Mathematics ECAT Pre Engineering Online Test With Answers

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Mathematics ECAT Pre Engineering Online Test

Sr. # Questions Answers Choice
1 The value of k (k > 0) for which the equation x2+ kx + 64 = 0 and x2- 8x + k = 0 both will have real roots is 8 -16 -64 16
2 The set of real roots of the equation log(5x + 4)(2x +3)3- log(2x + 3)(10x2+ 23x + 12) = 1 is {-1} {-3/5} Empty set {-1/3}
3 (a - c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a - c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup>
4 If x2 + px + 1 is a factor of ax3+ bx +c, then a<sup>2</sup>+ c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= ab None of these
5 n if n is even 0 for any natural number n 1 if in odd None of these
6 The roots of the equation 22x- 10.2x+ 16 = 0 are 2, 8 1, 3 1, 8 2, 3
7
8 The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in
9 If the roots of ax2+ bx + c =0 are equal in magnitude but opposite in sign, then a = 0 b = 0 c = 0 None of these
10 b = c a = c a = c b = 0
11 The quadratic equation 8 sec2θ- 6 secθ+1 = 0 has Infinitely many roots Exactly two roots Exactly four roots No roots
12 If a > 0, b > 0, c > 0, then the roots of the equation ax2+ bx + c = 0 are Real and negative Non-real with negative real parts Real and positive Nothing can be said
13 If one root of the equation ix2- 2(i + 1) x +(2 - i) = 0 is 2 - i, then the other root is -i 2 + i i 2 - i
14 If the roots of ax2+ b = 0 are real and distinct then ab &gt; 0 a = 0 ab &lt; 0 a &gt; 0, b &gt; 0
15 If ax2+ bx + x = 0 is satisfied by every value of x, then b = 0, c = 0 c = 0 b = 0 a = b = c = 0
16 Both the roots of the equation (x - b) (x - c) + (x - c)(x - a) + (x - a)(x - b) = 0 are always Positive Negative Real None of these
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19 The condition for polynomial equation ax2+ bx + c = 0 to be quadratic is
20 9/4 4/9 1 None of these
21 2s<sup>2</sup> 2s<sup>3</sup> s<sup>3</sup> 3s<sup>3</sup>
22 K/6 2K 3K 6K
23 Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =
24 0 Independent of a Independent of b Independent of c
25 0 abc 1/abc None of these
26
27 Orthogonal Involutary Idempotent Nilpotent
28 a = 4, b = 1 a = 1, b = -4 a = 0, b = 4 a = 2, b = 4
29
30 Symmetric Skew-symmetric Hermitian Skew hermitian
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