Download OU B.Pharma 1st Year 2014 8035 Mathematics Question Paper

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b) If x=1+log_abc, y=1+log_bca and z=1+log_cab. Prove that Xyz = Xy + yz + zX.

In a triangle ABC, prove that Sin²A + Sin²B — Sin²C = 4 cos A cos B sin C.

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OR

If tan a = ⁵/₈ and tan ß = ¹/₃ then show that tan(2a + ß)=1.

If a^x=b^y=c^z and y²=zx. Prove that log_b a = log_c b.

Find the derivative of cotx using first principle.

Show that the function is not differentiable at 2 where f(x)= |x-2| / x²

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OR

Find the maximum and minimum values of the polynomial f (x)=x³-6x² + 9x + 15.

If u=log (x²+y²)^1/2 prove that x ?u/?x + y ?u/?y = 1

Evaluate ? ¹/_3+5x-2x² dx

Evaluate ?(xv(1 +e^x))dx

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OR

Evaluate ? ¹/_4+5cosx dx

Show that | bc b+c 1 ca c+a 1 ab a+b 1 | = ( a - b ) ( b - c ) ( c - a )

Solve the equations 3x + 4y + 5z = 18, 2x —y + 8z = 13 and 5x - 2y +7z = 20 by matrix inversion method.

OR

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Find the rank of the matrix A= [ 1 -4 5 2 1 3 ]

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5 a) i) Find the equation of the circle passing through the points (1, 2), (3, -4) and (5, -6).

ii) Find the equation of the line having intercepts a and b on the axes such that a + b=5 and ab=6.

OR

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b) i) Find the equation of the line passing through the point (2, -3) and having intercepts whose ratio is 3 : 2.

iy Find the centre and radius of the circle 3x² + 3y² +6x—12y—1=0.

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