Download PTU B.Pharmacy 2020 March 2nd Sem 46012 Remedial Mathematics Question Paper

Roll No. _________________________ Total No. of Pages : 03

Total No. of Questions : 10 B.Pharmacy (Sem.-1,3)

REMEDIAL MATHEMATICS

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Subject Code: PHM-112

M.Code : 46012 Max. Marks : 80

INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of FIFTEEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.

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3. SECTION-C contains FOUR questions carrying TEN marks each and students have to attempt any THREE questions.

1. Write short notes on :
   1. Solve the equation x² + y² + 7 = 0.
   2. For what values of x and y the following pair of matrices A and B equal
      A = $$\left[\begin{array}{cc}3x+7& 5\\ y/2\; -\; 3x& y\; +\; 8\end{array}\right]$$ and B = $$\left[\begin{array}{cc}0& y-2\\ 8& 4\end{array}\right]$$
   3. Find the value of x so that the determinant $$\left|\begin{array}{cc}3x+7& 5\\ 1& 2-3x\end{array}\right|$$ is zero.

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   4. If tan x = 3/5 find the value of sin 2x.
   5. Show that (1+cos x)/(1-cos x) = cot²(x/2)
   6. Find the x and y intercepts of the line 3x + 4y - 7 = 0.
   7. Find the angle between the line x + y + 1 = 0 and -x + 2y + 5 = 0.
   8. In a moderately skewed distribution, the median is 20 and the mean is 22.5. Using these values, find the approximate value of the mode.

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   9. Define mean and median.
   10. Differentiate the function f(x) = x² sin x with respect to x.
   11. If x² + sin xy = 7, find dy/dx
   12. Solve the integral ? cos x e^sinx dx.
   13. Solve ? x e^x dx.

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   14. Find the derivative of f(x) = x² + sin x with respect to x.
   15. Find the value of tan 225°.

2. Solve the following system of equations by using Cramer's law
   3x - 2y + 3z = 8, 2x + y - z = 1, 4x - 3y + 2z = 4.

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3. Show that 2sin² ß + 4 cos (a + ß) sin a sin ß + cos 2 (a + ß) = cos 2a.
4. Find the foot of perpendicular of the point (2, 3) on the line x + y - 11 = 0
5. Solve the integral ? (2x-3)/((x²-1)(2x+3)) dx.
6. Differentiate v((x-3)(x²+4))/(3x²+4x+5)) with respect to x.

7. Find inverse of the matrix A = $$\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& -3\\ 2& -1& 3\end{array}\right]$$

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8. The weight of coffee in 70 jars in shown in the following table :
   

   Weight (in grams)	200-201	201-202	202-203	203-204	204-205	205-206
   Frequency	13	27	18	10	1	1

   
   Determine the mean, median, variance and standard deviation of the above distribution.
9. 1. Find dy/dx if x = a (? - sin ?), y = a (1 + cos ?).
   2. Solve the integral ? v(tan x) / (sin x cos x) dx.

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10. 1. Find the equation the line perpendicular to the line 2x - y + 7 = 0 and pass through the point (1,1)
    2. Show that sin 20° sin 40° sin 60° sin 80° = 3/16

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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