In triangle `ABC,` the value of `|[e^(-i2A),e^(iC),e^(iB)],[e^(iC),e^(-i2B),e^(iA)],[e^(iB),e^(iA),e^(-i2C)]|`

If A , B ,C are angles of a triangle, then the value of |[e^(2i A),e^(-i C),e^(-i B)],[e^(-i C),e^(2i B),e^(-i A)],[e^(-i B),e^(-i A),e^(2i C)]| is (a) 1 (b) -1 (c) -2 (d) -4

If A+B+C=pi and e^(itheta)=costheta+isintheta and z=|[e^(2iA), e^(-iC), e^(-iB)] , [e^(-iC), e^(2iB), e^(-iA)], [e^(-iB), e^(-iA), e^(2iC)]| , then

If e^(itheta)=costheta+isintheta, find the value of |[1,e^(ipi//3),e^(ipi//4)],[e^(-ipi//3),1,e^(i2pi//3)],[e^(-ipi//4),e^(-i2pi//3),1]|

If e^(itheta)=costheta+is intheta, find the value of |1e^(ipi//3)e^(ipi//4)e^(-ipi//3)1e^(i2pi//3)e^(-ipi//4)e^(-i2pi//3)1|

In !ABC , least value of (e^(A))/A+(e^(B))/B+(e^(C))/C is equal to

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

If alpha + beta + gamma = pi , then the value of the determinant |(e^(2i alpha),e^(-i gamma),e^(-i beta)),(e^(-i gamma),e^(2i beta),e^(-i alpha)),(e^(-i beta),e^(-i alpha),e^(2i gamma))| , is

Statement-1 : If e^(itheta)=cos theta +isintheta and the value of e^(iA).e^(iB).e^(iC) is equal to -1, where A,B,C are the angles of a triangle. and Statement -2 : In any triangleABC , A + B +C = 180^(@)

x gt0 , then the sum of the series e^(-x)-e^(-2x)+e^(-3x)-... i s

Given below are a set of half-cell reactions (acidic medium) along with their E_(@) with respect to normal hydrogen electrode values. Using the data obtain the correct explanation to question given below. {:(I_(2)+2e^(-)rarr2I^(-),E^(@)=0.54),(Cl_(2)+2e^(-)rarr2Cl^(-),E^(@)=1.36),(Mn^(2+)+e^(-)rarrMn^(2+),E^(@)=1.50),(Fe^(3+)+e^(-)rarrFe^(2+),E^(@)=0.77),(O_(2)+4H^(+)+4e^(-)rarr2H_(2)O,E^(@)=1.23):} While Fe^(2+) is stable, Mn^(3+) is not stable in acid solution because: