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1., , From 6 different novels and 3 different dictionaries, 4, novels and I dictionary are to be selected and arranged, , 6., , in a row on a shelf so that the dictionary is always in the, middle. The number of such arrangements is, [2018], , (a) less, , (b), (c), (d), , If the four letter words (need not be meaningful) are to be, formed using, the, letters from, the word, "MEDITERRANEAN" such that the first letter is R and, the fourth letter is E, then the total number of all such, words is, , than 500, , Online 2016, 11, , least 500 but less than 750, 750 but less than 1000, least, at, at least 1000, at, , (a), , The number of numbers between 2,000 and, , 5,000 that can,, , be formed with the digits 0, 1, 2, 3, 4, (repetition of digits, , (b) 59, , 110, , The value of, , 56, , C, 15C-, , is equal to:, , Online 2016], , (d) 36, c) 24, (b) 48, A man X has 7 friends, 4 of them are ladies and, 3 are men. His wife Y also has 7 friends, 3 of them, 30, , are ladies and 4 are men. Assume X and Y have, no common friends. Then the total number of ways, , (a), , 8., , 9., , in which X and Y together can throw a party inviting, 3 ladies and 3 men, so that 3 friends of each of X and Y, , 1240, , (b), , 560, , (c), , 1085, , (d), , 680, , The number of points, having both co-ordinates as, integers, that lie in the interior ofthe triangle with vertices, , (0, 0), (0, 41) and (41, 0) is, b) 780, (c) 901 ( d ), (a) 820, The number of integers greater than 6,000, formed, using the digits 3, 5, 6. 7 and, , 2015], 861, , that, , can, , be, , 8. without, , 2015, , repetition,is, , Ifall the words, with or without meaning, are wTitten using, , (c) 216, (d) 192, Let A and B be two sets containing four and two elements, respectively. Then the number of subsets of the set A B., , the letters of the word QUEEN and are arranged as in, , each having at least three elements is :, , [2017], , are in this party, is, , (a) 484 (b) 485, 4., 4., , 2, , r=, , Online 2018], 3.., , d), , 15 C, , is not allowed) and are multiple of 3 is?, (a), , (C) (21), , (c), , 468, , (d), , 469, , English dictionary, then the position of the word QUEEN, is, [Online 2017], (a) 44th, 46th, (b) 45th, (d) 47th, (c), IIf all the words (with or without meaning) having five, word SMALL, theposition, letters, formed, the letters, and, ardnged, as in ausing, dictionary;, thenofthe, of the word, , SMALL is, (a), , 524, , 2016, (b) 58, , (c), , 46th, , (d), , 59th, , (a), , 10., , 120, , b) 72, , *, , 11., , Online 2015], , and a woman, 1s:, , 12., 12., , [2015], , (c) 219, (d) 256, (b) 510, (a) 275, The number of ways of selecting 15 teams from 15 men, and 15 women, such that each team consists of a man, , (d), 1240, 1120, (c) 196%, (b) 1880, numbers, The sum of, formed, the digits, by using, i in the the, unit's, numbers, place1Online, of all4.the, 5 4-digit, and, 2014], 6., , (a), , without repetition, is:, 432, (b) 108, , (a), , (c), , 6, , (d), , 18

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1., , Consider three set of parallel lines in, , 'a, 'b'and'c'parallel, , plane containing, lines respectively.What is the highest, a, , (c)[ab+bc+ca + (a-1)(b-1c-1)], , number of parallelograms that can be formed with these, , of parallel line?, , set, , (a)laba-1Xb-1)+ be(tb-1)(c-1)+ac(a- 1c-1)], , 2., , (d) None of these, Let A= {x|x isa prime number andx < 30}.The number of, different rational numbers whose numerator and, denominator belong to A is, , (a), (b), , [abe+(a- 1)(b- 1)(c-)), , 90, , (b), , 180, , (c) 9, , (d), , 100

