If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is ________

(a)

sinx cosx

(b)

1

(c)

2

(d)

none

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

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 \(\alpha ={ tan }^{ -1 }\left( \frac { \sqrt { 3 } }{ 2y-x } \right) ,\beta ={ tan }^{ -1 }\left( \frac { 2x-y }{ \sqrt { 3y } } \right) \) then \(\alpha -\beta \) __________

(a)

\(\frac { \pi }{ 6 } \)

(b)

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

(c)

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

(d)

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

y² - 2x - 2y + 5 = 0 is a _________

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

If \(\overset { \rightarrow }{ a } \) and \(\overset { \rightarrow }{ b } \) are two unit vectors, then the vectors \(\left( \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right) \times \left( \overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } \right) \) is parallel to the vector ___________

(a)

\(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

(b)

\(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

(c)

2\(\overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \)

(d)

2\(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \)

Equation of the normal to the curve y = 2x²+3 sin x at x = 0 is __________

(a)

x + y = 0

(b)

3y = 0

(c)

x + 3y = 7

(d)

x + 3y = 0

If x = r cos θ, y = r sin, then \(\frac { \partial r }{ \partial x } \) = ....................

(a)

sec θ

(b)

sin θ

(c)

cos θ

(d)

cosec θ

The I.F. of (1+y²) dx = (tan^-1-t-x) dy is ________.

(a)

e^tan-1 y

(b)

e^tan-1 x

(c)

tan^-1 y

(d)

tan^-1x

Define * on Z by a * b = a + b + 1 ∀ a,b \(\in \) Z. Then the identity element of z is ________

(a)

1

(b)

0

(c)

1

(d)

-1