C 14-dce-102-engg maths-1
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The document is a past exam paper for engineering mathematics from October/November 2016. It contains 18 questions testing various calculus and algebra concepts. The questions cover topics like partial fractions, matrices, trigonometric identities, limits, differentiation, maxima and minima problems, and rates of change. The exam has two parts, with part A containing 10 multiple choice questions worth 4 marks each and part B containing 4 answer questions worth 10 marks each.
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C14–CE–102/C14–CM–102
4015
BOARD DIPLOMA EXAMINATION, (C–14)
OCT/NOV—2016
DCE—FIRST YEAR EXAMINATION
ENGINEERING MATHEMATICS—I
Time : 3 hours ] [ Total Marks : 80
PART—A 4×10=40
Instructions : (1) Answer all questions.
(2) Each question carries four marks.
1. (a) Define improper fraction and give an example.
(b) Resolve
1
2 3( )( )x x+ +
into partial fractions.
2. (a) If
A =
-
é
ë
ê
ù
û
ú
2 3 1
0 1 5
, B =
-
-
é
ë
ê
ù
û
ú
1 2 6
0 1 3
find A B+ .
(b) Define non-singular matrix.
/4015 1 [ Contd...
* 4 0 1 5 *](https://image.slidesharecdn.com/c-14-dce-102-enggmaths-1-170112034652/85/C-14-dce-102-engg-maths-1-1-320.jpg)
C 14-dce-102-engg maths-1
- 1. 046 046 046 046 * * * C14–CE–102/C14–CM–102 4015 BOARD DIPLOMA EXAMINATION, (C–14) OCT/NOV—2016 DCE—FIRST YEAR EXAMINATION ENGINEERING MATHEMATICS—I Time : 3 hours ] [ Total Marks : 80 PART—A 4×10=40 Instructions : (1) Answer all questions. (2) Each question carries four marks. 1. (a) Define improper fraction and give an example. (b) Resolve 1 2 3( )( )x x+ + into partial fractions. 2. (a) If A = - é ë ê ù û ú 2 3 1 0 1 5 , B = - - é ë ê ù û ú 1 2 6 0 1 3 find A B+ . (b) Define non-singular matrix. /4015 1 [ Contd... * 4 0 1 5 *
- 2. 046 046 046 046 * * * 3. (a) If 2 1 3 1 x = , then find x. (b) Find the value of cosec cosec q q q q cot cot 4. (a) Write the formula for tan ( )A B+ . (b) If sin A = 4 5 , then find cos tanA A+ . 5. (a) Simplify cos sin cos 4 4 2 A A A - (b) If Ð = °A 15 then find sin cos3 3A A+ . 6. (a) If z i= +cos sinq q, then find z3 . (b) Find the amplitude of 1 + i. 7. (a) Write the general equation of a straight line. (b) Find the distance between two parallel lines 3 4 6 0x y+ - = and 3 4 2 0x y+ + = . 8. (a) Find the radius of circle x y x y2 2 2 3 5 0+ - - + = . (b) Find the equation of circle whose centre (2, 3) and radius is 4. 9. (a) Find lim x x x® - -2 2 4 2 (b) Find lim tan x x x® 0 8 /4015 2 [ Contd...
- 3. 046 046 046 046 * * * 10. (a) Differentiate 2 3 45 3 x x x+ + w.r.t. x (b) Differentiate sin ( )2 3x + w.r.t. x. PART—B 10×4=40 Instructions : (1) Answer any four questions. (2) Each question carries ten marks. 11. (a) Find the adjoint of the matrix 1 3 3 1 4 3 1 3 4 é ë ê ê ê ù û ú ú ú (b) Prove that 1 1 1 2 2 2 a b c a b c a b b c c a= - - -( )( )( ) 12. (a) Show that cos cos sin sin cot 8 6 8 6 7 A A A A A + + = (b) Show that tan tan tan- - - + =1 1 11 3 1 5 4 7 13. (a) Solve cos sin3 2A A= . (b) Solve DABC if a =1; b = 3; c = 2. 14. (a) Find the equation of the parabola whose focus is ( , )1 1- and directrix is x y- + =2 1 0. (b) Find the equation of the ellipse which passes through the points ( , )7 2 and ( , )3 4 and whose centre is the origin, and axes are the axes of coordinates. /4015 3 [ Contd...
- 4. 046 046 046 046 * * * 15. (a) Find the dy dx if x y xy3 3 9+ = (b) If y x x x= + + + ¥tan tan tan L to , then find dy dx . 16. (a) If y x x x= - - +2 5 6 144 2 , then find ¢y , ¢¢y . (b) If u x y z= + +2 2 2 , then show that x u x y u y z u z u ¶ ¶ ¶ ¶ ¶ ¶ + + = 2 17. (a) Find the lengths of tangent, normal to the curve y x x= + -2 2 4 at ( , )1 1- (b) A ladder 5 m long rests against a vertical wall. If the foot of the ladder is pulled away at the rate of 5 cm/sec, find the rate at which the other end of the ladder is descending, when the lower end is 3 m, away from the wall. 18. (a) Find the maxima and the minima of the function x x x3 2 4 5- + . (b) The radius of the spherical balloon is increased by 4%. Find the approximate percentage increase in its surface area. H H H /4015 4 AA6(T)—PDF