Answer: D) 10!/2 Explanation: As A1 speaks always after A2, they can speak only in  1st  to 9th places and    A2 can speak in 2nd to 10 the places only when A1 speaks in 1st place    A2 can speak in 9 places the remaining     A3, A4, A5,...A10  has no restriction. So, they can speak in 9.8! ways. i.e   when A2 speaks in the first place, the number of ways they can speak is 9.8!.   When A2 speaks in second place, the number of ways they can speak is  8.8!.   When A2 speaks in third place, the number of ways they can speak is  7.8!. When A2 speaks in the ninth place, the number of ways they can speak is 1.8!       Therefore,Total Number of ways they can  speak = (9+8+7+6+5+4+3+2+1) 8! = 92(9+1)8! = 10!/2

Answer: B) 7! x 6! Explanation: The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in 7P6ways. 7 teachers can sit in (7-1)! ways.    Required no.of ways is = 7P6.6! = 7!.6!

Answer: A) 2520 Explanation: The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520  (since n = 8)

Answer: A) 360 Explanation: CAPITAL = 7   Vowels = 3 (A, I, A)   Consonants = (C, P, T, L)   5 letters which can be arranged in  5P5=5!   Vowels A,I = 3!2!   No.of arrangements = 5! x 3!2!=360

Answer: C) 48 Explanation: DESIGN = 6 letters   No consonants appear at either of the two ends.  = 2 x 4P4 =  2 x 4 x 3 x 2 x 1=  48

Answer: C) 3439 Explanation: The numbers 0,1,2,3,4,5,6,7,8,9 are 10 in number while preparing telephone numbers any number can be used any number of times.   This can be done in 105ways, but '0' is there   So, the numbers starting with '0' are to be excluded is 94 numbers.    Total 5 digit telephone numbers = 105- 94 = 3439

Answer: C) 40 triangles, 7 Squares Explanation: The figure may be labelled as shown      Triangles :   The Simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e 18 in number   The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ,LJI, LKD, KDE, DEL and ELK i.e 16 in number.   The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e 6 in number.   Total number of triangles in the figure = 18 + 16 + 6 =40.   Squares :   The Squares composed of two components each are MGNH, NIOJ, and OKPL i.e 3 in number   The Squares composed of four components each are BGHA, GIJH, IKJL and KDEL i.e 4 in number   Total number of squares in the figure = 3 + 4 =7

1. Answer : 2 Explanation : Productivity = Total production/area of Agr.land  Productivity of UP = [ (35000+30000+25000) / (30/100) ] = 300000   Productivity of MP = [ (30000+37500+27500) / (25/100) ] = 380000   Productivity of Bihar = [ (22500+27500+25000) / (20/100) ] = 375000  Productivity of Odisha = [ (22500+15000+10000) / (5/100) ]= 950000   Productivity of Haryana = [ (30000+25000+35000) / (8/100) ] = 1125000   Productivity of Punjab = [ (40000+35000+30000) / (12/100) ] = 875000  The Productivity of Haryana is the maximum.       2. Answer : 5   Explanation : Production of Punjab is maximum = 105000 tonnes      3. Answer : 3  Explanation : Production of Wheat in Punjab = 40000 tones Production of Maize in Odisha = 10000 tones Required % = (40000 - 10000)/100 = 300%      4. Answer : 4  Explanation : The ratio of prodution of Rice in Bihar to the production of Wheat in Haryana = 25000 tonnes : 25000 tonnes = 1 : 1       5. Answer : 1   Explanation : Income of MP from export of 40% of Rice at the rate of Rs.30 per kg = Rs.39crore Income of UP from export of 30% of Rice at the rate of Rs.32 per kg = Rs.28.8 crore  Required ratio = 39 : 28.8 = 390 : 288 = 65 : 48