Maharashtra State Board of Technical Education 2012-1st Sem Diploma Computer Engineering of Summer for in Computer Science and Engineering Subject :- -Basic Mathematics(12003) - Question
MSBTE ques. paper for Diploma in Computer Science and Engineering
First Semester
Subject :- -Basic Mathematics(12003)
Seat No.
Instructions: (1) All Questions are compulsory.
(2) Figures to the right indicate full marks.
(3) Use of Non-Programmable Electronic Pocket Calculator is permissible.
(4) Mobile Phone, Pager and any other Electronic Communication devices are not permissible in Examination Hall.
Marks
20
Attempt any TEN :
(a) Given that log102 = 0.3010 find log108.
(b) Resolve into partial fractions .
x -x
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find 2A-3B. | ||||||||||||
|
= 0 | |||||||||||||
x 8 2 x
(d) Find x if
, . , cosec A cosec A ,
(e) Prove that-rr +-TTT = 2 sec A
v 7 cosec A - 1 cosec A + 1
( iY
(f) Expand \x + ~ using Binomial theorem.
\ xj
(g) If 0 = 30, find sin 15
|
71 -l |
fiYI |
|
2 - cos |
Nl i |
(h) Find the value of sin
(i) Find centroid of the triangle whose vertices are (2, -2), (5, 7) and (-
1,1).
P.T.O.
12003 [2]
(j) Find the slope & y-intercept of the line 3x - 4y + 5 = 0.
(k) Prove that the lines 3x - 2y + 6 = 0 & 2x + 3y - 1 = 0 are perpendicular to each other.
(1) Find centre and radius of the circle x2 + y1 + 8x+10y-7 = 0.
2. Attempt any FOUR :
16
, X C- J f lpg* log 64
(a) Find jc if log4=|ogl6
3x - 1
(b) Resolve into partial fractions (2x + 1) (x- 1)
, x 2
(c) Resolve into partial fractions + j
(d) Solve the equations by Cramers Rule
x + y + z = 3;x-y + z=l;A: + y-2z = 0
(e) Using Binomial theorem, prove that
(3 + l)5-(V3-l)5 = 152
10
(f) Find the sixth term of Lx3
(a) If A =
(b) If A =
verify that (AB) = B A
B =
4-3 4
L 3 -3 4 J
1 2 -1
3 0 2
L 4 5 0 J
1 0 0
2 1 0
L 0 1 3 J
prove that A2 = I.
(c) Find adjoint of matrix A, if A = 3 4 5
_ 0 -6 -7 J
(d) Solve the simultaneous equations by matrix method :
;c + y + z = 3;;t + 2y + 3z = 4;* + 4y + 9z = 6
cos 2A + 2 cos 4A + cos 6A ...
(e) Prove that cos A + 2 cos 3A + cos 5A = s A - sin A tan 3A
3
(f) Prove that sin 20 sin 40 sin 60 sin 80 = yg .
4. Attempt any FOUR : 16
tan A + sec A - 1 1 + sin A
(a) Prove that tan A _ sec A + j = "T
(b) Prove that tan 70 - tan 50 - tan 20 = tan 70 tan 50 tan 20
, . . sin 40 + sin 20
(c) Prove that 77 7: = tan 20 v 1 + cos 20 + cos 40
.. cos2( 180 - 0) cos2 (270+ 0)
(d) Simplify -. . m + .A or.c m
v 7 v 3 sin (-0) sin (180+ 0)
(e) Prove that cos 2A = 2 cos2A - 1
>\
+ cos-'l jf) = cos-'(H
-ilf
(f) Prove that cos
5. Attempt any FOUR : 16
(a) Show that the points (2, -2), (8, 4), (5, 7) form the right angled triangle.
(b) In what ratio does C(3, 11) divide the line joining A(l, 3), B(2, 7).
(c) Find the equation of perpendicular bisector of the join of A(-2, 3), B(8, -1)
(d) Find the equation of straight line passing through the point of intersection of the lines Ax + 3y = 8; x + y = 1 and parallel to the line 5x-7y = 3.
P.T.O.
12003 [4]
(e) Find the equation of the line whose intercepts are equal and positive and passes through the point (3, 5).
(f) Find the equation of straight line passing through the points (-4, 6) & (8, -3).
6. Attempt any FOUR : 16
(a) Prove that the area of triangle whose vertices are A (-1, 5), B (3, 1) & C(5, 7) is four times the area of triangle formed by the lines joining the mid points of the sides of AABC.
(b) Find the equation of circle passing through origin and the points (2, 0) &
(0, 4).
(c) Find the equation of a circle whose diameters are 2x - 3y = 12 & x + 4y -5 = 0 and the area of circle is 154.
(d) If a = 2i - j + k, b = i + 2j - 3k, c = 5i - 4k find a x (b x c).
(e) Find the work done by a force F = 3i - 2j + 4k when point of application moves from A(3, 2,-1) to B(2, 5, 4).
(f) Find the moment of the force 3i + 4j - 5k about the point (1, 2, 3) if the force acts at the point (2, -1, 4).
12003 [4]
(e) Find the equation of the line whose intercepts are equal and positive and passes through the point (3, 5).
(f) Find the equation of straight line passing through the points (-4, 6) & (8, -3).
6. Attempt any FOUR : 16
(a) Prove that the area of triangle whose vertices are A (-1, 5), B (3, 1) & C(5, 7) is four times the area of triangle formed by the lines joining the mid points of the sides of AABC.
(b) Find the equation of circle passing through origin and the points (2, 0) &
(0, 4).
(c) Find the equation of a circle whose diameters are 2x - 3y = 12 & x + 4y -5 = 0 and the area of circle is 154.
(d) If a = 2i - j + k, b = i + 2j - 3k, c = 5i - 4k find a x (b x c).
(e) Find the work done by a force F = 3i - 2j + 4k when point of application moves from A(3, 2,-1) to B(2, 5, 4).
(f) Find the moment of the force 3i + 4j - 5k about the point (1, 2, 3) if the force acts at the point (2, -1, 4).
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Attachment: |
| Earning: Approval pending. |
