If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2 is inconsistent then k is ___________

(a)

-3, -\(\frac{1}{2}\)

(b)

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

(c)

1

(d)

2

If a = cos θ + i sin θ, then \(\frac { 1+a }{ 1-a } \) = ___________

(a)

cot \(\frac { \theta }{ 2 } \)

(b)

cot θ

(c)

i cot \(\frac { \theta }{ 2 } \)

(d)

i tan\(\frac { \theta }{ 2 } \)

(1+i)³ = ______

(a)

3 + 3i

(b)

1 + 3i

(c)

3 - 3i

(d)

2i - 2

Let a > 0, b > 0, c >0. Theh n both the root of the equation ax²+bx+c = 0 are _________

(a)

real and negative

(b)

real and positive

(c)

rational numbers

(d)

none

If u = y^x then \(\frac { \partial u }{ \partial y } \) = ............

(a)

xy^x-1

(b)

yx^y-1

(c)

0

(d)

1

\(\int _{ 0 }^{ 2a }{ f(x) } dx=2\int _{ 0 }^{ 2a }{ f(x) } dx\) if _________

(a)

f(2a -x) = f(x)

(b)

f(a -x) = f(x)

(c)

f(x) = - f(-x)

(d)

f(-x) = f(x)

The I.F of y log y \(\frac{dx}{dy}+x-log\ y=0\) is __________

(a)

log(log y)

(b)

log y

(c)

\(\frac{1}{log\ y}\)

(d)

\(\frac{1}{log(log\ y)}\)

If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0 is the p.d.f, of x then c is _____________

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 4 }{ 3 } \)

(c)

\(\frac { 8 }{ 3 } \)

(d)

\(\frac { 3 }{ 8 } \)

Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q

If p is true and q is unknown, then _________

(a)

~ p is true

(b)

p v (~p) is false

(c)

p ∧ (~p) is true

(d)

p v q is true