Download OU B.Pharma 1st Year 2019 Aug 13242 NON Mathematics Question Paper

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FACULTY

B. Pharmacy I-Year (Non CBCS)(Backlo) Examination, Auust 2019

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Subject: Mathematics

Time: 3 hrs Max. Marks : 70

Note: Answer all questions. All questions carry equal marks.

1. a) i) Find the solution of the equation 10^x+3 = 6^2x.
   ii) If tan 35° = K then the value of $$\frac{\tan {145}^{°}\tan {125}^{°}}{1+\tan {145}^{°}\tan {125}^{°}}$$
   

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   OR
   b) i) log₂ x + log₂ (x-2) = 3.
   ii) if tan a = 1/3 and tan ß = 1/7 then show that tan (2a+ß)=1.
2. a) i) Find the derivative of tan x using first principle.
   ii) Show that the function is not differentiable at 2 where
   

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   f(x) = $$\{\begin{array}{ll}x;& 0=x=2\\ 2;& x=2\end{array}.$$
   OR
   b) i) Find the maximum and minimum values of the polynomial f(x) = x³ – 4x² + 8x – 6
   ii) If u = xy f(x/y) prove that x ?u/?x + y ?u/?y = 2u.
3. a) i) Evaluate ? 1/(3+5cos2x) dx
   

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   OR
   ii) ? (1+sin²x)/(1+cos²x) dx
   b) i) Evaluate ? 1/(4+5sinx) dx
   ii) Evaluate ? (2x+6)/(x²+3x-6) dx
4. a) i) If A = $$\left[\begin{array}{ccc}{a}^2& ab& ac\\ ab& b^2& bc\\ ac& bc& c^2\end{array}\right]$$ and a² + b² + c² = 1 then find |A²|.
   

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   ii) Solve the equation 7x + 5y – 13z + 4 = 0, 9x + 2y + 11z – 37 = 0, 3x - y + z = 2 by matrix inversion method.
   OR
5. b) i) Find the rank of the matrix A = $$\left[\begin{array}{cccc}1& 1& 2& 3\\ 2& 2& 3& 4\\ 3& 4& 5& 6\end{array}\right]$$
   ii) If A = $$\left[\begin{array}{ccc}0& 2& 1\\ 2& 0& 2\\ 1& x& 0\end{array}\right]$$ is a skew symmetric matrix, then find the value of x.
6. a) i) Find the equation of circle passing through the points (1, 0) (0, 1) (1, 1).
   

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   ii) Find the equation of the line having intercepts a and b on the axes such that a + b = 3 and ab = 1.
   OR
   b) i) Write the basic mathematical principles are used in Biological testing.
   ii) Find the equation of circle passing through (7, 1) and having centre at (4, 3).

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