Uttar Pradesh Technical University (UPTU) 2009 B.Pharm Remedial Mathematics - Question Paper

B. Pharm (UPTU)
First Semester Theory Examination, 2009-10
Remedial Mathematics

Time: three Hours Total Marks: 80

Note: Attempt all ques. in Section-A and 6 ques. in Section-B and any 4 ques. in Section-C.

Section-A

1) State whether actual or false for ques. (i) to (iv): (1×16=6)
i) If then A is known as singular matrix.
ii) The inverse of a symmetric matrix is symmetric.
iii) A system of equations is stated to be consistent if there exist atleast 1 solution for the equations.
iv) The value of
select the accurate ans for the ques. (v) to (viii):
v) If A is Hermitian, then i A is:
a) Hermitian
b) Skew-Hermitian
c) Symmetric
d) Skew symmetric.
vi)
a) 2
b)
c) 4
d) None of these.
vii) The differential formula (ex + 1) y dy = (y + 1) ex dx has the solution:
a) (1 + y) (ex + 1) = c
b) (1 – y) (ex + 1) = c
c) (1 + y) (ex + 2) = c
d) None of these.
viii) The angle ranging from the pair of lines x2 – y2 – 2y – one = 0 is
a) 36°
b) 60°
c) 75°
d) 90°

Fill in the blanks for ques. (ix) to (xvi)
ix) The value of
is _______.

x) The length of subtangent to the curve at the point (4,1) is _______.
xi) The value of is _______.
xii) is _______.
xiii) Every diagonal element of a skew symmetric matrix is _______.
xiv) _______.
xv) The slope of the line joining the points (2, –5), and (4, 1) is _______.
xvi) The value of is _______.

Section-B

2) Answer any 4 parts of the following: (4×6=24)
a) If, verify that (A + B)C = AC + BC.
b) Find the area of the circle centred at (1, 2) and passing through (4, 6).
c) If, then prove that, .
d) Evaluate: .
e) Solve the differential equation: (D2 – 5D + 6)y = x, where, .
f) Solve: (D2 – 4D + 4)y = x3 e2x , where .
g) If, x = a cos3?, y = a sin3? then obtain .
h) Evaluate: .

Section-C

ans any 4 ques. of the following: (10×4=40)
3) Find the adjoint and inverse of the subsequent matrix:
.
4) If, show that .
5) Evaluate: .
6) Solve: (D2 – 3D + 2) y = 6e2x + sin 2x, where .
7) If the points A(K, –1), B(2, 1) and C(4, 5) are collinear, then obtain the value of K.

Earning:   Approval pending.