lower triangular matrix when aij = 0 for all i<j bij = 0 cij = 0 dij = 0
19 Cofactor of an element aij denoted by Aij is (-2)i+j Mij (-1)i+j Mij None of above
20 Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for BA A2 AB B2
21 A and B be two square matrices and if their inverse exist the (AB)-1 = A-1 B-1 AB-1 A-1B B-1A-1
22 If A and B are two matrices such that AB = B and BA = A then A2 + B2 = 2 AB 2 BA A + B AB
23 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
24 (ABC)' = CBA' CBA C'B'A C'B'A'
25 The set (Z, +) forms a group Forms a group w.r.t addition Forms a group w.r.t multiplication Non commutative group w.r.t multiplication Doesn't form a group
26 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
27 The set {Z\ {0} } is group w.r.t Addition Multiplication Division Subtraction
28 The set R is ........w.r.t subtraction Not a group A group No conclusion drawn Non commutative group
29 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
30 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
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