JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD Pharm. D I Year REMEDIAL MATHEMATICS Previous Question Paper (October/November - 2019 - R08)

Pharm. D | I Year | I Year | R08 | October/November - 2019

Answer PaperPaper Code: PH106Maximum Marks: 70Time: 3hours

Answer any five questions. All questions carry equal marks.

Main

114 marks
a

Find AB and BA where A =

[[1, 2, 1], [2, 4, -1], [1, 1, 1]]
and B =
[[1, 1, 1], [3, -2, 3], [1, 4, -6]]

7 marks

Answer

To find the product AB, we multiply the rows of A by the columns of B:

AB = [[1, 2, 1], [2, 4, -1], [1, 1, 1]] * [[1, 1, 1], [3, -2, 3], [1, 4, -6]] = [[1+6+1, 1-4+4, 1+6-6], [2+12-1, 2-8-4, 2+12+6], [1+3+1, 1-2+4, 1+3-6]] = [[8, 1, 1], [13, -10, 20], [5, 3, -2]]

To find the product BA, we multiply the rows of B by the columns of A:

BA = [[1, 1, 1], [3, -2, 3], [1, 4, -6]] * [[1, 2, 1], [2, 4, -1], [1, 1, 1]] = [[1+2+1, 2+4+1, 1-1+1], [3-4+3, 6-8+3, 3+2-3], [1+8-6, 2+16-6, 1-4-6]] = [[4, 7, 1], [2, 1, 2], [3, 12, -9]]
b

Solve the following equations by using Cramer’s Rule:

x - 2y + 3z = 2; 3x + 2y - z = 12; 2x - y + 3z = 7

7 marks

Answer

The system of equations is: x - 2y + 3z = 2; 3x + 2y - z = 12; 2x - y + 3z = 7. The determinant of the coefficient matrix D is:

D = |1, -2, 3; 3, 2, -1; 2, -1, 3| = 1(6-1) + 2(9+2) + 3(-3-4) = 5 + 22 - 21 = 6

Calculating the determinants for x, y, and z:

Dx = |2, -2, 3; 12, 2, -1; 7, -1, 3| = 2(6-1) + 2(36+7) + 3(-12-14) = 10 + 86 - 78 = 18
Dy = |1, 2, 3; 3, 12, -1; 2, 7, 3| = 1(36+7) - 2(9+2) + 3(21-24) = 43 - 22 - 9 = 12
Dz = |1, -2, 2; 3, 2, 12; 2, -1, 7| = 1(14+12) + 2(21-24) + 2(-3-4) = 26 - 6 - 14 = 6

Applying Cramer's Rule:

x = Dx/D = 18/6 = 3; y = Dy/D = 12/6 = 2; z = Dz/D = 6/6 = 1

The solution is x = 3, y = 2, z = 1.

214 marks
a

Prove that

(4cos^2 A - 1)(cot(15 - A)tan(15 + A)) = 1 + 2sin^2 A

7 marks

Answer

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b

Prove that

cos(π/9)cos(2π/9)cos(3π/9)cos(4π/9) = 1/2^4

7 marks

Answer

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314 marks
a

Find the equation of the line passing through the point (1, 1) and perpendicular to the line passing through the points (3, 5) and (-6, -2).

7 marks

Answer

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b

Find the equation of the circle whose centre is (5, 7) and radius 4.

7 marks

Answer

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414 marks
a

Find the differential coefficient of

y = x^sin x + (log x)^x

7 marks

Answer

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b

Find the derivative of

(log x)^x / e^x

7 marks

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514 marks
a

If

u = (x^2 + y^2 + z^2)^(-1/2)
, then show that
∂^2u/∂x^2 + ∂^2u/∂y^2 + ∂^2u/∂z^2 = 0

7 marks

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b

If

u = sin^(-1)(x/y) + tan^(-1)(y/x)
, then prove that
x(∂u/∂x) + y(∂u/∂y) = 0

7 marks

Answer

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614 marks
a

Evaluate

∫ x^2 e^x dx

7 marks

Answer

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b

Evaluate

∫[0 to π/2] (sin x) / (sin x + cos x) dx

7 marks

Answer

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714 marks
a

Solve:

(xy + x^2)dx + (y^2 + xy)dy = 0

7 marks

Answer

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b

Solve:

dy/dx = (x + y) / x

7 marks

Answer

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814 marks
a

Find

L{5sin 2t + 2sin 3t}

7 marks

Answer

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b

Find

L{e^(-t) sin^2 t}

7 marks

Answer

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About this paper

This page contains the question paper of REMEDIAL MATHEMATICS from JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD for Pharm. D I Year I Year, October/November - 2019, R08.

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