Office Of The Controller Of Examinations
Sanothimi, Bhaktapur
Regular/Back Exam - 2077, Chaitra
Program : Diploma In Engineering All
Level: DIPLOMA
Year/Part: First Year/Second Part (New+Old Course)
Subject: Engineering Mathematics-II
Full Marks - 80
Pass Marks - 32
Time - 3 hrs.

### DOWNLOAD PDF | of Question Paper | Engineering Mathematics-II | CTEVT | 1st Year/2nd Part | 2077.

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

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### Group 'A'

Attempt All questions.

1.

a) If a and b are unit vectors and 𝜃 be an angle between them, prove that 1/2(a-b)=sin𝜃/2. 

b) State De-Moivere's theorem. Use it to find the cube roots of unity. 

2.

a) Define direction cosine. Find the angle between the lines whose direction cosines are given by l,m,n and l,m,n. [1+4=5]

b) Find the projection of the line AB on CD if the co-ordinates of the points A, B, C, and D are (0, 5, 0) (1, 2, 4) (-1, 3, 0) and (3, 5, 6) respectively. 

3.

a) Solve by Cramer's rule or inverse matrix method of the equation 𝑥 + 𝑦 - z = 3, 2𝑦 + z =10 and 5𝑥 - 𝑦 -2z = -3. 

b) Find the local Maxing and local Minima of the function f(x) = 2𝑥³ - 3𝑥² - 36𝑥. Also, find the point of inflection. 

4.

a) Find the area of the circle 𝑥² + 𝑦² = 36 using method of integration. 

5. A class consists of 60 boys and 40 girls. If two students are choosen at random what is the probability that:  

i) both are boys.
ii) one boy and one girl.

6. Prove that: 

7. Show that by using vector method the angle between two diagonals of a cube is 𝛳 = cos⁻¹ (1/3) 

8. If w be the cube root of unity prove that: 

(1-𝜔)(1-𝜔²)(1-𝜔⁴)(1-𝜔⁸) = 9.

9. Maximize and minimize F = 34𝑥 + 6𝑦 subject to 𝑥 + 𝑦 ≤ 6, 𝑥 + 𝑦 ≥ 1, 1 ≤ 𝑥 ≤ 3. 

10. Find the equation of the plane through the points (1, 2, 1), (2, 2, 2) and (0, 1, 0). 

11. Find standard deviation and coefficient of variation (CV) of the data given below. 

 Class Frequency 0-10 10-20 20-30 30-40 40-50 50-60 4 6 8 10 4 3

12. Find the regression equation of y on x from the following data: 

 X Y 2 4 6 8 10 12 5 6 13 16 13 24

Also estimate the value of Y when X = 5.

13. Find the correlation coefficients between 𝑥 and 𝑦 of the following data: 

 X Y 2 3 6 5 10 15 12 20 11 19 17 17 10 17 15 13 14 12

Good Luck!

Check and Download Engineering Mathematics-II Question Paper 2077-2021 | CTEVT | Diploma in Engineering All | 1st Year/2nd Part.

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