B.Tech / B.E. – Semester I / II Examination Subject: Higher Engineering Mathematics (MA-101) Code: [As per your scheme]
Max. Marks: 70
Trace the curve ( r = a(1 + \cos\theta) ) (Cardioid) and find the area enclosed. (7 marks) Unit – B: Multiple Integrals & Vector Calculus Q3 (a) Evaluate: [ \int_0^1 \int_0^\sqrt1-x^2 \int_0^\sqrt1-x^2-y^2 \fracdz , dy , dx\sqrt1-x^2-y^2-z^2 ] (7 marks) higher engineering mathematics b s grewal
Verify Cauchy-Riemann equations for ( f(z) = e^z ) and find ( f'(z) ). (7 marks) (7 marks) Unit – B: Multiple Integrals &
Using convolution theorem, evaluate: [ \mathcalL^-1 \left \frac1s(s^2 + a^2) \right ] (7 marks) Unit – E: Numerical Methods & Complex Variables Q9 (a) Using Newton-Raphson method, find a real root of ( x \log_10 x = 1.2 ) correct to 4 decimal places. (7 marks) higher engineering mathematics b s grewal