Find the vector of magnitude units which is perpendicular to both the vectors

a i -2j 3k and b =2i 4j -k.

By Simpson's role, evaluate integral of 2x dx with limits 0 to 4 by taking n 4.

Three urns B and C contain 6 red and 4 black balls, 2 red and 6 black balls, 1 red and 8 black balls respectively. An urn is chosen at random and a ball is drawn from the urn. If the ball drawn is red, find the probability that the ball was drawn from urn A.

The following data gives the marks obtained by the students of a class in two subjects, Mathematics (Maths.) and Statistics (Stats.)

Maths.56 55 58 58 57 56 60 54
Stats. 68 67 67 70 65 68 70 66

Estimate the marks of a student In Mathematics who scores 62 marks In Statistics, by using appropriate equation of line of regression.

If sin y x sin show that dy/dx sin^2 a

If y a cos (log b sin (log show that d^2y/dx^2 x dy/dx

Evaluate: integral of 2x dx

Evaluate: integral of 1 dx/x^2+8x+20

In a spherical triangle PZX, x 90°00' and z 73°12'. Calculate the side p and the angle P.

In a spherical triangle PQR, p 62°10.1', q 111°35.2' and 63°33'. Find the angle P.

Find the equation of a hyperbola referred to its principal axes, whose length of transverse axis is 8 and the distance between foci is 10.

Find the coordinates of vertex, focus and end points of latus rectum, equation of directrix and length of latus rectum of a parabola whose equation is y^2 -4x -4y

Note It is not a standard parabola with vertex at origin but with shifted vertex.