JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD Pharm. D I Year REMEDIAL MATHEMATICS Previous Question Paper (October/November - 2020 - R08)
Answer any five questions. All questions carry equal marks.
Main
Solve the equations x + y - z = 5, x + y + z = 2, 3x + 2y + 4z = 7 by using Cramer’s rule.
Answer
To solve the system using Cramer's Rule, we first find the determinant of the coefficient matrix D:
Next, find the determinants Dx, Dy, and Dz by replacing the respective columns with the constants (5, 2, 7):
The solutions are:
If A = [[1, 3, 2], [0, 2, 1], [1, 3, 5]] and B = [[-1, 6, 2], [0, 5, 7], [1, -1, 5]], then find determinant of A + B and A - B.
Answer
First, calculate the sum and difference matrices:
Calculate the determinant of A + B:
Calculate the determinant of A - B:
If sin A = 3/5, cos B = 9/41 then find the value of sin(A-B) and sin(A+B).
Answer
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Prove that (tan A + sec A - 1) / (tan A - sec A + 1) = (1 + sin A) / cos A.
Answer
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Find the equation of the line passing through the points (9, 8) and (8, 9). Does the point (5, 2) lie on this line?
Answer
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Find the equation of the parabola whose axis is parallel to X-axis and which passes through the points (3, 3), (6, 5) and (6, -3).
Answer
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Find the value of lim x→∞ (sqrt(x^2 + x) - x).
Answer
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Find the derivative of (sin^2 x + 5^x) / (e^x + log x).
Answer
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Find the value of integral 0 to 1 of x(1-x)^n dx.
Answer
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Find the value of integral dx / (x^2 - 1).
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Find the value of integral x^3 sin x dx.
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Solve the differential equation dy/dx + xy = xe^-x^2.
Answer
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Define: i) Differential equation, ii) Order of a differential equation, iii) Degree of a differential equation, iv) Linear differential equation with an example.
Answer
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Find Laplace transform of e^-4t sin 2t cos 5t.
Answer
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Define Laplace transform and find Laplace transform of e^2x + 7x^6 + 2sin 3x - 3cos 3x.
Answer
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Find ∂u/∂x, ∂u/∂y, ∂^2u/∂x^2, ∂^2u/∂y^2, ∂^2u/∂x∂y where u = x^3 + y^3 - 3x^2y^2 + 5x + 6y.
Answer
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Find the equation of the circle passing through the points (1, 2), (3, -4) and (5, -6).
Answer
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