PTU MATHEMATICS-1

DOWNLOAD MATHEMATICS 1 - MATHS 1 PREVIOUS YEARS QUESTION PAPER B.TECH PTU FIRST YEAR

PTU MATHEMATICS - 1 B.TECH PREVIOUS QUESTION PAPER

AMA - 1 MATHEMATICS - 1(B.TECH 1st & 2nd SEMESTER,2122)

1(a) If z = u2 + v2 and u = at2, v = 2at, find dz/dt.

(b) Expand sin x in powers of x.

(c) Prove that:

where S is the length of the arc measured from fixed point and p is the radius of curvature.

(d) Change the order of integration in

(e) Find the centre of pressure of a triangular area immersed in a homogeneous liquid with one side in the free surface.

(f) Show that :

(g) Find the value of Log (i)i. (i raised to the power of i)

(h) Find the general value equation of cone which touches the three co-ordinate planes.

(i) The order of convergence of Newton-Raphson method is : (i) 1.168 (ii)1 (iii) 2 (iv) 3

(j) Apply Gauss-Jordan method to solve:

x + y + z = 9

2x - 3y + 4z = 13

3x +4y + 5z = 40.

SECTION - A

2. (a) The period of a simple pendulum with small oscillation is T = 2π(l/g)1/2. If T is computed using l = 8 ft, and g = 32 ft./sec2, find the % error in T if the true values are l = 8.05 ft. and g = 32.01 ft/sec2. What is the approximate error in T ?

(b) If u = tan-1(y2/x)., prove that :

3. (a) Find the maximum and minimum distances of the point (3, 4, 12) from the sphere x2 + y2 + z2 = 1.

(b) For the cardiode show that p2/r is constant.

4. (a) If the density at any point of the solid octant of the ellipsoid

varies as x,y,z find the co-ordinates of C.G. of the solid.

(b) By using the transformation x + y = u, y = uv, show that :

5. (a) Using double integral, find the M.I. about x-axis of the area enclosed by the lines: x = 0, y = 0, (x/a) + (y/b) = 1.

(b) Transform the following to Cartesian form and hence evaluate :

SECTION - B

6. (a) What is necessary condition for the convergence of a positive term series? Test the convergence of

(b) State and prove Cauchy's root test. Test the convergence of

7. (a) Sum the series

(b) Use De Moivre's theorm to solve :

x4 - x3 + x2 - x + 1 = 0.

8. (a) A plane passes through a fixed point (a, b, c), show that the locus of the foot of the perpendicular from the origin on the plane is a sphere.

(b) The radius of a normal section of a right circular cylinder is 2 unit, the axis lies along the straight line:

9. (a) Using Regula-Falsi method, compute a root of xex = sin x. Correct to three decimal places. (b) Solve by Guass elimination method:

2x + 2y + z = 7

x - 2y - u = 2

3x - y - 2z - u = 3.

x - 2u = 0.