**Office Of The Controller Of Examinations**

**Regular/Back Exam - 2077, Chaitra**

**Year/Part: First Year/Second Part (New+Old Course)**

### 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 Engineering Physics-II | Question Paper 2077 | CTEVT Diploma | 1st Year/2nd Part.

Download PDF of Engineering Chemistry-II | Question Paper 2077 | CTEVT Diploma | 1st Year/2nd Part.

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

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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. [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 𝑥 + 𝑦 - z = 3, 2𝑦 + z =10 and 5𝑥 - 𝑦 -2z = -3. [5]

b) Find the local Maxing and local Minima of the function f(x) = 2𝑥³ - 3𝑥² - 36𝑥. Also, find the point of inflection. [5]

4.

a) Find the area of the circle 𝑥² + 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-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. [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 𝑥 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.

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