The conjugate of a complex number is \(\cfrac { 1 }{ i-2 } \). Then the complex number is

(a)

\(\cfrac { 1 }{ i+2 } \)

(b)

\(\cfrac { -1 }{ i+2 } \)

(c)

\(\cfrac { -1 }{ i-2 } \)

(d)

\(\cfrac { 1 }{ i-2 } \)

The principal argument of \(\cfrac { 3 }{ -1+i } \) is

(a)

\(\cfrac { -5\pi }{ 6 } \)

(b)

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

(c)

\(\cfrac { -3\pi }{ 4 } \)

(d)

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

The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\) is a positive integer is ____________

(a)

16

(b)

8

(c)

4

(d)

2

If α, β and γ are the zeros of x³ + px² + qx + r, then \(\Sigma \frac { 1 }{ \alpha } \) is

(a)

\(-\frac { q }{ r } \)

(b)

\(-\frac { p }{ r } \)

(c)

\(\frac { q }{ r } \)

(d)

\(-\frac { q }{ p } \)

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 the function f(x) = sin^-1(x² - 3), then x belongs to

(a)

[-1, 1]

(b)

[\(\sqrt2\), 2]

(c)

\(\\ \\ \\ \left[ -2,-\sqrt { 2 } \right] \cup \left[ \sqrt { 2 } ,2 \right] \)

(d)

\([-2,-\sqrt{2}]\)

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (-3, 0) then PF₁  + PF₂ is

(a)

8

(b)

6

(c)

10

(d)

12

The locus of a point whose distance from (-2,0) is \(\frac { 2 }{ 3 } \) times its distance from the line x = \(\frac { -9 }{ 2 } \) is

(a)

a parabola

(b)

a hyperbola

(c)

an ellipse

(d)

a circle

P is the amount of certain substance left in after time t. If the rate of evaporation of the substance is proportional to the amount remaining, then

(a)

P = Ce^kt

(b)

P = Ce^-kt

(c)

P = Ckt

(d)

Pt = C

Which one of the following is not true?

(a)

Negation of a negation of a statement is the statement itself

(b)

If the last column of the truth table contains only T then it is a tautology.

(c)

If the last column of its truth table contains only F then it is a contradiction

(d)

If p and q are any two statements then p↔️q is a tautology.