Punjab Technical University 2010-1st Sem B.Sc BioInformatics (BI) (st) CALCULUS FUNCTION AND NUMBER SYSTEMS - Question Paper
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Total No. of Questions : 13] [Total No. of Pages : 02
J-3818 [2037] B.Sc. (BI) (Semester - 1st)
CALCULUS FUNCTION AND NUMBER SYSTEMS (B.Sc. (BI) - 104) Time : 03 Hours Maximum Marks : 75
Instruction to Candidates:
1) Section-A is compulsory.
2) Attempt any Nine questions from Section-B.
Section - A
Q1) (15 x 2 = 30)
a) What do you mean by number system and define real numbers?
b) Differentiate Rational and Irrational numbers.
c) What are complex numbers? With an example define Real and Imaginary parts of a Complex number.
d) Discuss the Modulus and Argument of a Complex Number. Also define Complex Conjugate.
e) State De-Moivres Theorem.
f) What do you mean by Domain and Range of a function?
g) Discuss in brief the Concept of Limit with suitable example.
h) What are Asymptotes?
i) Find derivative of Sin x and Cos x w.r.t. x.
j) What do you understand by Inverse Trigonometry?
1
k) Find Real part of --where z = x + iy .
1 - z
l) When does a function is derivable?
m) Define Rectangular Asymptote.
n) What do you mean by Rectification and length of a Curve?
o) Prove that the function f (x) = x3 - 3x2 + 3x -100 is increasing on R.
(ii) Find the domain and range of the function f (x)
Q3) (i) High light the term Removable discontinuity.
(ii) Find the value of the constant K so that the given function is continuous
at the indicated point :
Kx2, if x < 2
f (x)
3, if x > 2 at x = 2
Q4) Prove that xf0 Sin
does not exist.
Vl + x2 +V1 - x2
-1
Q5) If j = tan 1
Vl + x2 -V 1 - x2
x 4
dy - x , prove that -
dx yfi
Q6) If n is any integer then (Cos 0 + i Sin 0)n = Cos 0 + i Sin n0 Q7) Find the Cube root of unity?
3 1
Q8) Find the intervals in which the function / given by f (x) = x3 + 3, x 0 is
x
i) Increasing ii) Decreasing.
Q9) Trace the Curve y = x3.
Q10) Find the absolute maximum and minimum value of function f given by f(x) = Cos2 x + Sin x; x e [0, n].
Qll) Find the length of the arc of the parabola y2 = 4ax
i) from the vertex to an extremity of the latus rectum
ii) cut off by the latus rectum
Q12) Prove that Addition, Subtraction, Multiplication and Division of a Complex number is also a Complex number.
, n
Q13) Find the slope of the normal to the curve x = 1- a Sin0 , y = b Cos20 at 0 = .
J-3818 2
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