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    WWW - Manaresults.co - In: Engineering Mathematics - I

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    This document is an exam for Engineering Mathematics - I consisting of 3 parts: Part A contains 10 multiple choice questions worth 3 marks each. Part B contains 5 multi-part problems worth 8 marks each. Part C contains 1 longer form problem worth 10 marks involving finding lengths related to a curve at a given point. The exam is out of a total of 80 marks and students are instructed to show working for full marks.

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    WWW - Manaresults.co - In: Engineering Mathematics - I

    Uploaded by

    vk.pendyala06
    13 views3 pages
    This document is an exam for Engineering Mathematics - I consisting of 3 parts: Part A contains 10 multiple choice questions worth 3 marks each. Part B contains 5 multi-part problems worth 8 marks each. Part C contains 1 longer form problem worth 10 marks involving finding lengths related to a curve at a given point. The exam is out of a total of 80 marks and students are instructed to show working for full marks.

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    C20-EC-102102021

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    This document is an exam for Engineering Mathematics - I consisting of 3 parts: Part A contains 10 multiple choice questions worth 3 marks each. Part B contains 5 multi-part problems worth 8 marks each. Part C contains 1 longer form problem worth 10 marks involving finding lengths related to a curve at a given point. The exam is out of a total of 80 marks and students are instructed to show working for full marks.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    13 views3 pages

    WWW - Manaresults.co - In: Engineering Mathematics - I

    Uploaded by

    vk.pendyala06
    This document is an exam for Engineering Mathematics - I consisting of 3 parts: Part A contains 10 multiple choice questions worth 3 marks each. Part B contains 5 multi-part problems worth 8 marks each. Part C contains 1 longer form problem worth 10 marks involving finding lengths related to a curve at a given point. The exam is out of a total of 80 marks and students are instructed to show working for full marks.

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    7 0 2 8 * C20-EC-CHPC-PET–102

    7028
    BOARD DIPLOMA EXAMINATION, (C-20)
    SEPTEMBER/OCTOBER—2021
    DECE - FIRST YEAR EXAMINATION
    ENGINEERING MATHEMATICS – I
    Time : 3 hours ] [ Total Marks : 80

    PART—A 3×10=30

    Instructions : (1) Answer all questions.


    (2) Each question carries three marks.

    1. If the function f is defined by f (x )  2x 3 , then find the values of


    5
    (i) f (–2), (ii) f (0) and (iii) f (3).

    1
    2. Resolve into partial fractions
    (x  1)(x  3)

    2 3 1   1 2 6
    * 3. If A    and B  0 1 3  , then find 2A – 3B.
     0 1 5   

    4. Prove that tan  45  A  . tan  45  A   1

    3
    5. Prove that cos10º cos 50º cos 70º 
    8

    /7028 1 [ Contd...

    www.manaresults.co.in
    6.
    *
    Find the modulus of the complex number  
    .
    3 4i 
     5  7i 

    7. Find the distance between the two parallel lines 3x – 4y + 7 = 0 and


    3x – 4y + 5 = 0.

    x 4  16
    8. Find lim .
    x 2 x  2

    9. Differentiate x.secx with respect to x.

    10. Differentiate log(1 + tan–1x).

    PART—B 8×5=40

    Instructions : (1) Answer all questions.


    (2) Each question carries eight marks.

    2 7 13
    11. (a) If A  3 9 4 , find the adjoint and inverse of the matrix.
    1 5 3 
    OR

    (b) Solve the following system of equations using Cramer’s Rule :


    x + 2y – z = – 3, 3x + y + z = 4 and x – y + 2z = 6

    * 3 2
    12. (a) If sin x  sin y  and sin x  sin y  , then prove that
    4 5

    x y 15 cot x y


    8 cot 
    2 2
    OR

    (b) Show that sin1 3  sin1 8  cos 1 36


    5 17 85

    /7028 2 [ Contd...

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    13. (a) Solve sin*6 cos 2  sin 5 cos 

    OR
    c b
    (b) In a  ABC, if A = 60º, then prove that   1.
    a b c a

    14. (a) Find the centre and radius of the circle

    3x 2 + 3y 2 – 12x + 6y + 11 = 0

    OR

    (b) Find the equation of the rectangular hyperbola whose focus is


    the point (1, 2) and directrix is the line 3x + 4y – 5 = 0.

     2x   2x 
    15. (a) Find the derivative of tan1  with respect to sin1  .


    1  x 
    2 1  x 2 

    OR

    (b) If y = sin(log x), then show that x 2y 2 + xy1 + y = 0.

    PART—C 10×1=10

    Instructions : (1) Answer the following question.


    (2) It carries ten marks.

    * 16. Find the lengths of tangent, normal, sub tangent and subnormal to
    the curve y = x 3 – 2x 2 + 4 at the point (2, 4).

    ★★★

    /7028 3 AA21-PDF

    www.manaresults.co.in

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