JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD Pharm. D I Year REMEDIAL MATHEMATICS Previous Question Paper (September/October - 2021 - R08)
Answer any five questions
All questions carry equal marks
Main
Solve: 2x + 3x + 4x = 0; 2x + 3x + 4x = 0; 2x + 3x + 4x = 0
Answer
The given equations are 2x + 3x + 4x = 0, which simplifies to 9x = 0. Since this equation is identical for all three instances, the system reduces to a single linear equation in one variable: 9x = 0. Dividing both sides by 9 gives x = 0. As there are no constraints provided for y or z, the system is underdetermined, resulting in a solution set where x = 0 and y, z can be any real numbers.
Solve the following system of equations by Cramer’s rule: x – y + 2z = 7, 3x + 4y – 5z = –5, 2x – y + 3z = 12.
Answer
To solve the system using Cramer's rule, we first calculate the determinant of the coefficient matrix D:
Next, we calculate the determinants Dx, Dy, and Dz by replacing the respective columns with the constants column (7, -5, 12):
Finally, the values of the variables are determined by dividing these determinants by D:
The solution is x = 2, y = 1, z = 3.
If a = 18, b = 24 and c = 30 then find sin A, sin B and sin C.
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If tan(A-B) = 7/24 and tan A = 4/3, then find A+B.
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Find the equation of the line passing through the point (-2, 2) and the sum of the intercepts on the coordinate axes is 3.
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Find the equation of the circle passing through the point (2, -1) and whose centre is (2, 3).
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Find the derivative of the function y = (1 + 2sec x) / (2 + 5sec x)
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If z = xy + 3sin x - 4cos y + 1, then find ∂z/∂x and ∂z/∂y.
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Evaluate the integral of x^2 * e^(3x) dx.
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Evaluate the integral of dx / (4sin^2 x + 5cos^2 x).
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Evaluate the integral from 0 to π/2 of (cos x / (1 + sin x)) dx.
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Solve the differential equation dy/dx + (x - y)e^x = y^2 e^x.
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Solve the differential equation (x^2 - 4xy - 2y^2)dx + (y^2 - 4xy - 2x^2)dy = 0.
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Solve the linear differential equation dy/dx + (2x/(1+x^2))y = (x^2 + 4)/(1+x^2).
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Find L{t^2 + 3e^(4t) - 2sin3t}.
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State and prove first shifting theorem.
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