1 |
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}
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2 |
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(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>
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3 |
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
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4 |
|
n if n is even
0 for any natural number n
1 if in odd
None of these
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5 |
The roots of the equation 22x- 10.2x+ 16 = 0 are |
2, 8
1, 3
1, 8
2, 3
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6 |
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7 |
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 |
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8 |
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
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9 |
|
b = c
a = c
a = c
b = 0
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10 |
The quadratic equation 8 sec2θ- 6 secθ+1 = 0 has |
Infinitely many roots
Exactly two roots
Exactly four roots
No roots
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11 |
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
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12 |
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
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13 |
If the roots of ax2+ b = 0 are real and distinct then |
ab > 0
a = 0
ab < 0
a > 0, b > 0
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14 |
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
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15 |
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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16 |
|
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17 |
|
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18 |
The condition for polynomial equation ax2+ bx + c = 0 to be quadratic is |
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19 |
|
9/4
4/9
1
None of these
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20 |
|
2s<sup>2</sup>
2s<sup>3</sup>
s<sup>3</sup>
3s<sup>3</sup>
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21 |
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K/6
2K
3K
6K
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22 |
Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| = |
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23 |
|
0
Independent of a
Independent of b
Independent of c
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24 |
|
0
abc
1/abc
None of these
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25 |
|
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26 |
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Orthogonal
Involutary
Idempotent
Nilpotent
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27 |
|
a = 4, b = 1
a = 1, b = -4
a = 0, b = 4
a = 2, b = 4
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28 |
|
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29 |
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Symmetric
Skew-symmetric
Hermitian
Skew hermitian
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30 |
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4A - 3I
3A - 4I
A - I
None of these
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