Download AKTU B-Tech 2nd Sem 2015-16 EBT 201 Elementary Mathematics Ii Question Paper

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EBT-201

Paper ID: 154204

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B.TECH.

Theory Examination (Semester-II) 2015-16

ELEMENTARY MATHEMATICS-II

Time: 3 Hours

Max. Marks: 100

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Section-A

Q1. Attempt all section. All section carries equal marks. Write answer of each questions in short. (2×10=20)

1. Express the following complex number in the form of a + ib, (5i)(-3).
2. Solve the linear inequality 4x + 3 < 5x + 7 .
3. Find the value of n for ⁿC₁ = ⁿC₅ .

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4. Find the nth term of an A.P. 5, 8, 11, ...
5. Find the slope of line passing through the points (3,-2) and (-1, 4).
6. If a line makes angles 90°, 135°, 45° with the x, y and z-axis respectively. Find its direction cosine.
7. Find the equation of plane with intercepts 2, 3 and 4 on the x, y and z axis respectively.

Section-B

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Q2. Attempt any five questions from this section. (5×10=50)

1. Solve the following system of inequalities by graphical method. 2x+y = 6, 3x+4y=12.
2. Find the number of arrangements of the letters of the word "INDEPENDENCE". In how many these arrangement
   1. do the words start with P.
   2. do the all vowel always occur together.
   3. do the words begin with 'I' and end in 'E'.

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3. Find the length of latus rectum for the ellipse x²/36 + y²/16 = 1
4. Find the area of parallelogram whose adjacent sides are given by vectors a=3i+j+4k and b=i-2j+k.

Section-C

Attempt any two question. (15×2=30)

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Q3. If p and p' be the perpendiculars from origin upon the straight lines xsec? + ycosec? = a and xcos? - ysin? = acos2? respectively. Prove that 4p² + p'² = a²

Q4. Find angle between the line vectors a₁ =3i-2j+k and a₂ = 4i+5j+7k

Q5. Find shortest distance between two lines whose vector equations are r₁ = (i+2j+k)+?(i-3j+2k) and r₂ = (2i-j-k)+µ(2i+j+2k)

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