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C 14-met-mng-aei-102-engg maths-1

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Srinivasa Rao
Srinivasa Rao

This document appears to be an exam for a first year engineering mathematics course. It contains 18 questions across two sections - Part A contains 10 multiple choice questions worth 4 marks each, and Part B contains 4 extended response questions worth 10 marks each. The exam covers topics in algebra, trigonometry, matrices, coordinate geometry, calculus, and other areas of mathematics. Students are instructed to show their work and provide comprehensive answers for the extended response questions.

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046 046 046 046 * * * A/AA/CH/CHST/AEI/FW/MNG/ MET/IT/TT/PKG–102 4002 BOARD DIPLOMA EXAMINATION, (C–14) OCT/NOV—2016 FIRST YEAR ( COMMON) 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. (3) Answers should be brief and straight to the point. 1. (a) Define proper fraction and give an example. (b) Resolve x x( )+12 into partial fraction. 2. (a) Find sin 75°. (b) If tan A = 1 2 and tan B = 1 3 , find tan( )A B+ . 3. (a) Find tan 22 1 2 °. (b) Find 8 20 6 203 cos cos° ° - . /4002 1 [ Contd... * 4 0 0 2 *
046 046 046 046 * * * 4. (a) Define symmetric and skew-symmetric matrices. (b) If A = é ë ê ù û ú 1 2 3 4 , find A2 . 5. (a) Write the formula to find A-1 . (b) Define singular and non-singular matrices. 6. (a) Find the intercepts made by the straight line 2 3 5 0x y+ - = on the coordinate axes. (b) Write the formula to find the distance between parallel lines. 7. (a) Find the radius of the circle x y x y2 2 6 4 12 0+ - + - = (b) Write the equation of tangent to the circle x y r2 2 2 + = at ( , )x y1 1 . 8. (a) Find the amplitude of 1 3+ i . (b) State de Moivre’s theorem. 9. (a) Evaluate : lt x xx ®¥ + + 1 2 (b) Evaluate : lt x xx ®0 7sin 10. (a) Differentiate : x xx3 3 3+ + (b) Differentiate : x x + + 1 3 /4002 2 [ Contd...
046 046 046 046 * * * PART—B 10×4=40 Instructions : (1) Answer any four questions. (2) Each question carries ten marks. (3) Answers should be comprehensive and the criterion for the valuation is the content but not the length of the answer. 11. (a) Prove that 1 1 1 2 2 2 a a b b c c a b b c c a= - - -( )( )( ) (b) Solve x y z+ + = 6, x y z- + = 2, 2 1x y z+ - = using matrix-inversion method. 12. (a) In any triangle ABC, prove that cos cos cos cos cos cos2 2 2 1 4A B C A B C+ + = - - (b) Prove that tan tan- -æ è ç ö ø ÷ + æ è ç ö ø ÷ =1 11 4 3 5 4 p 13. (a) Solve cos sinq q+ =3 1. (b) In a triangle ABC, prove that ( )cosa b C a b c+ = + +å . 14. (a) Find the equation of the parabola whose focus is (3, 4) and directrix is 2 3 4 0x y- + = . (b) Find the eccentricity, centre, vertices, foci, length of latus rectum and equation of directrices of the ellipse 3 4 12 8 4 02 2 x y x y+ - + + = /4002 3 [ Contd...
046 046 046 046 * * * 15. (a) Find the derivative of tan x using first principle. (b) Find the derivative of e x4 2 w.r.t. 1 4 2 + x . 16. (a) Find dy dx , if y x x x= + + + ¥3 3 3 L . (b) If y x= sin(log ), prove that x y xy y2 2 1 0+ + = 17. (a) Find the lengths of the tangent, normal, sub-tangent and sub-normal to the curve y x x= - +3 2 5 at (1, 4). (b) The side of an equilateral triangle is increasing at the rate of 2 cm/sec. Find the rate of increase of its area and perimeter given, its side is 25 cm. 18. (a) Prove that the maximum rectangle that can be inscribed in a circle is a square. (b) Find approximately the value of 1233 . H H H /4002 4 AA6(T)—PDF

