Find the value of e is :
( a )  e <2
( b )   e >3
( c )   e < 3

Find the value of [-e ] is ( a ) -2 ( b ) -3 ( c ) -1 ( d ) 0

Find the value of e^x + e^(-x)

Let E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(1) uu E_(2))=0.4 and P(E_(2))=x . Find the value of x such that (i) E_(1) and E_(2) are mutually exclusive, (ii) E_(1) and E_(2) are independent.

The minimum value of x(log)_(e)x is equal to e (b) 1/e(c)-1/e (d) 2e( e )e

In a A B C , D and E are points on the sides A B and A C respectively such that D E B C If A D=8x-7, D B=5x-3, A E=4x-3 and E C=(3x-1) , find the value of x . (ii) If A D=4x-3, A E=8x-7, B D=3x-1 and C E=5x-3 , find the volume x . (iii) If A D=2. 5 c m , B D=3. 0 c m and A E=3. 75 c m , find the length of A C .

When the tangent to the curve y=xlogx is parallel to the chord joining the points (1, 0) and (e ,\ e) , the value of x is e^(1//1-e) (b) e^((e-1)(2e-1)) (c) e^((2e-1)/(e-1)) (d) (e-1)/e

In Fig. 4.178, D E B C (FIGURE) If D E=4c m , B C=6c m and Area ( A D E)=16 c m^2 , find the area of A B C . (ii) If D E=4c m , B C=8c m and Area ( A D E)=25 c m^2 , find the area of A B C . (iii) If D E : B C=3:5 . Calculate the ratio of the areas of A D E and the trapezium B C E D .

If A , B ,C are angles of a triangles, 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 1 b. -1 c. -2 d. -4

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