Sujeet Kumar

(I) Choose the correct option from the given alternatives: Question 1. respectively……..(a) 2, 1(b) 1, 2(c) 3, 2(d) 2, 3Answer:(d) 2, 3 Question 2. Question 3. Question 4.The differential equation of all circles having their centres on the line y = 5 and touching the X-axis is Question 5.(a) circles(b) parabolas(c) ellipses(d) hyperbolasAnswer:(a) circles Hint: … Read more

Question 1.In a certain culture of bacteria, the rate of increase is proportional to the number present. If it is found that the number doubles in 4 hours, find the number of times the bacteria are increased in 12 hours.Solution:Since the number doubles in 4 hours, i.e. when t = 4, x = 2×0 ∴ … Read more

Question 1.Solve the following differential equations: This is the general solution. Solution: Solution: Solution: This is the linear differential equation of the formThis is the general solution. Solution: This is the general solution. This is the linear differential equation of the formThis is the general solution. Solution: Solution: Question 2.Find the equation of the curve … Read more

I. Solve the following differential equations: Question 1. Solution: Question 2. Question 3. Solution: Question 4.Substituting these values in (1), we get Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11.x dy + 2y · dx = 0, when x = 2, y = … Read more

Question 1.In each of the following examples verify that the given expression is a solution of the corresponding differential equation.Solution:xy = log y + cDifferentiating w.r.t. x, we get Hence, xy = log y + c is a solution of the D.E. Differentiating w.r.t. x, we getDifferentiating again w.r.t. x, we get Differentiating w.r.t. x, … Read more

Question 1.Obtain the differential equation by eliminating the arbitrary constants from the following equations: Differentiating again w.r.t. x, we getSubstituting the value of A in (1), we getThis is the required D.E. Alternative Method:Differentiating again w.r.t. x, we get,The equations (1), (2) and (3) are consistent in A and B.∴ determinant of their consistency is … Read more

1. Determine the order and degree of each of the following differential equations: Question (ii). Question (iv). Question (v). Question (vii). Question (viii). ∴ the given D.E. has order 3 and degree 3. Question (x).On squaring both sides, we get∴ the given D.E. has order 2 and degree 1.

I. Choose the correct option from the given alternatives: Question 1.The area bounded by the region 1 ≤ x ≤ 5 and 2 ≤ y ≤ 5 is given by(a) 12 sq units(b) 8 sq units(c) 25 sq units(d) 32 sq unitsAnswer:(a) 12 sq units Question 2. Question 3. Question 5. Question 6.The area of … Read more

1. Find the area of the region bounded by the following curves, X-axis, and the given lines: (i) y = 2x, x = 0, x = 5.Solution: (v) xy = 2, x = 1, x = 4.Solution: (vi)  = x, x = 0, x = 4.Solution:The required area consists of two bounded regions A1 and … Read more

I. Choose the correct option from the given alternatives: Question 5. Question 7. Question 9. Question 10.(a) 0(b) 1(c) 2(d) πAnswer:(a) 0 II. Evaluate the following: Question 1. Question 2. Solution: Question 3. Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: III. … Read more