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

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU)) B-Tech 2nd Semester (Second Semester) 2015-16 EBT 201 Elementary Mathematics Ii Question Paper

Printed Pages: 4 ? EBT-201
(Following PaperID and Roll No. to be ?lled in your
Answer Books)
RonNolelllllll
B.TECH.
Theory Examination (Semester-ll) 2015-16
ELEMENTARY MATHEMATICS-II
T ime : 3 Hours Max. Marks : 100
Section-A
Q1. Attempt all section. All section carries equal marks.
Write answer of each questions in short. (2X10=20)
(a) Express the following complex number in the form of a
+ ib, (5i)[-%t].
(b) Solve-the linear inequality 4x + 3 < 5x + 7 .
(c) Find the value of n for "C7 = "C5 .
(d) Find the nth term of an AP. 5, 8, 11, ......
(e) Find the slope of line passing through the points
(3,-2) and (-1, 4).
- 1 (1) P.T.O.
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(f)
(b)
(i)
(1')
Find the equation of circle whose centre is (3, 2) and
radius is 5.
Ifa=2E?3j'andi; =3f+2}'. Show that |E|=|5|.
Find the dot product of two vectors
a=2f+2j+12 and E=3?+4j+12?.
If a line makes on angle 90?, 60? and 30? with posi-
tive direction of x axis, y axis and z axis respec-
tively. Find its direction cosine.
Find theequation of plane with intercepts 2, 3 and
4 on the x, y and z axis respectively.
Section-B
QZ. Attempt any ?ve questions from this section. (5X10=50)
(a)
(b)
Solve the following system of inequalities by graphical
method
2x+y26, 3x+4ySlZ,
Find the number of arrangements of the letters of the
word "INDEPENDENCE". In how many these ar-
rangement-
(i) do the words start with P.
(ii) do the all vowel always occur together.
(iii) do the words begin with 'I' and end in 'P'.
(2)
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(C)
(d)
(e)
The ?rst terms of AP. is 2 and last term is 59. Find
common difference if sum of all its terms is 610.
Find the equation of line passing through the point (2, 2)
and cutting o?? intercepts on the axis whose sum is 9.
Find the equation of circle which passing through the
points (1, 0), (0, -6) and (3, 4).
(t) Find eccentricity, co-ordinate of foci, and length of latus
rectum for the ellipse ?+?=l
(g) Find the area of parallelogram whose adjacent sides ape
given by vectors E=3i+j+4i and Eaf-zhk'.
Section-C
(15X2=30))
Attempt any two question.
Q3. pr andp bethe perpendiculaxs from on'gin upon the straight
lines xsec0 + ycosec0 = a and xcos0 ? ysinO = acos20
respectiver Prove that 4p2 + p2 = (12
Q4. Find angle between the line vectors
7. =3i-2]+i and r, =4f+sj+712
(3) P.T.O.
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Q5.
Find shortest distance between two lines whose vector equa-
tions are
E+2i+i)+l(f?j?+l?)
21?~ '-l$)+p(21?+]?+2]3)
?u ?13
II
_ (4)
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