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

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

If p is true and q is unknown, then _________

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

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

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

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 ..................

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

The curve y = e^x is ________

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

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

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

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

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

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 ____________

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 __________

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

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

y² - 2x - 2y + 5 = 0 is a _________

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

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

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

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

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

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

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

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

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 ________