If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then _____________

(a)

a² + b² + c² = 1

(b)

abc ≠ 1

(c)

a + b + c =0

(d)

a² + b² + c² + 2abc =1

If A^T is the transpose of a square matrix A, then ___________

(a)

|A| ≠ |A^T|

(b)

|A| = |A^T|

(c)

|A| + |A^T| =0

(d)

|A| = |A^T| only

If A is a square matrix that IAI = 2, than for any positive integer n, |Aⁿ| = _______

(a)

0

(b)

2n

(c)

2ⁿ

(d)

n²

If A is a square matrix of order n, then |adj A| = ______________

(a)

|A|^n-1

(b)

|A|^n-2

(c)

|A|ⁿ

(d)

None

Every homogeneous system ______

(a)

Is always consistent

(b)

Has only trivial solution

(c)

Has infinitely many solution

(d)

Need not be consistent

If A is a non-singular matrix then IA^-1| = ______

(a)

\(\left| \frac { 1 }{ { A }^{ 2 } } \right| \)

(b)

\(\frac { 1 }{ |A^{ 2 }| } \)

(c)

\(\left| \frac { 1 }{ A } \right| \)

(d)

\(\frac { 1 }{ |A| } \)

If z = cos\(\frac { \pi }{ 4 } \) + i sin\(\frac { \pi }{ 6 } \), then ______

(a)

|z| = 1, arg(z) =\(\frac { \pi }{ 4 } \)

(b)

|z| = 1, arg(z) = \(\frac { \pi }{ 6 } \)

(c)

|z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg(z) = \(\frac { 5\pi }{ 24 } \)

(d)

|z| = \(\frac { \sqrt { 3 } }{ 2 } \), arg (z) = tan^-1\(\left( \frac { 1 }{ \sqrt { 2 } } \right) \)

.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 + iy = \(\frac { 3+5i }{ 7-6i } \), they y = ___________

(a)

\(\frac { 9 }{ 85 } \)

(b)

-\(\frac { 9 }{ 85 } \)

(c)

\(\frac { 53 }{ 85 } \)

(d)

none of these

The value of (1+i)⁴ + (1-i)⁴ is __________

(a)

8

(b)

4

(c)

-8

(d)

-4

If z = a + ib lies in quadrant then \(\frac { \bar { z } }{ z } \) also lies in the III quadrant if _________

(a)

a > b > 0

(b)

a < b < 0

(c)

b < a < 0

(d)

b > a > 0

If zⁿ = \(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z₁, z₂ ..... z₆ is _________

(a)

1

(b)

-1

(c)

i

(d)

-i

If ω is the cube root of unity, then the value of (1-ω) (1-ω²) (1-ω⁴) (1-ω⁸) is _________

(a)

9

(b)

-9

(c)

16

(d)

32

(1+i)³ = ______

(a)

3 + 3i

(b)

1 + 3i

(c)

3 - 3i

(d)

2i - 2

For real x, the equation \(\left| \frac { x }{ x-1 } \right| +|x|=\frac { { x }^{ 2 } }{ |x-1| } \) has ________

(a)

one solution

(b)

two solution

(c)

at least two solution

(d)

no solution

If \((2+\sqrt{3})^{x^{2}-2 x+1}+(2-\sqrt{3})^{x^{2}-2 x-1}=\frac{2}{2-\sqrt{3}}\) then x = _________

(a)

0, 2

(b)

0, 1

(c)

0, 3

(d)

0, √3

If \({ tan }^{ -1 }\left\{ \cfrac { \sqrt { 1+{ x }^{ 2 } } -\sqrt { 1-{ x }^{ 2 } } }{ \sqrt { 1+{ x }^{ 2 } } +\sqrt { 1-{ x }^{ 2 } } } \right\} =\alpha \) then x² = _____________

(a)

\(sin2\alpha \)

(b)

\(sin\alpha \)

(c)

\(cos2\alpha \)

(d)

\(cos\alpha \)

\({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 11 } \right) \) = ____________

(a)

0

(b)

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

(c)

-1

(d)

none

The value of \({ cos }^{ -1 }\left( \cos\cfrac { 5\pi }{ 3 } \right) +sin^{ -1 }\left( \sin\cfrac{5\pi }{ 3 } \right) \) is ______________ 

(a)

\(\cfrac { \pi }{ 2 } \)

(b)

\(\cfrac { 5\pi }{ 3 } \)

(c)

\(\cfrac { 10\pi }{ 3 } \)

(d)

0

If \({ cos }^{ -1 }x>x>{ sin }^{ -1 }x\) then _________

(a)

\(\cfrac { 1 }{ \sqrt { 2 } }

(b)

\(0\le x<\frac { 1 }{ \sqrt { 2 } } \)

(c)

\(-1\le x<\frac { 1 }{ \sqrt { 2 } } \)

(d)

x>0

If \(\theta ={ sin }^{ -1 }\left( sin(-{ 60 }^{ 0 }) \right) \) then one of the possible values of \(\theta\) is _________

(a)

\(\frac { \pi }{ 3 } \)

(b)

\(\frac { \pi }{ 2 } \)

(c)

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

(d)

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

The eccentricity of the ellipse 9x²+ 5y² - 30y = 0 is __________

(a)

\(\frac13\)

(b)

\(\frac23\)

(c)

\(\frac34\)

(d)

none of these

The director circle of the ellipse \(\frac { { x }^{ 2 } }{ 9 } -\frac { { y }^{ 2 } }{ 5 } =1\) is ____________

(a)

x² + y² = 4

(b)

x² +y² = 9

(c)

x² +y² = 45

(d)

x² +y² = 14

If e₁, e₂ are eccentricities of the ellipse \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 and the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } \) = 1 then 

(a)

\({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\) = 1

(b)

\({ e }_{ 1 }^{ 2 }\)  + \({ e }_{ 2 }^{ 2 }\) = 1

(c)

\({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\) = 2

(d)

\({ e }_{ 1 }^{ 2 }\) - \({ e }_{ 2 }^{ 2 }\) = 2

The length of major and minor axes of 4x² + 3y² = 12 are ____________

(a)

4, 2\(\sqrt3\)

(b)

2, \(\sqrt3\)

(c)

2\(\sqrt3\), 4

(d)

\(\sqrt3\), 2