Solved question paper for MATH-1 May-2018 (DIPLOMA Electrical and Electronics Engineering 1st-2nd)

Question paper 1

1. SECTION-A

   Q1. Choose the correct answer.

   (i) The modulus of 1 + Ý…√3 is a) √2 b) -1 c) 2 d) 0

   Answer:

   z = 1 +

   |z| =

   Option C

2. (ii) The value of 3π/12 radians in degree is

   a) 60° b) 45° c) 90° d) 120°

   Answer:

   π radian = 180⁰

   

   Option B

3. (iii) Characteristic of log 0.07426 is

   a) 1 b) 2 c) 0 d) 1

   Answer:

   log0.07426 = -2.6001 (Find with the help of log table)

   option B

4. (iv) If Sin (A-B) = ½ and Cos (A+B) = ½ then value of A and B will be

   a) A=15° , B=45° b) A=45°, B=15° c) A=45°, B=45° d) A=30°, B=60°

   Answer:

   We know that 

   

   

   

   Option B

6. (v) The centroid of a triangle with two vertices (3,4) (-1,-9) is (2, -4) then third vertex is a) (-4 , -7) b) (4, -7) c) (4,7) d) (-4,7)

   Answer:

   Vertices of triangle are (3,4),(-1,-9) and let third vertices is (x,y).

   Its centroid is (2,-4)

   Formula of centroid

   

   

   

    =

    

   

   

   

    

   Option B

7. Q2. State True or False.

   a. The series of the R.H.S of the expansion (1 + x)ⁿ extends to infinity

   Answer:

   False

8. b. If k, k+1, k+3 are in G.P, then k=2

   Answer:

   k, k+1,k+3, ------

       k = 2

   2,3,5,….. is not in G.P.

   False

9. c. Value of tan 120° is √3

   Answer:

   False

   

11. d. Sec(270 ÌŠ + θ) = Cosecθ

    Answer:

    True

12. e. The point (3,4); (7,7); (x,4) are collinear, if x=3

    Answer:

    (3,4),(7,7) and (x,4) are collinear if x=3

    A (3,4), B (7,7), C(3,4)

    By distance formula

    

    

    

    

    True

13. Q3. Fill in the blanks.

    i. Radius is a -------- angle.

    Answer:

    constant

14. ii. The revolving line is always ---------

    Answer:

    rotate about fixed point.

16. iii. If CosA = ½ then Cos3A =

    Answer:

    cos3A = -1

17. iv. The conic is parabola if ---------

    Answer:

    e = 1

18. v. Equation of line perpendicular to line ax+by+c=0 is -------

    Answer:

    -bx+ay+c = 0

19. SECTION-B

    Q4. Attempt any six questions.

    a. In how many ways, 3 boys and 3 girls are seated at round table, so that no two girls sit together.

    Answer:

    3 boys can be seated at a round table in  i.e.  Ways

    When 3 boys have occupied their seats in any one of these  Ways, then 3 girls can occupy any 3 out of 3 seats between boys so that no two girls are sitting together. This can be done in  ways

    Hence required number of ways 

                                                                     

                                                                    = 12 Ans

    

21. b. Find the co-ordinates of the incentre of the triangle whose vertices are (-36,7), (20,7) and (0,-8)

    Answer:

    

    Formula of the center of the triangle is

     

     , where a,b,c are the length of the sides of triangle.

    To find a,b and c by distance formula

     

    

     

      

    e

     

    

     

      

     

    

    

    

    Put all values in formula

    

    

    

    

22. c. Resolve  \((3x+7) \over (x+3)(x^2 + 1)\)  into partial fractions

    Answer:

    Resolve     into partial fractions.

     =

     

     =

     

     

    

    Comparing coefficients of x, x² and constant terms

            ----- 1

               ----- 2

              ----- 3

     

    From 2

    

    This is put in 1

        ------ 4

    Subtract 4 from 3

    

    

    

    As  

    From 3

    

    

    

     

     =  Ans

23. d. A (10, 4); B (-4, 9); C (-2,-1) are the vertices of a triangle ABC, find the equation of the median through A.

    Answer:

    

    D is mid point of BC

    To find the co-ordinate of D is

    

    

    

    We write the equation of line AB by using Two-point form,

    

    

    

    

    

24. e. Prove that Cos α + Cos(α+2π/3) + Cos(α+4π/3) = 0

    Answer:

    Prove that  

    L.H.S.

    

    

    

    

    

    

    

    

    

26. f. If   l\({log x \over y-z} = {logy \over z-x} = {log z \over x-y} \)  then show that x²y²z²  = 1

    Answer:

    If   then  Show that 

    Sol : 

    

    

    And

    

    

    Take  

    Taking log on both sides

    

    

    

    Using 1 and 2

    

    

    

    

    

    

    

    Hence it is proved that

    

27. g. Prove that  \(sinA Sin3A Sin5A Sin7A\over CosA Cos 3A Cos 5A cos 7A\) = tan4A

    Answer:

    Prove that  

    Sol. L.H.S.

    

    By using C,D formulae from trignomentary

    

    

    

    

    

28. h. Prove that \( { cot\theta + Coses\theta - 1\over cot\theta + Coses\theta + 1} = {1+Cos \theta \over sin \theta}\)

    Answer:

    Prove that

    Sol:

    L.H.S.

    

    

    

    

    

    

    

    

    

    

    

29. i. How many terms of the series 3+8+13+18+ ------ must be taken so that their sum is 1010?

    Answer:

    3+8+13+18+  ……………

    This is A.P

    

    

    Formula