Sujeet Kumar

I. Choose the correct options from the given alternatives: Question 1. Question 2. Question 3. (a) log(3x) – log(9x) + c(b) log(x) – (log 3) . log(log 9x) + c(c) log 9 – (log x) . log(log 3x) + c(d) log(x) + log(3) . log(log 9x) + cAnswer:(b) log(x) – (log 3) . log(log 9x) … Read more

I. Integrate the following w. r. t. x: Question 1.Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question 14. Question 15. Solution: Question 16. Solution: Question … Read more

I. Evaluate the following: Question 1.∫ log x dxSolution: Question 2.∫ sin 3x dxSolution: Question 3.∫x  x dxSolution: Question 4.∫  x dxSolution: Question 5. Question 6. Question 7. Question 8.∫x . x dxSolution: Question 9.∫ log x dxSolution: Question 10.∫ cos 3x dxSolution: Question 11.∫x  x dxSolution: Question 12.∫  x dxSolution: Question 13. Solution:= t(log t – 1) + c= (log … Read more

I. Evaluate: Question 1. Question 2. Question 3. Question 4. Question 5. 7x + 3 = A(2 – 2x) + B∴ 7x + 3 = -2Ax + (2A + B)Comparing the coefficient of x and constant on both the sides, we get-2A = 7 and 2A + B = 3 Question 6. Solution:Comparing the coefficients … Read more

I. Evaluate the following: Question 1.Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question 14. Solution: Question 15. Solution: Question 16. Solution: Question 17. Solution: Question … Read more

I. Integrate the following functions w.r.t. x: Question 1.Solution: Question 2. Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13.Dividing numerator and denominator by cos2x, we get Question 14. Solution: Question 15. … Read more

I. Integrate the following functions w.r.t. x: (i)  +  – x + 1Solution: Solution: Solution: Solution: Solution: II. Evaluate: (i) ∫ta x . dxSolution: Solution: Solution: Solution: Solution: = -cot x – tan x + c Solution: Solution: Solution: Solution: (x) ∫sin 4x cos 3x dxSolution: III. Evaluate: (i) ∫⋅dxSolution: Solution: Solution: Solution: Solution: Solution: Solution: (viii) … Read more

I. Choose the correct option from the given alternatives: Question 1.(a) 1, -6(b) -2, 1(c) -1, -6(d) -1, 6Answer:(a) 1, -6 a + b + 11 = 27a + 9b + 3326a + 8b = -2213a + 4b = -11Only a = 1, b = -6 satisfy this equation. Question 2. (a) 1(b) 0(c) -1(d) … Read more

I) Select the appropriate alternatives for each of the following :Question 1.The value of objective function is maximum under linear constraints _______.(A) at the centre of feasible region(B) at (0, 0)(C) at a vertex of feasible region(D) the vertex which is of maximum distance from (0, 0)Solution:(C) at a vertex of feasible region Question 2.Which … Read more

Question 1.Maximize : z = 11x + 8y subject to x ≤ 4, y ≤ 6,x + y ≤ 6, x ≥ 0, y ≥ 0.Solution:First we draw the lines AB, CD and ED whose equations are x = 4, y = 6 and x + y = 6 respectively. The feasible region is shaded … Read more