Maharashtra State Board of Technical Education 2008 Diploma in Hospital Management Basic Mathematics - Question Paper

Sample Question Paper - I

9003

-    All Engineering Branches

-    First

-    Basic Mathematics

-    3 hours

Instructions :

1.    All the Questions are compulsory.

2.    Figures to the right indicate full marks.

3.    Assume suitable additional data, if necessary.

4.    Use of Non-programmable Electronic pocket calculator is permissible.

Q1. Attempt Any Eight

1

a. Resolve into partial fractions ₂

x + x

b. Evaluate

-1 2 -3 2 -3 -1 3 -1 2

2 1 11

c.    Find the 7th term in the expansion of (x )

x

d.    Show that the vectors

a =2 i + 3 j + k and b = 4i - 3 j + k are perpendicular to each other.

e.    If cos A = find the value of cos (3A)

2

r , sin 2 A

f.    Prove that-= tan A

1 + cos 2A

g.    If 2 sin 60 cos 20 =sin A+sin B, Find A and B

h. Verify tan"¹ro=sin"¹(-2 )+cos^-1(2)

a. Resolve into partial fractions 3x 1

(x 4)(2 x +1)( x 1)

b. Resolve into partial fractions

x⁴

x³ 1

c. Using Binomial theorem prove that

((V3+1)⁵ (V3 1)⁵ = 152

d. In a given electrical work the simultaneous equations for currents I1,I2 and I3 are

I1 + 2I2 - I3 = -1 3Ii + 8I₂ - 2I₃ = 28 4Ix + 9I2 + I3 = 14 Find I₁ & I₂ by using Cramers rule

Q3. Attempt Any Three

	' 1 2 '		' 2 1 "
a. If A=		B =
	1 3 2 - 1		2 3

then verify that A[ B + C ] = AB + AC

b. If A=

"5 6 -1' " 1 -1 1" 2 3 2 B = 0 1 -1 1 2 -3 1 -1 0

Verify that (AB) '=B' A'

c. Prove that

1 cos A

d. Prove that

Tan(3A) - tan(2A) - tan(A) = tan(A) tan(2A)tan(3A)

Q4. Attempt Any Four

a. Find adjoint of matrix A if

	1	0	-1
A=	3	4	5
	0	-6	7

b.    Using matrix inversion method solve the simultaneous equations x+ 3y + 3z = 12

x + 4y + 4z = 15 x + 3y + 4z = 13

c.    Find the unit vector perpendicular to vectors a = i - j + k and b = 2i + 3 j - k

d.    Find the equation of the line which makes an equal intercepts of opposite sign on coordinate axis and passing through the point (4,3).

e.    Prove that

cos3 A sin 3 A

-+-= 4cos 2 A

cos A sin A

f.    Prove that

sin 2 A + 2sin4 A + sin 6 A _A . _A

-= cos A + sin A cot 3 A

sin A + 2 sin 3A + sin 5 A

Q5. Attempt Any Three    Marks-12

a.    A(3,1),B(1,-3) and C(-3,-2) are vertices of A ABC. Find the equation of median AD

b.    Find the equation of line passing through the point of intersection of lines 2x+y=10 2x-y=14 and perpendicular to the line 3x-y+6=0

c.    Find the equation of the which is perpendicular bisector of the line joining the points (4,8) and (-2,6).

d.    Prove that

tan^-1(1) + tan^-1(2) + tan^-1(3) = n

Q6. Attempt Any three    Marks-12

a.    If in a AABC

sin A

cosB=-. Prove that the AABC is an isosceles triangle.

2sin C

b.    Find the area of quadrilateral whose vertices are (-5,12),(-2,-3),(9,-10) and (6,5).

c.    Find the equation of the cirle passing through (6,4) and concentric with the circle x²+y²-4x-2y-35=0.

d.    Find the equation of the circle joining (-3,4) and (1,-8) as diameter.

e.    Find the work done by a force

F =3i - 2 j + 4k when its point of application moves from A(3,2,-1) to B(2,5,4)

1

Prove that the points (2,3), (-1,0) and (4,5) are collinear.

Attachment: maharashtra-state-board-of-technical-education-2008-diploma-in-hospital-management-31169-1.pdf

Earning:   Approval pending.