The number of solutions of the system of equations 2x+y = 4, x - 2y = 2, 3x + 5y = 6 is ____________

(a)

0

(b)

1

(c)

2

(d)

infinitely many

.If a = 3+i and z = 2-3i, then the points on the Argand diagram representing az, 3az and - az are _________

(a)

Vertices of a right angled triangle

(b)

Vertices of an equilateral triangle

(c)

Vertices of an isosceles

(d)

Collinear

If x_r = \(cos\left( \frac { \pi }{ 2^{ r } } \right) +isin\left( \frac { \pi }{ 2^{ r } } \right) \) then x₁, x_2, x₃ ... x_∞ is _________

(a)

-∞

(b)

-2

(c)

-1

(d)

0

The equation \(\sqrt { x+1 } -\sqrt { x-1 } =\sqrt { 4x-1 } \) has ____________

(a)

no solution

(b)

one solution

(c)

two solution

(d)

more than one solution

If \(\alpha ={ tan }^{ -1 }\left( tan\frac { 5\pi }{ 4 } \right) \) and \(\beta ={ tan }^{ -1 }\left( -tan\frac { 2\pi }{ 3 } \right) \) then ___________

(a)

\(4\alpha =3\beta \quad \)

(b)

\(3\alpha =4\beta \)

(c)

\(\alpha -\beta =\frac { 7\pi }{ 12 } \)

(d)

none

The value of sin 2(tan^-1 0.75) is ___________

(a)

0.75

(b)

1.5

(c)

0.96

(d)

sin^-1(1.5)

If a parabolic reflector is 20 cm in diameter and 5 cm in diameter and 5 cm deep, then its focus is ____________

(a)

(0, 5)

(b)

(5, 0)

(c)

(10, 0)

(d)

(0, 10)

The line y = mx +1 is a tangent to the parabola y² = 4x if m = ______________

(a)

1

(b)

2

(c)

3

(d)

4

The least value of a when f f(x) = x² + ax + 1 is increasing on (1, 2) is __________

(a)

-2

(b)

2

(c)

1

(d)

-1

If u = log (x³ + y³ + z³ - 3xyz) then \(\frac { { \partial }u }{ \partial { x } } +\frac { { \partial }u }{ { \partial y } }+ \frac { { \partial }u }{ \partial z } \) = _____________

(a)

\(\frac { 3 }{ x+y+z } \)

(b)

x+y+z

(c)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)

(d)

\(\frac { -9 }{ { (x+y+z) }^{ 2 } } \)