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Find the divergence of the vector 

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Find the angle between any two diagonals of a cube.

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Prove that the general equation of first degree in x, y, z represents a plane.

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Find the angle between the lines,


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Prove that the lines,

  are perpendicular 

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Find the shortest distance between the lines.


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Find the equation of the plane containing the point (2, 1, 1) and the line,


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Find the constant 'a' so that the vectors  are co-planar.

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If  and then prove that  is perpendicular to and also find


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Find the volume of the parallelopiped whose co-terminal edges are represented by the vectors


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 Find the velocity and acceleration of a particle moves along the curve  at any time t". 

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Find the directional derivative of x2yz3 at(1, 1, 1) in the direction of 

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Solve (D2 + 2D + 1) = x2 + 2x.

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 show that 

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Show that the vector field, is solenoidal.

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Find the constants a, b, c such that the vector field,


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Prove that L(sin at)= 

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Find L[sint  sin 2t  sin 3t].

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Find L[cos3t].

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Find the inverse Laplace transform of 

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Find 

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Find 

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Solve the differential equation,  under the condition  by Laplace transform techniques. 

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Solve the differential equation,   by Laplace transform techniques.

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Obtain reduction formula for  where n is positive integer.

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Find the modulus and amplitude of 1 + cos+ i sin.

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Find the cube root of 1 - i.

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Find the nth derivative of eax cos (bx+c).

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Find the nth derivative of 

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If y= sin_1 x, prove that 

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Find the angle of intersection of the curves 

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Find the nodal equation of the curve r (1-cos) - 2a.

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Expand log (secx) upto the term containing x4 using Maclaurin's series.

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If u = x3 - 3xy2 + x + ex cosy + 11 show that uxx + tyy = 0.

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If prove that 

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Find , where u = x+y+z, v= y + z ,w=z. 

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Express the complex number

 in the form a + ib. 

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Evaluate 

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Evaluate 

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Prove that: i) and    ii) (n+1) = n! for a positive integer n. 

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Prove that 

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Show that 

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Solve 

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Solve  dy = 0.

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Solve  + y cotx =cosx.

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Solved 

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Solve (D2 - 4D + 13)y = cos 2x.

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