Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 The roots of (x - a)(x - b) = ab x2 are always Real Depends upon a Depends upon b Depends upon a and b
2 Ifα,β are non-real roots of ax2 + bx +c =0 (a,b,c∈ Q),then α = β αβ = 1 α = β α = 1
3 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
4 The condition for polynomial equation ax2 + bx + c = 0 to be quadratic is a > 0 a < 0 a≠ 0 a≠ 0,b ≠ 0
5 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
6 If for the matrix A,A5 = 1,then A-1= A2 A3 A None of above
7 For a square matrix A, if A = At, then A is called Matrix Transpose Symmetric Non-symmetric
8 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
9 We solve the system of non-homogeneous linear equations by a and b b and c c and a a,b and c
10 Trival solution of homogeneous linear equation is (0, 0, 0) (1, 2, 3) (1, 3, 5) a.b and c
11 For non-trival solution |A| is non zero A = 0 |A| = 0 At = 0
12 For trival solution |A| is A |A| = 0 A = 0 |A|≠ 0
13 System of linear equation is inconsistent if System has no solution System has one solution System has two solution None of above
14 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
15 The matrix A is Hermitian when (A)' = A -A A A'
16 The square matrix A is skew Hermitian when (A)'= A A' -A A
17 The square matrix A is skew-symmetric when At = -B -C -A -D
18 A square matrix A = [aij] is upper triangular when cij = 0 bij = 0 aij = 0 for all i > j dij = 0
19 A square matrix A = [aij] is lower triangular matrix when aij = 0 for all i<j bij = 0 cij = 0 dij = 0
20 Cofactor of an element aij denoted by Aij is (-2)i+j Mij (-1)i+j Mij None of above
21 Matrices A = [aij] 2 x 3 and B = [bij] 3 x 2 are suitable for BA A2 AB B2
22 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
23 If A and B are two matrices such that AB = B and BA = A then A2 + B2 = 2 AB 2 BA A + B AB
24 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
25 (ABC)' = CBA' CBA C'B'A C'B'A'
26 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
27 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
28 The set {Z\ {0} } is group w.r.t Addition Multiplication Division Subtraction
29 The set R is ........w.r.t subtraction Not a group A group No conclusion drawn Non commutative group
30 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
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