Which of the following is not an elementary transformation?

(a)

R_i ↔️ R_j

(b)

R_i ⟶ 2R_i + R_j

(c)

C_j ⟶ C_j + C_i

(d)

R_i ⟶ R_i + C_j

If z = \(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) = ___________

(a)

0

(b)

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

(c)

cot\(\frac { \theta }{ 2 } \)

(d)

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

If z₁, z₂, z₃ are the vertices of a parallelogram, then the fourth vertex z₄ opposite to z₂ is _____

(a)

z₁ + z₂ - z₂

(b)

z₁ + z₂ - z₃

(c)

z₁ + z₂ - z₃

(d)

z₁ - z₂ - z₃

If ∝, β, ૪ are the roots of 9x³-7x+6 = 0, then ∝ β ૪ is __________

(a)

\(\frac{-7}{9}\)

(b)

\(\frac{7}{9}\)

(c)

0

(d)

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

If \({ tan }^{ -1 }\left( \frac { x+1 }{ x-1 } \right) +{ tan }^{ -1 }\left( \frac { x-1 }{ x } \right) ={ tan }^{ -1 }\left( -7 \right) \) then x is ___________

(a)

0

(b)

-2

(c)

1

(d)

2

In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is ________

(a)

\(\frac { 4 }{ 5 } \)

(b)

\(\frac { 1 }{ \sqrt { 52 } } \)

(c)

\(\frac { 3 }{ 5 } \)

(d)

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

If \(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } \times \left( \overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } \right) +\overset { \rightarrow }{ b } \times \left( \overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \right) +\overset { \rightarrow }{ c } \times \left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \), then __________

(a)

\(\left| \overset { \rightarrow }{ d } \right| \)

(b)

\(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)

(c)

\(\overset { \rightarrow }{ d } =\overset { \rightarrow }{ 0 } \)

(d)

a, b, c are coplanar

The equation of the tangent to the curve y = x²-4x+2 at (4, 2) is __________

(a)

x + 4y + 12 = 0

(b)

4x + y + 12 = 0

(c)

4x - y - 14 = 0

(d)

x + 4y - 12 = 0

If f (x, y) = x³ + y³ - 3xy² then \(\frac { { \partial }f }{ \partial { x } } \) at x = 2,_____________

(a)

-15

(b)

15

(c)

-9

(d)

16

The ratio of the volumes generated by revolving the ellipse \(\frac { { x }^{ 2 } }{ 9 } +\frac { { y }^{ 2 } }{ 4 } \) = 1 about major and minor axes is __________

(a)

4 : 9

(b)

9 : 4

(c)

2 : 3

(d)

3 : 2