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3., , Ia how many ways can this diagram be coloured subject, , 12., , to the following two conditions?, Each of the smaller triangle is, , ), , to be, , with, , painted, , C,+CC, +*C,yC, ++C, , one, , of three colours: red, blue or green., , No, , (1i), , two, , adjacent regions, , have the, , same, , Ifx,y and rare positive integers, then, , xly!, , (a), , colour., , 13., , (x+y)! (c), *C,, r!, , (b), , The number of values of, , r, , satisfying, , (d), the, , C, , equation, , C-13c2 ="C>_-C3, is, (a), (a), 4., , (b), , 20, , 24, , (c), , (d), , 28, , 14., , 30, , A parallelogram is cut by two sets of m lines parallel to its, sides. The number of parallelograms thus formed is, , 5., , 6., , (d) None of these, There are 5 historical momuments, 6 gardens and 7 shopping, malls in the city. In how many ways a tourist can visit the, city, if he visits at least one shopping mall?, , (a) 23.20. (2-1), , b) 24.26 (27-1), , (c) 2.20(20-1), , (d) None of these, , If 8, , (b) 5, , c) 3, , 2 34X5, , (a), , 1800, , (c), , 1400, , ABC is, , a, , (d), , triangle. 4, 5, points, , The set S, , =, , sets A, B, C of equal size. Thus A B, , the second writer must write 4 chapters and fourth writer, must write three chapters. The number of ways that can, be found to divide the book between four writers, is, , b), , (41), 17., , 17!, , then m, , 51413!2!, , 9., , (5! x 4x3, , 3!(4!)°, , (d), , 12!, , 3(41)", , (b) 9, , (d) 17, , c) 13, , 18. Number of divisors ofthe number N = 23.33.5.7 which, , 11 things taken all at a time such that a = 182 bc, then the, , value ofx will be, (a) 12, b) 10, , are perfect square is, 19., , (d), , (c)8, , n, , and k be, , positive integers such, , Points A,, 4,,A,, , that can be drawn using these points as vertices, is, , 20., , kk+1), , that n2-, , which one of the following assume that 2n = 2p + k +k?, , b) kp-1C, (d) None of these, , (a) n (n-1), , b) n (n-1, , (c)n(n-1), , (d)n (n1), , Number of ways in which 20 different pearls of two colours, can be set, necklace, there being 10 pearls of, , alternately ona, , 2, , The number ofsolutions (x,, x,, ... x), x, e22,... , X,C2k, all integers, satisfying x, + x, +.. +x,= n is given by, (a) k*pC, (c) kip-1C, , (c) 119, (b) 60, Twostraight line intersect at apoint O., , Ifthe point O is not to be used, the number of triangles, , 6, , 4 buses runs between Bhopal and Gwalior. If a man goes, from Gwalior to Bhopal by a bus and comes back to Gwalior, , Let, , (d) 120, , (a) 24, , are taken on one line and points B,, B, .., B. on the other., , by another bus, then the total possible ways are, (a) 12, (b) 16, (d) 8, (c) 4, 11., , (41), , 12!, , If a denotes the number of permutations of x + 2 things, , taken all at a time, b the number of permutations ofx things, taken 11 at a time and c the number ofpermutations ofx-, , 10., , (c), , +ma is equal to, , (a) 10, , (d), , 12!, , Ifm andm,satisaytherelation P+(m-1)Pn, , 17!, , (51) 413!, , u C =S,, , AnB= BnC= AnC= ¢. The number of ways to, , (d) 2, , (a) 12!, , (c), , (d) 4x5x6, , {1,2,3,.12} isto bepartitionedintothree, , 8., , 17!, , None of these, marked on the sides, , are, , (b) (4-1)(5-1)(6-1), , (a) (4+5+6)!, c) 514! 6, , partition S is, , (b), , 1600, , different side is, , (a) 1, (b) 2, (d) 4, C) 3, Four writers must write a book containing 17 chapters., The first and third writer must write 5 chapters each,, , (5) 4!312!, , (d) 4, , integral solution of the equation, , 6, , The tens digits of 1! +2!+3!+.+49! is, , (a), , 3, , 1050 is, , =, , b), , 7., , 17!, , (c), , AB, BC, CA, respectively, the number of triangles on, , 16., , P, thenthe value ofris equal to, , (a) 4, , 15., , (b) 2, , The number of positive, , X, , (b) (+C,)?, , (a) (C,)2, , (c) ( 2C,)?, , 1, , each colour., , (a) 6x(9), 21., , (b) 12!, , (c) 4x (8!), , (d)5 x (9!¥, , The 120 permutations of MAHES are arranged in dictionary, , order, as ifeach, , were an, , ordinary five-letter word., , The last, , letter of the 86th word in the list is, (a) A, , (b) H, , c) S, , (d) E

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22. Thenumber of distinctrational numbers.r such that 0<x<1, and, and =, , straight line except 8 which are all in a straight line. The, , number of triangles that can be formed by joining them, , where p, qe{l, 2, 3, 4, 5, 6, is, , equals., 23., , 23., , (a) 15, (b) 13, (c) 12, (d) 11, Seven people leave their bags outside temple and while, , (a) 504, 28., , random. In how many ways at least one and at most three of, them get their correct bags?, , 2"+3" +5" is formed. Total number, of ways of selecting'n, so that the formed number is, divisible by 4, is equal to, (a) 50, (b) 49, , (a), , ()48, , returning after worshiping the deity, picked one bag each at, , 9+ 'C5 44+ 'G 265, 29., , (b)C 265+ 'Cg 9+'C7 44, (d), A, , None of these, , person writes letters to six friends and addresses the, , corresponding envelopes. Let x be the number of ways so, that at least two of the letters are in wrong envelopes and y, be the number of ways so that all the letters are in wrong, , 25., , envelopes. Then x -y=, (a) 719, (c) 454, (b) 265, (d) None, The number of ordered 4-tuples, (,y,z, w), X,y,Z, wE [0, 10)) which satisfies the inequality,, 9sin x.20cos y .4sin".5coS" W.2120 is, , (a), 26., , A, , 0, , b), , point (a, b), , 144, , (c), , is called, , a, , 81, , good point, , (d) infinite, if both, , a, , and b, , are, , intgers. Number of good points on the curve xy= 225 are, (a) 20, 27., , There, , b) 18, are, , 16, , points, , in, , (c) 16, a, , plane,, , no, , three, , (d) 14, , of which are in a, , (C), 30., , (d), , IfS=(1)(1!) +(2)(2!)+(3) (3!) +, (a), , )Cs9+ 'C2 44+ 'CG 265, 24., , b) 552, (c) 560, (d) 1120, 'n' is selected from the set {1,2,3,.., 100} and the number, , S+1 E, , integer, , n!, , None of these, ..+n, , (n!), then, , b), , S+ integer, , (d), , None of these, , n, , S+1, n!, , cannot be discussed, , Eighteen guests, , are to be seated, half on each side of a, long table. Four particular guests desire to sit on one, particular side and three others on the other side of the, table. The number of ways in which the seating arrangement, can be done equals, , (a) c, 9, , (b) "c, 9, , (c)Px°Po, , (d) None of these