Find a so that the sum and product of the roots of the equation 2x²+ (a - 3) x + 3a - 5 = 0 are equal is

(a)

1

(b)

2

(c)

0

(d)

4

If a and b are the roots of the equation x²- kx + 16 = 0 and a²+ b² = 32, then the value of k is

(a)

10

(b)

-8

(c)

-8, 8

(d)

6

The number of solution of x² + |x - 1| = 1 is

(a)

1

(b)

0

(c)

2

(d)

3

The equation whose roots are numerically equal but opposite in sign to the roots 3x²- 5x -7 = 0 is

(a)

3x²- 5x - 7 = 0

(b)

3x²+ 5x - 7 = 0

(c)

3x²- 5x + 7 = 0

(d)

3x² + x - 7

If 8 and 2 are the roots of x²+ ax + c = 0 and 3, 3 are the roots of x² + dx + b = 0; then the roots of the equation x²+ ax + b = 0 are

(a)

1, 2

(b)

-1, 1

(c)

9, 1

(d)

-1, 2

If a and b are the real roots of the equation x²- kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

(a)

\(\sqrt { { k }^{ 2 }-4c } \)

(b)

\(\sqrt { { 4k }^{ 2 }-c } \)

(c)

\(\sqrt { 4c-{ k }^{ 2 } } \)

(d)

\(\sqrt { k-8c } \)

If  \(\frac { kx }{ (x+2)(x-1) } =\frac { 2 }{ x+2 } +\frac { 1 }{ x-1 } \), then the value of k is

(a)

1

(b)

2

(c)

3

(d)

4

If  \(\frac { 1-2x }{ 3+2x-{ x }^{ 2 } } =\frac { A }{ 3-x } +\frac { B }{ x+1 } \), then the value of A + B is

(a)

\(\frac { -1 }{ 2 } \)

(b)

\(\frac { -2 }{ 3 } \)

(c)

\(\frac { 1 }{ 2 }\)

(d)

\(\frac { 2 }{ 3 } \)

The number of roots of (x + 3)⁴+ (x + 5)⁴ = 16 is

(a)

4

(b)

2

(c)

3

(d)

0

The value of log₃ 11.log₁₁ 13.log₁₃ 15.log₁₅ 27.log₂₇ 81 is

(a)

1

(b)

2

(c)

3

(d)

4