Engineering-Mathematics-II-Question-Paper-2077-CTEVT-Diploma-1st-Year-2nd-Part
Council for Technical Education and Vocational Training
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.

Also Check:

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Download PDF of Safety Rules and Regulation | Question Paper 2077 | CTEVT Diploma | 1st Year/2nd Part.

Download PDF of Principle of Electrical Engineering | Question Paper 2077 | CTEVT Diploma | 1st Year/2nd Part.

Group 'A'

Attempt All questions.

1.

a) If a and b are unit vectors and πœƒ be an angle between them, prove that 1/2(a-b)=sinπœƒ/2. [5]

b) State De-Moivere's theorem. Use it to find the cube roots of unity. [5]

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. [5]

3.

a) Solve by Cramer's rule or inverse matrix method of the equation π‘₯ + 𝑦 - z = 3, 2𝑦 + z =10 and 5π‘₯ - 𝑦 -2z = -3. [5]

b) Find the local Maxing and local Minima of the function f(x) = 2π‘₯³ - 3π‘₯² - 36π‘₯. Also, find the point of inflection. [5]

4.

a) Find the area of the circle π‘₯² + 𝑦² = 36 using method of integration. [5]

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

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

6. Prove that: [5]

7. Show that by using vector method the angle between two diagonals of a cube is 𝛳 = cos⁻¹ (1/3) [5]

8. If w be the cube root of unity prove that: [5]

(1-πœ”)(1-πœ”²)(1-πœ”⁴)(1-πœ”⁸) = 9.

9. Maximize and minimize F = 34π‘₯ + 6𝑦 subject to π‘₯ + 𝑦 ≤ 6, π‘₯ + 𝑦 ≥ 1, 1 ≤ π‘₯ ≤ 3. [5]

10. Find the equation of the plane through the points (1, 2, 1), (2, 2, 2) and (0, 1, 0). [5]

11. Find standard deviation and coefficient of variation (CV) of the data given below. [5]

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

12. Find the regression equation of y on x from the following data: [5]

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

Also estimate the value of Y when X = 5.

13. Find the correlation coefficients between π‘₯ and 𝑦 of the following data: [5]

X 2 3 6 5 10 15 12 20 11
Y 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.

Engineering-Mathematics-II-Question-Paper-2077-CTEVT-Diploma-1st-Year-2nd-Part

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