इन संख्याओं को निकटतम दहाई तक सन्निकटित कीजिए: 28 32 52 41 39 48
64 59 99 215 1453 2936

100 plants each were planted in 100 schools during Van Mahotsava. After one month, the number of plants that survived were recorded as: 95 67 28 32 65 65 69 33 98 96 76 42 32 38 42 40 40 69 95 92 75 83 76 83 85 62 37 65 63 42 89 65 73 81 49 52 64 76 83 92 93 68 52 79 81 83 59 82 75 82 86 90 44 62 31 36 38 42 39 83 87 56 58 23 35 76 83 85 30 68 69 83 86 43 45 39 83 75 66 83 92 75 89 66 91 27 88 89 93 42 53 69 90 55 66 49 52 83 34 36 Tabulate the given data in suitable groups using tally marks.

100 plants each were planted in 100 schools during Van Mahotsava. After one month, the number of plants that survived were recorded as: 95 67 28 32 65 65 69 33 98 9676 42 32 38 42 40 40 69 95 9275 83 76 83 85 62 37 65 63 4289 65 73 81 49 52 64 76 83 9293 68 52 79 81 83 59 82 75 8286 90 44 62 31 36 38 42 39 8387 56 58 23 35 76 83 85 30 6869 83 86 43 45 39 83 75 66 8392 75 89 66 91 27 88 89 93 4253 69 90 55 66 49 52 83 34 36 Tabulate the given data in suitable groups using tally marks.

Directions (Questions 11 to 15): Study the following table carefully and answer the questions given below: Number (N) of Candidates (In lakhs) Appearing For An Entrance Examination From Six Different States And The Percentage (P) of Candidates Clearing the Same Over the Years STATE -> A B C D E F YEAR darr N P N P N P N P N P N P 2004 1.23 42 1.04 51 1.11 32 1.32 24 1.23 36 1.33 31 2005 1.05 43 1.12 62 1.07 47 1.15 49 1.18 55 1.24 24 2006 2.04 38 1.48 32 1.08 28 1.96 35 1.42 49 1.58 26 2007 1.98 41 2.07 43 1.19 30 1.88 46 1.36 47 1.79 29 2008 1.66 53 1.81 50 1.56 42 1.83 60 1.73 57 1.86 34 2009 1.57 39 1.73 36 1.64 52 2.01 56 1.69 55 1.95 37 What is the ratio of the total number of candidates clearing the entrance examination from State B in the year 2004 to that of those clearing the entrance examination from State C in the same year? (a) 221 : 148 (b) 218 : 143 (c) 148 : 221 (d) 143 : 218 (e) None of these

Directions (Questions 1 to 5): Study the given table carefully and answer the questions that follow: Number of candidates appeared and qualified for a test (in hundreds) in 6 different years from 5 different zones. Year P Q R S T App. Qual. App. Qual. App. Qual. App. Qual. App. Qual. 2005 3.2 2.5 3.5 1.4 3.8 2.2 4.2 2.4 6.2 2.6 2006 4.6 3.4 6.9 4.2 6.9 4.4 7.4 3.3 6.2 4.8 2007 6.5 4.9 7.7 4.5 5.9 4.8 8.3 5.6 6.4 4.2 2008 7.4 5.7 5.4 3.4 7.2 3.2 9.3 6.4 7.8 6.2 2009 8.8 4.8 6.6 5.2 8.6 6.8 11.4 5.2 9.9 6.9 2010 9.2 5.6 10.6 6.4 10.3 7.4 14.2 11.4 11.8 9.4 Note: Here App. means Appeared and Qual. means Qualified. In which years was in zones the difference between the appeared candidates and qualified candidates the second lowest? (a) 2005 (b) 2007 (c) 2008 (d) 2009 (e) 2010

Suppose the cube x^3""p x""+""q has three distinct real roots where p"">""0 and q"">""0 . Then which one of the following holds? (1) The cubic has minima at ( 2) (3)sqrt(( 4) (5) (6) p/( 7)3( 8) (9) (10))( 11) (12) (13) and maxima at ( 14) (15)-sqrt(( 16) (17) (18) p/( 19)3( 20) (21) (22))( 23) (24) (26) The cubic has minima at ( 27) (28)-sqrt(( 29) (30) (31) p/( 32)3( 33) (34) (35))( 36) (37) (38) and maxima at ( 39) (40)sqrt(( 41) (42) (43) p/( 44)3( 45) (46) (47))( 48) (49) (51) The cubic has minima at both ( 52) (53)sqrt(( 54) (55) (56) p/( 57)3( 58) (59) (60))( 61) (62) (63) and ( 64) (65)-sqrt(( 66) (67) (68) p/( 69)3( 70) (71) (72))( 73) (74) (76) The cubic has maxima at both ( 77) (78)sqrt(( 79) (80) (81) p/( 82)3( 83) (84) (85))( 86) (87) (88) and ( 89) (90)-sqrt(( 91) (92) (93) p/( 94)3( 95) (96) (97))( 98) (99) (100)

We are given the following marks secured by 25 students in an examination . 23,28,30,32,35,36,36,40,41,43,44,44,45,48,49,52,53,54,56,56,58,61,62,65,68. (i)Arrange this data in the form of a frequency distribution taking the following class intervals. 20-29,30-39,40-49,50-59, and 60-69 (ii) Draw the frequency polygon and ogive for the above data.