FE Engineering Mathematics-II Past Paper PDF May/June 2023

Total No. of Questions : 9] SEAT No. : 8 23 P3924 [Total No. of Pages : 4...

Total No. of Questions : 9] SEAT No. : 8 23 P3924 [Total No. of Pages : 4 ic- -4009 tat F.E. 7s ENGINEERING MATHEMATICS-II 3:3 (2019 Pattern) (Semester - I/II) (107008) 02 91 0:3 0 Time : 2½ Hours] [Max. Marks : 70 31 3/0 13 Instructions to the candidates: 1) Q. No.1 is compulsory. 0 8/2 2) Solve Q.2 or Q.3, Q.4 or Q.5, Q.6 or Q.7, Q.8 or Q.9..23 GP 3) Neat diagrams must be drawn wherver necessary. 4) Figures to the right indicate full marks. E 80 5) Use of electronic pocket calculator is allowed. 8 C 23 6) Assume suitable data, if necessary. ic- 16 Q1) Write the correct option for the following multiple choice questions tat 8.2 7s  2  sin  dt  4.24 3:3 a) 91 0 49 0:3 30 3 3 31 i) ii) 16 8 01 02 8/2 GP 3 3 iii) iv) 3/0 16 8 CE 80 8 23.23 b) The equation of the tangent to the curve y (1  x 2 )  x at origin, if exist is ic- 16 tat 8.2 7s i) X=0 ii) Y=0.24 3:3 91 49 x  1, x  1 yx 0:3 iii) iv) 30 31 01 02 1 1 1 1   2 1  y 2 dxdy  8/2  GP c) The value of double integration 0 0 1 x 3/0 CE 80  2 i) ii).23 2 2 16  2 8.2 iii) iv) 4 8.24 49 P.T.O. Other PYQs => www.studymedia.in/fe/pyqs  d) Centre (C) of sphere x 2  y 2  z 2  2 z  4 is 8 23 i) C  (0,0,0) ii) C  (0,0,1) ic- tat iii) C  (0,1,0) iv) C  (1,0,0) 7s 3:3 02 91 e) The curve r  2a sin  is symmetrical about 0:3 0 31 i) Pole 3/0 13 ii)  0   0 8/2 iii)  iv) .23 GP 2 4 E 80 8 C 23  ic- f) dxdydz represents 16 tat V 8.2 7s i) Area ii) Mass.24 3:3 91 iii) Mean Value iv) Volume 49 0:3 30 31 01  2 02  n 2 4 n2 8/2 Q2) a) If In =  sec  d , then prove that In =  In-2 n GP n 1 n 1 3/0 0 CE 80 5 8   x  2   5  x  dx 3 2 23 b) Evaluate.23 ic- 2 16 tat  e  x  e ax 1  a2  1  Using DUIS, prove that  dx  log  ,a  0 8.2 7s c) x sec x 2  2 .24 0 3:3 91 49 0:3 OR 30 31 Q3) a) Evaluate 01 02 8/2 2   GP  sin d 2 i) cos10 3/0 0 2 2 CE 80  2  cos t.23 4 ii) dt 16  2 8.2.24 49 -4009 2 Other PYQs => www.studymedia.in/fe/pyqs  8 1 23   x log x  4 b) Evaluate : dx ic- 0 tat 1 d 1 d erfc (ax)   7s c) Prove that: erf (ax) x da a dx 3:3 02 91 0:3 Q4) a) Trace the curve x 2 y 2  a 2 ( y 2  x 2 ). 0 31 b) 3/0 13 Trace the curve r  a (1  cos ). 0 c) Find the are length of Astroid x 2 3  y 2 3  a 2 3 8/2.23 GP OR E 80 8 C 23 Q5) a) Trace the curve x 3  y 3  3axy. ic- b) Trace the curve r  a cos 2 16 tat Trace the curve x  a (t  sin t ), y  a (1  cos t ). 8.2 c) 7s.24 3:3 91 Show that the plane x  2 y  2 z  7 touches the sphere x 2  y 2  z 2  49 Q6) a) 0:3 30 10 y  10 z  31  0. Also find the point of contact. 31 b) Find the equation of right circular cone whose vertex is at origin, whose 01 02 x y 8 8/2 GP axis is the line   and which has a semi-vertical angle of 60°. 1 2 3 3/0 CE 80 8 c) Find the equation of right circular cylinder of radius 3 and axis is the line 23.23 x 1 y  2 z  3  . ic- 16 tat 2 1 2 8.2 7s OR.24 3:3 Q7) a) Show that the two spheres: x 2  y 2  z 2  25 and x 2  y 2  z 2 91 49 0:3 18 x  24 y 40 z  225  0 touches externally. Also find the point of 30 31 contact. 01 b) Find the equation of right circular cone whose vertex is at (0,0,10), axis 02 8/2  2  GP is the Z-axis and the semi-vertical angle is cos 1   3/0  5 CE 80 c) Find the equation of right circular cylinder of radius 6, whose axis.23 1 1 1 , ,. 16 passes through the origin and has direction cosines 3 3 3 8.2.24 49 -4009 3 Other PYQs => www.studymedia.in/fe/pyqs  8 23 Q8) a) Evaluate  xy dx dy, where R is x 2  y, y 2   x. ic- R tat b) Find area of cardioide r  a (1  cos ) using double integration. 7s c) Find the moment of inertia of one loop of the lemniscate 3:3 r 2  a 2 cos 2 about initial line. Givenl that density   2m 02 91 , m is a mass 0:3 a2 0 31 of the area. 3/0 13 0 OR 8/2.23 GP 5 2 x Q9) a) Change order of integration   f ( x, y ) dxdy. E 80 8 0 2 x C 23 b) Find the volume bounded by the cone x 2  y 2  z 2 and paraboloid ic- 16 tat x2  y 2  z. 8.2 7s c) Find the x - co-ordinate of centre of gravity of one loop of r  a cos 2 ,.24 3:3  a2 91 which is in the first quadrant, given that area of loop is A . 49 0:3 8 30 31 01 02 8/2 GP  3/0 CE 80 8 23.23 ic- 16 tat 8.2 7s.24 3:3 91 49 0:3 30 31 01 02 8/2 GP 3/0 CE 80.23 16 8.2.24 49 -4009 4 Other PYQs => www.studymedia.in/fe/pyqs