Sujeet Kumar

पत्रलेखन एक कला है आजकल इसका साहित्यिक महत्त्व भी स्वीकारा जाने लगा है। एक अच्छे पत्र की पाँच विशेषताएँ होती हैं। पत्र लिखते समय निम्नलिखित वातों को ध्यान में रखना चाहिए – पत्र के प्रकार: मुख्य रूप से औपचारिक और अनौपचारिक दो तरह के पत्र माने गए है। औपचारिक पत्र : इस पत्र में संदेश, … Read more

(I) Select the appropriate option from the given alternatives. Question 1. Hint: Question 2.Hint: Question 3.Hint: Question 4.Hint: Question 5.Suppose f(x) is the derivative of g(x) and g(x) is the derivative of h(x).If h(x) = a sin x + b cos x + c, then f(x) + h(x) =(A) 0(B) c(C) -c(D) -2(a sin x … Read more

(I) Differentiate the following w.r.t. x Question 1. Solution: Question 2.y = √x + tan x – x3Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: (II) Diffrentiate the following w.r.t. x Question 1.y = x5 tan xSolution: Question 2.y = x5 log xSolution: Question 3.y = (x2 + 2)2 sin xSolution: Question 4.y = … Read more

Question 1.Find the derivatives of the following w.r.t. x by using the method of the first principle. By first principle, we get (b) sin(3x)Solution:Let f(x) = sin 3xf(x + h) = sin3(x + h) = sin(3x + 3h)By first principle, we get (c) e2x+1Solution: (d) 3xSolution: (e) log(2x + 5)Solution:Let f(x) = log(2x + 5)∴ … Read more

(I) Select the correct answer from the given alternatives. Question 1. Hint: Question 2. Hint: Question 3.Hint: Question 4. (A) f is discontinuous at x = 2(B) f is discontinuous at x = -4(C) f is discontinuous at x = 0(D) f is discontinuous at x = 2 and x = -4Answer:(B) f is discontinuous … Read more

Question 1.Examine the continuity of(i) f(x) = x3 + 2 x2 – x – 2 at x = -2Solution:Given, f(x) = x3 + 2 x2 – x – 2f(x) is a polynomial function and hence it is continuous for all x ∈ R.∴ f(x) is continuous at x = -2. Solution: = 8 for x = 3, at x … Read more

I. Select the correct answer from the given alternatives. Question 1. (A) 23(B) 32(C) -32(D) -16Answer:(C) -32Hint: Question 2. Hint: Question 3. Hint: Question 4. Hint: Question 5. Hint: Question 6. (A) 0(B) 1(C) 2(D) 3Answer:(C) 2Hint: Question 7.Hint: Question 8. (A) log 15(B) log 3 + log 5(C) log 3 . log 5(D) 3 … Read more

I. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: II. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: III. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution:

I. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: II. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: III. Evaluate the following limits: Question 1. Solution: Question 2. Solution: Question … Read more

I. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: II. Evaluate the following: Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: