Objective Question (MCQ)
[ marks]07 1. =_____
[ marks]0 (b) 1 (c) 0.5 (d) doesn’t exist 2. =_____
[ marks](b) (c) (d) 3. The jaco bian of polar coordinates with respect to Cartesian coordinates (x, y) is
[ marks](b) (c) (d)None of these 4. The cur ve is symmetric about___
[ marks]X – axis (b) Y – axis (c) Origin (d) None of these 5.
[ marks]1 (b) (c) (d) 6. Which o f following series diverges? 7. The improper Integral is
[ marks]0 (b) 1 (c) 2 (d) Diverges
[ marks]07 1. If then
[ marks]u (b) 0 (c) – u (d) 2u is 2.
[ marks]0 (b) – 1 (c) 1 (d) doesn’t exist 3. Which o f the following is homogeneous function of degree one?
[ marks](b) (c) tan (d) 4. The Ma claurin’s Series expansion of the function has coefficient of
[ marks]6 (b) 3! (c) 36 (d) 1/3! 5. The radius of convergence of the series 1+2+4+8+……+ +…..
[ marks]0 (b) 1 (c) 2 (d) 6. Standard linear approximation of at (1,1,1) is
[ marks]x+y+z – 2 (b) x+y+z+2 (c) x – y+z+2 (d) None of these 7. The stationary point of the function is
[ marks](1,0) (b) (1,1) (c) (0,0) (d) (0, - 1)
[ marks]03 Find the value of b for which .= 9.04
[ marks]Evaluate (i) (ii)
[ marks]Find taylor series expansion of the function in powers of h and hence find the value of correct up to three decimal places.
[7 marks]03
[ marks]Determine whether exists or not? It they exist, find the value.
[ marks]04 If z , show that = 4 .
[ marks]State Euler’s theorem for homogeneous function. Verify Euler’s theorem for f(x,y) = .
[7 marks]The radius of a sphere is found to be 10 cm with a possible error of 0.02 cm. What is the relative error in computing the volume?
[3 marks]04 Find tangent plane and normal line of the surface at the point P(1,2,4).
[ marks]Find the numbers x,y and z such that xyz = 16 and 18xy+16yz+12xz is minimum, using the Lagrange’s method of undetermined coefficients.
[7 marks]Find the interval of convergence of the series ……
[3 marks]Find the volume of the region Denclosed by surfaces and .
[4 marks]07 Define jacobian. Evaluate using change of variables x + y = u and y – 2x = v.
[ marks]03
[ marks]Show that the p- series ( p a real constant) converges if p >1.
[ marks]04 Evaluate by changing the order of integration.
[ marks]Test the convergence of the series. If converges find the sum.
[7 marks](ii) ,
[ marks]The region bounded between the graph of and and is rotating around the line y = 4. Find its volume.
[3 marks]State the types of the improper integrals. Test the convergence of .
[4 marks]Trace the curve .
[7 marks]