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 \(\rho\) (A) = \(\rho\) ([A/B]) = number of unknowns, then the system is _________--

(a)

consistent and has infinitely many solutions

(b)

consistent

(c)

inconsistent

(d)

consistent and has unique solution

If \(\rho\) (A) ≠ \(\rho\) ([AIB]), then the system is _____________

(a)

consistent and has infinitely many solutions

(b)

consistent and has a unique solution

(c)

consistent

(d)

inconsistent

If, i² = -1, then i¹ + i² + i³ + ....+ up to 1000 terms is equal to ________

(a)

1

(b)

-1

(c)

i

(d)

0

The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \)  = 1 lies on _________

(a)

circle x²+ y² = 1

(b)

x-axis

(c)

y-axis

(d)

the lines x+y = 1

If x = cosθ + i sinθ, then the value of xⁿ+\(\frac { 1 }{ { x }^{ n } } \) is ___________

(a)

2 cosθ

(b)

2i sin nθ

(c)

2i sin nθ

(d)

2i cos nθ

If x is real and \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then ________

(a)

\(\frac{1}{3}\) ≤ k ≤

(b)

k ≥ 5

(c)

k ≤ 0

(d)

none

lf the root of the equation x³ + bx²+ cx - 1 = 0 form an lncreasing G.P, then ___________

(a)

one of the roots is 2

(b)

one of the roots is 1

(c)

one of the roots is -1

(d)

one of the roots is -2

If ax² + bx + c = 0, a, b, c \(\in\) R has no real zeros, and if a + b + c < 0, then __________

(a)

c>0

(b)

c<0

(c)

c=0

(d)

c≥0

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)

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

If tan^-1(3) + tan^-1(x) = tan^-1(8) then x = ____________ 

(a)

5

(b)

\(\frac { 1 }{ 5 } \)

(c)

\(\frac { 5 }{ 14 } \)

(d)

\(\frac { 14 }{ 5 } \)

If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is _____________

(a)

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

(b)

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

(c)

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

(d)

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

y² - 2x - 2y + 5 = 0 is a _________

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

If the distance between the foci is 2 and the distance between the direction is 5, then the equation of the ellipse is __________

(a)

6x² + 10y² = 5

(b)

6x² + 10y² = 15

(c)

x² + 3y² = 10

(d)

none

The area of the circle (x - 2)² + (y - k)² = 25 is _________

(a)

25ㅠ

(b)

5ㅠ

(c)

10ㅠ

(d)

25

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 area of the parallelogram having diagonals \(\overset { \rightarrow }{ a } =3\overset { \wedge }{ i } +\overset { \wedge }{ j } -2\overset { \wedge }{ k } \) and \(\overset { \rightarrow }{ b } =\overset { \wedge }{ i } -3\overset { \wedge }{ j } +\overset { \wedge }{ 4k } \) is ____________

(a)

4

(b)

2\(\sqrt { 3 } \)

(c)

4\(\sqrt { 3 } \)

(d)

5\(\sqrt { 3 } \)

The value of \({ \left| \overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ a } -\overset { \rightarrow }{ b } \right| }^{ 2 }\) is _____________

(a)

\(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }+{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

(b)

4 \(\overset { \rightarrow }{ a } .\overset { \rightarrow }{ b } \)

(c)

\(2\left( { \left| \overset { \rightarrow }{ a } \right| }^{ 2 }-{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 } \right) \)

(d)

4 \({ \left| \overset { \rightarrow }{ a } \right| }^{ 2 }{ \left| \overset { \rightarrow }{ b } \right| }^{ 2 }\)

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

The curve y = e^x is ________

(a)

convex

(b)

concave

(c)

convex upwards

(d)

concave upwards

If f(x, y) = 2x² - 3xy + 5y + 7 then f(0, 0) and f(1, 1) is _____________

(a)

7, 11

(b)

11, 7

(c)

0, 7

(d)

1, 0

If u = sin-1 \(\left( \frac { { x }^{ 4 }+{ y }^{ 4 } }{ { x }^{ 2 }+{ y }^{ 2 } } \right) \) and f = sin u then f is a homogeneous function of degree ..................

(a)

0

(b)

1

(c)

2

(d)

4

\(\int _{ 0 }^{ \infty }{ { e }^{ -mx } } { x }^{ 7 }\) dx is __________

(a)

(b)

(c)

(d)

\(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ \frac { sin \ x-cos \ x }{ 1+sin \ x cos \ x } dx= } \) ............

(a)

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

(b)

0

(c)

\(\frac { \pi }{ 4 } \)

(d)

\( \pi\)

The I.F of \(\frac{dy}{dx}-y\) tan x = cos x is _________

(a)

sec x

(b)

cos x

(c)

e^{tan x}

(d)

cot x

The number of binary operations that can be defined on a set of 3 elements is _____________

(a)

3²

(b)

3³

(c)

3⁹

(d)

3¹

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

In (N, *), x * y = max(x, y), x, y \(\in \) N then 7 * (-7)

(a)

7

(b)

-7

(c)

0

(d)

-49