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C 14-met-mng-aei-102-engg maths-1

  • 1. 046 046 046 046 * * * A/AA/CH/CHST/AEI/FW/MNG/ MET/IT/TT/PKG–102 4002 BOARD DIPLOMA EXAMINATION, (C–14) OCT/NOV—2016 FIRST YEAR ( COMMON) 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. (3) Answers should be brief and straight to the point. 1. (a) Define proper fraction and give an example. (b) Resolve x x( )+12 into partial fraction. 2. (a) Find sin 75°. (b) If tan A = 1 2 and tan B = 1 3 , find tan( )A B+ . 3. (a) Find tan 22 1 2 °. (b) Find 8 20 6 203 cos cos° ° - . /4002 1 [ Contd... * 4 0 0 2 *
  • 2. 046 046 046 046 * * * 4. (a) Define symmetric and skew-symmetric matrices. (b) If A = é ë ê ù û ú 1 2 3 4 , find A2 . 5. (a) Write the formula to find A-1 . (b) Define singular and non-singular matrices. 6. (a) Find the intercepts made by the straight line 2 3 5 0x y+ - = on the coordinate axes. (b) Write the formula to find the distance between parallel lines. 7. (a) Find the radius of the circle x y x y2 2 6 4 12 0+ - + - = (b) Write the equation of tangent to the circle x y r2 2 2 + = at ( , )x y1 1 . 8. (a) Find the amplitude of 1 3+ i . (b) State de Moivre’s theorem. 9. (a) Evaluate : lt x xx ®¥ + + 1 2 (b) Evaluate : lt x xx ®0 7sin 10. (a) Differentiate : x xx3 3 3+ + (b) Differentiate : x x + + 1 3 /4002 2 [ Contd...
  • 3. 046 046 046 046 * * * PART—B 10×4=40 Instructions : (1) Answer any four questions. (2) Each question carries ten marks. (3) Answers should be comprehensive and the criterion for the valuation is the content but not the length of the answer. 11. (a) Prove that 1 1 1 2 2 2 a a b b c c a b b c c a= - - -( )( )( ) (b) Solve x y z+ + = 6, x y z- + = 2, 2 1x y z+ - = using matrix-inversion method. 12. (a) In any triangle ABC, prove that cos cos cos cos cos cos2 2 2 1 4A B C A B C+ + = - - (b) Prove that tan tan- -æ è ç ö ø ÷ + æ è ç ö ø ÷ =1 11 4 3 5 4 p 13. (a) Solve cos sinq q+ =3 1. (b) In a triangle ABC, prove that ( )cosa b C a b c+ = + +å . 14. (a) Find the equation of the parabola whose focus is (3, 4) and directrix is 2 3 4 0x y- + = . (b) Find the eccentricity, centre, vertices, foci, length of latus rectum and equation of directrices of the ellipse 3 4 12 8 4 02 2 x y x y+ - + + = /4002 3 [ Contd...
  • 4. 046 046 046 046 * * * 15. (a) Find the derivative of tan x using first principle. (b) Find the derivative of e x4 2 w.r.t. 1 4 2 + x . 16. (a) Find dy dx , if y x x x= + + + ¥3 3 3 L . (b) If y x= sin(log ), prove that x y xy y2 2 1 0+ + = 17. (a) Find the lengths of the tangent, normal, sub-tangent and sub-normal to the curve y x x= - +3 2 5 at (1, 4). (b) The side of an equilateral triangle is increasing at the rate of 2 cm/sec. Find the rate of increase of its area and perimeter given, its side is 25 cm. 18. (a) Prove that the maximum rectangle that can be inscribed in a circle is a square. (b) Find approximately the value of 1233 . H H H /4002 4 AA6(T)—PDF