IGNOU MSCANCHEM MCH 14 SOLVED ASSIGNMENT

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MCH 14 2025 - English

Tutor Marked Assignment MATHEMATICS FOR CHEMISTS (MCH-014)

Course Code: MCH-014

Assignment Code: MCH-014/TMA/2025

Maximum Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

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

your answer.

a) Derivative of  with respect to x is 1.

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.

c) If and  they are perpendicular to each other.

d) If probability of an event E is 1/2 and probability of the event is 1/6, then probability of the event F is 1/3, where events E and F are independent.

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

3. a) Prove that  is an orthogonal matrix.

4. a) Evaluate  .

b) Evaluate  .

5. a) Solve the differential equation  .

b) If and then find  .

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.

6. a) 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?

b) 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.

c) 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.

 

MCH 014 (January - 2025) - ENGLISH

Tutor Marked Assignment

MTMATHEMATICS FOR CHEMISTS (MCH-014)

Course Code: MCH-014

Assignment Code: MCH-014/TMA/2026

Maximum Marks: 100

Note: Attempt all questions. The marks for each question are indicated against it.

1. (a) Which of the following sets are finite, and which are infinite? 

(i) The set of points on the circumference of a circle.

(ii) ]0, 1[

(iii) [-1, 1]

(iv) {1, 2, ..., 100}

(b) If A = {1, 2, 3}, B = {2, 3, 4, 5}, and C = {1}, determine A ∪ B ∪ C and also verify

A ∪ B ∪ C = (A ∪ B) ∪ C = A ∪ (B ∪ C) 

(c) Define subjective, injective, and bijective functions with the examples. 

(d) 1.50 mol of PCl₅(g) is decomposes at room temperature to form PCl₃(g) and Cl₂(g). Determine their concentration at equilibrium, when K_c = 1.80. 

2. (a) Show that the set of following vectors form the sides of a right-angled triangle. 

2î - ĵ + k̂

î - 3ĵ - 5k̂

3î - 4ĵ - 4k̂

(b) Find the work done by the force, F = 5î + 2ĵ + 3k̂ when its point of application moves from A(1, -2, -2) to B(3, 1, 1).

(c) Prove, with the help of vectors, that the diagonals of a parallelogram bisect each other. 

3. (a) Evaluate the following limit. 

(b) If the law of motion of a particle is given as: s = -t³ + 3t² + 25, then (2+1)

i) find its velocity and acceleration.

ii) find the distance covered by the particle in time t = 5 units

(c) Find the derivative of the following functions with respect to x: (2+2)

(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)

(ii) 3x/√(5+2x²)

4. (a) Find all the second order partial derivatives of the following function. 

f(x, y) = x² - 8xy + y²

(b) Find the equation of tangent and normal to the curve f(x) = x³ - 3x² + 6x - 1 at x = 2. 

(c) Find the asymptotes of the following functions: 

(i) (3x-4)/(2x+6)

(ii) (x²-2x-8)/(x-1)

5. (a) State the order and the degree of the following differential equations: 

(i) (dy/dx)² = (7x)/(4y²)

(ii) √(d³y/dx³) = dy/dx + x⁴

(iii) (dy/dx)³ = √(1+(dy/dx)²)

(iv) (d²y/dx²)¹ᐟ⁵ = k[1+(dy/dx)²]⁵ᐟ²

(b) Evaluate the following integrals: 

(i) ∫(2eˣ - 3√x)dx

(ii) ∫((1+ln x)³)/x dx

(iii) ∫₁³ x²eˣ³ dx

6. (a) Find the differential equation whose solution is given by 

y = eˣ(A cos x + B sin x)

where, A and B are arbitrary constants.

(d) Using the ideal gas equation, estimate the change in the pressure of 1.0 mol of an ideal gas at 0°C when its volume is changed from 22.414 L to 21.414 L. 

(b) Solve the following differential equation: 

(1/y²) (dy/dt) = 1 - e⁻³ᵗ

(c) Show that the equation 

(y - 2x³)dx = x(1 - xy)dy

becomes exact on multiplication by x⁻² and solve it.

7. (a) If A =  then show that 

(i) 1/2 (A + A') is symmetric, and

(ii) 1/2 (A - A') is skew symmetric.

(b) Verify that the following matrix A is orthogonal 

(c) Solve the following system of equations using Cramer's rule. 

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

8. (a) Find eigenvectors for the matrix 

(b) Find A⁻¹, where 

9. (a) Two coins are tossed simultaneously then find probability of getting at least one head.

(b) A number is chosen at random from the first 40 natural numbers. Calculate the probability that the selected is divisible by 5 or 7. 

(c) A bag contains 8 red balls and 5 black balls. Two balls are drawn one by one without replacement. Find the probability that both balls are red. 

(d) Define Binomial, Poisson and Normal distribution with appropriate equation and name their terms. 

10. (a) Define Error and their types in quantitative chemical analysis. 

(b) In an iron determination from the same amount of sample, the five replicate results were obtained: 20.1, 19.6, 20.0 and 19.9 and 20.4 mg iron.

Calculate the standard deviation, variance, standard deviation of mean, coefficient of variation and relative standard deviation in ppm of the given data. 

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