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 (x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if a+b=c+d a+c=b+d a+d=b+c All are correct
2 The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is 2 1 -1 -2
3 The expression x2 - x + 1 has One proper linear factor No proper linear factor Two proper linear factors None of these
4 The condition for ax2 + bx c to be expressed as the product of linear polynomials is b4 - 4ac =0 b4- 4ac ≥0 b4- 4ac <0 b4= 4ac
5 If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is 1 3 2 4
6 Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when q = 0, r = 0,p ≠ 0 p = 0,qr≠ 0 r = 0,pq≠ 0 q = 0, pq≠ 0
7 If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is 0 ±1 ±5 ±7
8 The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0 4 64 8 All values of k
9 The sum of the roots of the equation x2 -6x +2 = 0 is -6 2 -2 6
10 The roots of ax2 + bx + c = 0 are always unequal if b2 - 4ac = 0 b2- 4ac ≠ 0 b2- 4ac > 0 b2- 4ac ≥ 0
11 A polynomial of arbitrary degree f(x) = o f(x) = x f(x) = a f(x) = ax + b,a ≠ 0
12 (1+w)(1+w2)(1+w4)(1+w8)....50 factors 0 -1 1 2
13 If x - 1 is a factor of x4 - 5x2 + 4 then other factor is (x + 2)2(x - 1) (x + 2)(x - 1)2 (x+2)(x2- x- 2) (x + 2)2(x - 1)2
14 The two parts into which 57 should be divided so that their product is 782 are 43,14 34,23 33,24 44,13
15 The roots of the equation 4x - 3.2x+2 + 32 = 0 would include 1 and 3 1 and 4 1 and 2 2 and 3
16 If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is 0 2 1 5
17 If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is 8 12 10 14
18 A diagonal matrix is always Identity Triangular Scalar Non-singular
19 The matrix A = [aij]mxn with m ≠n is always Symmetric Hermition Skew-symmetric None
20 The matrix A = [aij]1xn is a Vector Rectangular matrix Column vector Square matrix
21 The matrix A = [aij]mxn with m≠n is Rectangular Symmetric Square None
22 If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is 1 x 1 1 x 10 10 x 10 10 x 1
23 If A and B are skew-symmetric then (AB)t is At Bt AB -AB BA
24 Every identity matrix is Row-vector Scalar Column-vector All
25 A non-homogeneous linear system AX = B has no solution if |A| = 0 |A|≠ 0 Rank (a) = no of variables Rank > no of variables
26 If A is a non-singular matrix then adj A is Non-singular Symmetric Singular Non defined
27 Matrix multiplication is Commutative Not commutative Not associative Not distributive
28 If A = [aij]mxpand B =[aij]pxnthen order of BA is m x n p x n n x m None of these
29 A = [3] is a/an Square matrix Scalar matrix Diagonal matrix Identity matrix
30 all are correct
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