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Question 1. ∴ (n – 3) (n – 4) (n – 5) = 120∴ (n – 3) (n – 4) (n – 5) = 6 × 5 × 4Comparing on both sides, we getn – 3 = 6∴ n = 9 Question 2. (m + n) (m + n – 1) = 56Let m + … Read more

Question 1.Evaluate:(i) 8!Solution:8!= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1= 40320 (ii) 10!Solution:10!= 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1= 3628800 (iii) 10! – 6!Solution:10! – 6!= 10 × 9 × 8 × 7 × … Read more

Question 1.A teacher wants to select the class monitor in a class of 30 boys and 20 girls. In how many ways can the monitor be selected if the monitor must be a girl?Solution:There are 30 boys and 20 girls.A teacher can select any boy as a class monitor from 30 boys in 30 different … Read more

(I) Select the correct answer from the given alternative: Question 1.The common ratio for the G.P. 0.12, 0.24, 0.48, is(A) 0.12(B) 0.2(C) 0.02(D) 2Answer:(D) 2 Question 2. Answer:(C) -128Hint: Question 3. (A) 3(B) 2(C) 1(D) -1Answer:(A) 3Hint: Question 4.Which term of the geometric progression 1, 2, 4, 8, ….. is 2048.(A) 10th(B) 11th(C) 12th(D) 13thAnswer:(C) … Read more

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