MCH-14 2025 SOLVED ASSIGNMENT

Description

Tutor Marked Assignment
Maximum Marks: 100
Note: Attempt all questions. The marks for each question are indicated against it.
MATHEMATICS FOR CHEMISTS (MCH-014)

1. State whether the following statement are TRUE or FALSE. Give reason in
support of
your answer.

a) Derivative of 1
x with respect to x is 1. (3)
b) If A is a matrix of order 2 by 3 and B is a matrix of order 3 by 2, then
order of the matrix A B  is 2 by 3.
(3)
c) If ˆ ˆ ˆ ˆ ˆ ˆ a 3i 5j 4k and b 4i 4j 2k       they are perpendicular to each
other.
(3)
d) If probability of an event E is 1/2 and probability of the event E F  is
1/6, then probability of the event F is 1/3, where events E and F are
independent.
(3)
e) If the first term of an AP is 5 and 101 term of the AP is 1005 then
common difference
of the AP will be 105.
2. Solve the following system of equations using Cramer’s rule.
x + 3y + 2z = 6, – x + 4y + 5z = 8, 2x + 5y + 3z = 10
(10)
3. a) Prove that cos2 sin2 A sin2 cos2
          
is an orthogonal matrix.

(10)
4. a) Evaluate   5
3
5
x x dx.

 
(10)
b) Evaluate 2
lnx dx. x  (10)
5. a) Solve the differential equation dy sinx ycosx 1. dx  (5)
b) If ˆ ˆ ˆ ˆ ˆ ˆ a 2i 3j 4k and b 3i 5j 2k       then find a b.  (10)
c) In an iron determination (taking 1 g sample every time) the following
four replicate results were obtained: 24.8, 25.2, 23.6 and 24.7 mg iron.
Calculate the coefficient of variation and relative standard deviation in
ppm of the given data.

(10)
(3)
Course Code: MCH-014
Assignment Code: MCH-014/TMA/2025
6.
a)
b)
c)
In a factory there are three machines A, B, C which produce 10%,
40% and 50% items respectively. Past experience shows that
percentage of defective items produced by machines A, B, C are 5%,
4%, 2% respectively. An item from the production of these machines
is selected at random and it is found defective. What is the probability
that it is produced by machine A?
Assume that in a population each person is equally likely to have a
particular disease and disease status of each individual is
independent of each other, then find the probability that out of the 5
randomly selected individuals who are tested for this particular
disease exactly 3 have this disease.
A hospital specialising in heart surgery. In 2023 total of 1000 patients
were admitted for treatment. The average payment made by a patient
was Rs 1,00,000 with a standard deviation of Rs 20000. Under the
assumption that payments follow a normal distribution, find the
number of patients who paid between Rs 90,000 and Rs 1,10,000.