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(I) Select the correct answer from the given alternatives. Question 1.If n is an odd positive integer, then the value of 1 +  is:(A) -4i(B) 0(C) 4i(D) 4Answer:(B) 0Hint: = 1 – 1 + 1 – 1 …..(n odd positive integer)= 0 Question 2. (A) -2(B) 1(C) 0(D) -1Answer:(D) -1Hint: Question 3.√-3 √-6 is equal … Read more

Question 1.Find the value of Solution: Question 2. Question 3. Question 4.If α and β are the complex cube roots of unity, show that Solution:α and β are the complex cube roots of unity. Question 5.If x = a + b, y = αa + βb and z = aβ + bα, where α and … Read more

Question 1.Find the modulus and amplitude for each of the following complex numbers:(i) 7 – 5iSolution:Let z = 7 – 5ia = 7, b = -5i.e. a > 0, b < 0 Here, (7, -5) lies in 4th quadrant. (ii) √3 + √2 iSolution:Let z = √3 + √2 ia = √3, b = √2,i.e. … Read more

Question 1.Find the square root of the following complex numbers:(i) -8 – 6iSolution: (ii) 7 + 24iSolution: (iii) 1 + 4√3 iSolution: (iv) 3 + 2√10 iSolution: (v) 2(1 – √3 i)Solution: Question 2.Solve the following quadratic equations:(i) 8 + 2x + 1 = 0Solution:Given equation is 8 + 2x + 1 = 0Comparing with a + bx … Read more

Chapter 1 Complex Numbers Ex 1.1 Question 1.Simplify:(i) √-16 + 3√-25 + √-36 – √-625Solution: = 4i + 3(5i) + 6i – 25i= 25i – 25i= 0 (ii) 4√-4 + 5√-9 – 3√-16Solution: Question 2.Write the conjugates of the following complex numbers(i) 3 + iSolution:Conjugate of (3 + i) is (3 – i). (ii) 3 … Read more

(I) Select the correct answer from the given four alternatives. Question 1.There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is Question 2.In a jar, there are 5 black marbles and 3 green marbles. Two marbles are picked randomly one after the other without … Read more

Question 1.If odds in favour of X solving a problem are 4 : 3 and odds against Y solving the same problem are 2 : 3. Find the probability of:(i) X solving the problem(ii) Y solving the problemSolution:(i) Odds in favour of X solving a problem are 4 : 3.∴ The probability of X solving … Read more

Question 1.There are three bags, each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles and Bag 3 has 45 red and 55 blue marbles. One of the bags is chosen at random and marble is picked from the chosen bag. What is … Read more

Question 1.A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. If the first marble drawn is red, what is the probability that the second marble is blue?Solution: Alternate Method: Question 2.A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random … Read more

Question 1.First, 6 faced die which is numbered 1 to 6 is thrown, then a 5 faced die which is numbered 1 to 5 is thrown. What is the probability that sum of the numbers on the upper faces of the dice is divisible by 2 or 3?Solution:When a 6 faced die and a 5 … Read more