IGNOU MCH 14 SOLVED ASSIGNMENT

Ques 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}

Ques 2.

(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) 

Ques 3.

Define subjective, injective, and bijective functions with the examples. 

Ques 4.

 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. 

Ques 5.

(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

Ques 6.

 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).

Ques 7.

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

Ques 8.

(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

Ques 9.

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

(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)

(ii) 3x/√(5+2x²)

Ques 10.

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

f(x, y) = x² - 8xy + y²

Ques 11.

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

Ques 12.

Find the asymptotes of the following functions: 

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

(ii) (x²-2x-8)/(x-1)

Ques 13.

(dy/dx)² = (7x)/(4y²)

Ques 14.

√(d³y/dx³) = dy/dx + x⁴

Ques 15.

 (dy/dx)³ = √(1+(dy/dx)²)

Ques 16.

 (d²y/dx²)¹ᐟ⁵ = k[1+(dy/dx)²]⁵ᐟ²

Ques 17.

 ∫(2eˣ - 3√x)dx

Ques 18.

 ∫((1+ln x)³)/x dx

Ques 19.

∫₁³ x²eˣ³ dx

Ques 20.

 (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.

Ques 21.

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. 

Ques 22.

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.

Ques 23.

 (a) If A =  then show that 

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

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

Ques 24.

Verify that the following matrix A is orthogonal 

Ques 25.

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

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

Ques 26.

(a) Find eigenvectors for the matrix 

Ques 27.

Find A⁻¹, where 

Ques 28.

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

Ques 29.

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

Ques 30.

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. 

Ques 31.

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

Ques 32.

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

Ques 33.

 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. 

Ques 34.

 (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}

Ques 35.

(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) 

Ques 36.

Define subjective, injective, and bijective functions with the examples. 

Ques 37.

 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. 

Ques 38.

(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

Ques 39.

 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).

Ques 40.

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

Ques 41.

(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

Ques 42.

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

(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)

(ii) 3x/√(5+2x²)

Ques 43.

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

f(x, y) = x² - 8xy + y²

Ques 44.

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

Ques 45.

Find the asymptotes of the following functions: 

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

(ii) (x²-2x-8)/(x-1)

Ques 46.

(dy/dx)² = (7x)/(4y²)

Ques 47.

√(d³y/dx³) = dy/dx + x⁴

Ques 48.

 (dy/dx)³ = √(1+(dy/dx)²)

Ques 49.

 (d²y/dx²)¹ᐟ⁵ = k[1+(dy/dx)²]⁵ᐟ²

Ques 50.

 ∫(2eˣ - 3√x)dx

Ques 51.

 ∫((1+ln x)³)/x dx

Ques 52.

∫₁³ x²eˣ³ dx

Ques 53.

 (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.

Ques 54.

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. 

Ques 55.

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.

Ques 56.

 (a) If A =  then show that 

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

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

Ques 57.

Verify that the following matrix A is orthogonal 

Ques 58.

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

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

Ques 59.

(a) Find eigenvectors for the matrix 

Ques 60.

Find A⁻¹, where 

Ques 61.

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

Ques 62.

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

Ques 63.

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. 

Ques 64.

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

Ques 65.

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

Ques 66.

 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. 

Ques 67.

 (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}

Ques 68.

(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) 

Ques 69.

Define subjective, injective, and bijective functions with the examples. 

Ques 70.

 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. 

Ques 71.

(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

Ques 72.

 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).

Ques 73.

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

Ques 74.

(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

Ques 75.

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

(i) (x⁻¹ᐟ² - x¹ᐟ²)/(x⁻¹ᐟ² + x¹ᐟ²)

(ii) 3x/√(5+2x²)

Ques 76.

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

f(x, y) = x² - 8xy + y²

Ques 77.

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

Ques 78.

Find the asymptotes of the following functions: 

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

(ii) (x²-2x-8)/(x-1)

Ques 79.

(dy/dx)² = (7x)/(4y²)

Ques 80.

√(d³y/dx³) = dy/dx + x⁴

Ques 81.

 (dy/dx)³ = √(1+(dy/dx)²)

Ques 82.

 (d²y/dx²)¹ᐟ⁵ = k[1+(dy/dx)²]⁵ᐟ²

Ques 83.

 ∫(2eˣ - 3√x)dx

Ques 84.

 ∫((1+ln x)³)/x dx

Ques 85.

∫₁³ x²eˣ³ dx

Ques 86.

 (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.

Ques 87.

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. 

Ques 88.

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.

Ques 89.

 (a) If A =  then show that 

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

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

Ques 90.

Verify that the following matrix A is orthogonal 

Ques 91.

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

x + y - z = 6

3x - 2y + z = -5

x + 3y - 2z = 14

Ques 92.

(a) Find eigenvectors for the matrix 

Ques 93.

Find A⁻¹, where 

Ques 94.

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

Ques 95.

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

Ques 96.

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. 

Ques 97.

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

Ques 98.

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

Ques 99.

 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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