Verify:
a. 60 : 105 :: 84 : 147
b. 91 : 104: : 119: 136
c. 108 : 72 :: 129 : 86
d. 39: 65 :: 141 : 235

Verify the following: 1) "60:105:34:,147],[" (iil) "108:72:129:86

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

The weights in grams of 50 apples picked at random from a consignment are as follows 106, 107, 76, 82, 109, 107, 115, 93, 187, 195, 123, 125, 111, 92, 86, 70, 126, 68, 130 129, 139 119, 115, 128, 100, 186, 84, 99, 118, 204, 111, 141, 136 123, 90, 11 98, 110, 78, 90, 107, 81, 131, 75, 84, 104, 110, 80, 118, 82. Form the grouped frequency table by dividing the variable range into intervals of equal width, each corresponding to 70 gms in such a way that mid-value of the first class corresponds to 70 gms.

The weekly pocket expenses (in rupees) of 30 students of a class are given below: 62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115 Construct a frequency table with class intervals 60-70 (where 70 is not included), 70-80, 80-90. etc.

Find the HCF of the following numbers : (a) 18, 48 (b) 30, 42 (c) 18, 60 (d) 27, 63 (e) 36, 84 (f) 34, 102 (g) 70, 105, 175 (h) 91, 112, 49 (i) 18, 54, 81 (j) 12, 45, 75

In Fig.108, if A B C D then the value of x is (a) 87 (b) 93 (c) 147 (d) 141

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)

In Fig. 10.84, if A P=10 c m , then B P= (FIGURE) sqrt(91)c m (b) sqrt(127)c m (c) sqrt(119)c m (d) sqrt(109)c m

The cost of raw materials of a product increase 30%, the manufacturing cost increases by 20% and the selling price of the produce increases by 60%, The raw material and the manufacturing cost originally formed 40%, and 60% of the total cost respectively if the original profit percentage was one-fourth original manufacturing cost, find the approximate new profit percentage. a. 48. 39 % b. 54. 76 % c. 63. 85 % d. 66. 72 %

Three fourth of a number is 60 more than it sone-third.the number is a. 84 b. 108 c. 144 d. None of these