JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD Pharm. D I Year REMEDIAL MATHEMATICS Previous Question Paper (June/July - 2019 - R08)
Answer any five questions. All questions carry equal marks.
Main
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Answer
To simplify the expression, we first rewrite the denominators to have a common cyclic order. Note that (b-a) = -(a-b) and (c-a) = -(a-c), and (c-b) = -(b-c). The expression becomes:
Taking the common denominator (a-b)(b-c)(c-a), we adjust the terms:
Expanding the numerator:
Thus, the expression equals 0.
Solve 2x + 3y - 1 = 0, 3x - y + 2 = 0 by Crammer’s rule.
Answer
Given the system of equations: 2x + 3y = 1 and 3x - y = -2. According to Cramer's rule, the solution is given by x = Dx/D and y = Dy/D.
The determinant D is:
The determinant Dx is:
The determinant Dy is:
Calculating the variables:
The solution is x = -5/11 and y = 7/11.
Solve sin 2x + sin 4x + sin 6x = 0.
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If in any triangle ABC, a + b + c = 2s then prove that:
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Find the angle between the line OA and BC where O = (0,0), A = (2, 3), B = (2, -2) and C = (3, 5).
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Find the equation of the circle passing through the points (0, 2), (3, 0), (3, 2).
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Differentiate (x2-1)/(x+1) with respect to x.
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Find d2y/dx2 if y = log x + ax.
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Find ∂u/∂x and ∂u/∂y for u = ex(sin xy + cos xy).
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Differentiate x2e2xsec2x with respect to x.
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Evaluate ∫(sin(log x)/x) dx.
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Evaluate ∫x2 tan x dx.
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Form the differential equation from the equation x2 + y2 = 4ax, 'a' being an arbitrary constant.
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Solve y(1 + log x) dx - x log x dy = 0.
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Find the Laplace Transform of (1 + t2)/t.
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Find the Laplace Transform of e-t sin 2t cos 5t.
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