Q1) If x,y,z are integers and x≥ 0,y≥1,z≥2; x +y+z=15,then the number of values of the ordered triplets (x,y,z) is a) 91 b) 455 c) 17 C 15 d) None of these Q2) If a,b,c are positive integers such that a+b+c≤8 then the number of possible values of the ordered triplets (a,b,c) is a) 84 b) 56 c) 83 d) None of these Q3) The product of r consecutive integers is necessarily divisible by a) r b) r-1 ∑ k k=1 c) (r+1)! d) None of these Q4) In an election there are S candidates and three members are to be elected and an elector can vote for any number of candidates not greater than the number to be elected. Then the number of ways in which a elector may vote is a) 25 b) 30 c) 32 d) None of these Q5) The greater possible number of points of intersection of 8 straight lines and 4 circles is a) 32 b) 64 c) 76 d) 104 Q6) In a plane there are 37 straight lines of which 13 passes through the point A and 11 passes through thepoint B.Besides,no three lines pass through one point ,no line passes through both points A & B,no two are parallel. The number of intersection points the line have equal to a) 535 b) 601 c) 728 d) None of these Q7) There are 4 letters and 4 direct envelops .The number of ways in which all the letters can be put in the wrong envelop is a) 8 b) 9 c) 16 d) None of these Q8) The total number of natural numbers of 6 digits that can be made with digits 1,2,3, if all digits have to appear in the same number atleast once is a) 1560 b) 840 c) 1080 d) 480 Q9) All possible two factors products are formed from the number 1,2,3,4…,200. The number of factors obtained out of the total which are the multiple of 5 is a) 5040 b) 7180 c)8150 d) None of these Q10) The total number of ways in which 4 boys and 4 girls can form a line with boys and girls alternating is a) (4!)^2 b) 8! c) 2(4!) ^ 2 d) 4 ! x 5 P 4 Q11) Three apples and two bananas have to be distributed among 3 boys and two girls such that each person gets one fruit. In how many ways can this be done if atleast one girl gets an apple? a) 6 b) 5 c) 9 d) None of these Q12) Find the distinct numbers of 7 didgits number the sum of whose digits is even a) 90 x 10^6 b) 45 x 105 c) 640000 d) None of these Q13) Find the number of non-congruent rectangle that can be found on a chess board normal 8 x 8 chessboard a) 24 b) 36 c) 48 d) None of these Q14) Find the number of non negative integral solution to the system of the equation x +y z +u +t =20 & x+y+z=5 a) 336 b) 476 c) 582 d) 760 Q15) Find the number of integral solution of the equation x+y+z+t=29,x > 0,y>1,z>2 & t≥0. a) 27 C 3 b) 28 C 3 c) 2600 d) 29 C 4 Q16) Find the number of numbers between 2 x 10^4 & 6 x 10^4 having sum of the digits even. a) 20,000 b) 19,999 c) 24,000 d) 25,000 Q17) Eight straight lines are parallel to each other & the distance between any two adjacent lines is 1 cm.Another sets of 6 straight lines are parallel to each other & the distance between any two adjacent line is 1 cm. These 6 staright lines of second set intersects with the 1st set of 8 staright lines to form parallelogram.How many of such formed parallelogram will not be rhombus? a) 285 b) 365 c) 335 d) None of these Q18) Find the number of non negative integral solution of 2x+2y+z=10 a) 12 C 2 b) 14 C 4 c) 11 C 2 d) None of these Q19) If each of the m points on the one staright line be joined to each other of the n points on the other staright line,then excluding the points on the given two lines,number of points of intersection of these lines as a) ¼ mn(m-1)(n-1) b) m+n C 2 c) mn C 2 d) None of these __________________
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Q3) The ans is r.The answer is so conspicuous
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Q4) the answer is none of these.
as sC3+sC2+sc1+sc0=No: of ways
on simplification we get
(s3+5s)/6 + 1
None of the option is in the form as above.
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8*8=64 Xn pts
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