Sujeet Kumar

Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5.Find the sum 5 × 7 + 9 × 11 + 13 × 15 + ….. upto n terms.Solution:5 × 7 + 9 × 11 + 13 × 15 + ….. upto n termsNow, 5, 9, 13, … are in A.P. withrth … Read more

Question 1.Find Sn of the following arithmetico-geometric sequences. Here, 2, 4, 6, 8, 10,… are in A.P.∴ a = 2, d = 2∴ nth term = a + (n – 1)d= 2 + (n – 1)(2)= 2n nth term of arithmetico-geometric sequence is (iii) 1, 2 × 3, 3 × 9, 4 × 27, 5 … Read more

Question 1. ∴ The reciprocal sequence is not an A.P.∴ The given sequence is not a H.P. Solution:∴ The reciprocal sequence is an A.P.∴ The given sequence is a H.P. Question 2.Find the nth term and hence find the 8th term of the following HPs. Question 3. Question 5.Find G.M. of two positive numbers whose … Read more

Question 1.Determine whether the sum to infinity of the following G.P.s exist, if exists find them. Solution: Solution: Solution: Solution: (v) 9, 8.1, 7.29, ……Solution:9, 8.1, 7.29, ….. Question 2.Express the following recurring decimals as rational numbers. ∴ Sum to infinity exists.∴ Sum to infinity ∴ Sum to infinity exists.∴ Sum to infinity ∴ Sum … Read more

Question 1.For the following G.P.s, find .(i) 3, 6, 12, 24, ……..Solution: Solution: (iii) 0.7, 0.07, 0.007, …….Solution: (iv) √5, -5, 5√5, -25, …….Solution: Question 2.For a G.P. Solution: (ii) If = 1023, r = 4, find a.Solution: Question 3.For a G.P.(i) If a = 2, r = 3,  = 242, find n.Solution: (ii) For … Read more

Question 1.Check whether the following sequences are G.P. If so, write tn.(i) 2, 6, 18, 54, ……Solution: (ii) 1, -5, 25, -125, ………Solution: Solution: (iv) 3, 4, 5, 6, ……Solution: (v) 7, 14, 21, 28, ……Solution: Question 2.For the G.P. Solution: Solution: (iii) If r = -3 and  = 1701, find a.Solution: Solution: Question 3.Which … Read more

(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