Sujeet Kumar

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. ∴ The limit does not exist III. Evaluate the following limits: Question 1. … Read more

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

(I) Select the correct answer from the given alternatives. Question 1.If log (5x – 9) – log (x + 3) = log 2, then x = ________(A) 3(B) 5(C) 2(D) 7Answer:(B) 5Hint: Question 3.Find x, if 2 log2 x = 4(A) 4, -4(B) 4(C) -4(D) not definedAnswer:(B) 4Hint:∴ x = ±4∴ x = 4 Question 4. … Read more

Question 1.If f(x) = 3x + 5, g(x) = 6x – 1, then find(i) (f + g) (x)(ii) (f – g) (2)(iii) (fg) (3)(iv) (f/g) (x) and its domainSolution:f(x) = 3x + 5, g (x) = 6x – 1(i) (f + g) (x) = f (x) + g (x)= 3x + 5 + 6x – … Read more

Question 1.Check if the following relations are functions.(a) Solution:Yes.Reason: Every element of set A has been assigned a unique element in set B. (b) Solution:No.Reason: An element of set A has been assigned more than one element from set B. (c) Solution:No.Reason:Not every element of set A has been assigned an image from set B. … Read more

(I) Select the correct answer from the given alternative. Question 1.For the set A = {a, b, c, d, e} the correct statement is(A) {a, b} ∈ A(B) {a} ∈ A(C) a ∈ A(D) a ∉ AAnswer:(C) a ∈ A Question 2.If aN = {ax : x ∈ N}, then set 6N ∩ 8N =(A) … Read more

Question 1.If (x – 1, y + 4) = (1, 2), find the values of x and y.Solution:(x – 1, y + 4) = (1, 2)By the definition of equality of ordered pairs, we havex – 1 = 1 and y + 4 = 2∴ x = 2 and y = -2 Question 2. Question … Read more

Question 1.Describe the following sets in Roster form:(i) A = {x/x is a letter of the word ‘MOVEMENT’} (iii) C = {x/x = 2n + 1, n ∈ N}Solution:(i) A = {M, O, V, E, N, T}(ii) B = {-1, 0, 1, 2, 3, 4}(iii) C = {3, 5, 7, 9, … } Question 2.Describe … Read more

(I) Select the correct answers from the given alternatives. Question 1.The total number of terms in the expression of (x + y)100 + (x – y)100 after simplification is:(A) 50(B) 51(C) 100(D) 202Answer:(B) 51Hint: Question 2. Question 3. Question 4. Hint: Question 5.The number of terms in expansion of (4y + x)8 – (4y – x)8 is(A) 4(B) 5(C) … Read more

Question 1. Question 2. Question 3. Question 5. Question 7. Solution: