JEE Main & Advanced Mathematics Permutations and Combinations Question Bank

done Geometrical Problems Total Questions - 25

• question_answer1)
  The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line is
  A)
  \[^{8}{{C}_{3}}\] done clear
  B)
  \[^{8}{{C}_{3}}{{-}^{5}}{{C}_{3}}\] done clear
  C)
  \[^{8}{{C}_{3}}{{-}^{5}}{{C}_{3}}-1\] done clear
  D)
    None of these done clear
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• question_answer2)
  The number of diagonals in a octagon will be [MP PET 1984; Pb. CET 1989, 2000]
  A)
  28 done clear
  B)
  20 done clear
  C)
  10 done clear
  D)
  16 done clear
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• question_answer3)
  If a polygon has 44 diagonals, then the number of its sides are                 [MP PET 1998; Pb. CET 1996, 2002]
  A)
  7 done clear
  B)
  11 done clear
  C)
  8 done clear
  D)
  None of these done clear
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• question_answer4)
  How many triangles can be formed by joining four points on a circle
  A)
  4 done clear
  B)
  6 done clear
  C)
  8 done clear
  D)
  10 done clear
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• question_answer5)
  How many triangles can be drawn by means of 9 non-collinear points
  A)
  84 done clear
  B)
  72 done clear
  C)
  144 done clear
  D)
  126 done clear
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• question_answer6)
  The number of diagonals in a polygon of \[m\] sides is          [BIT 1992; MP PET 1999; UPSEAT 1999; DCE 1999; Pb. CET 2001]
  A)
  \[\frac{1}{2\ !}m(m-5)\] done clear
  B)
  \[\frac{1}{2\ !}m(m-1)\] done clear
  C)
  \[\frac{1}{2\ !}m(m-3)\] done clear
  D)
  \[\frac{1}{2\ !}m(m-2)\] done clear
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• question_answer7)
  The number of straight lines joining 8 points on a circle is [MP PET 1984]
  A)
  8 done clear
  B)
  16 done clear
  C)
  24 done clear
  D)
  28 done clear
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• question_answer8)
  The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line, is [Roorkee 1989; BIT 1989; MP PET 1995;Pb. CET 1997, 98; Roorkee 2000; DCE 2002; AMU 2005]
  A)
  185 done clear
  B)
  175 done clear
  C)
  115 done clear
  D)
  105 done clear
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• question_answer9)
  In a plane there are 10 points out of which  4 are collinear, then the number of triangles that can be formed by joining these points are [RPET 1990]
  A)
  60 done clear
  B)
  116 done clear
  C)
  120 done clear
  D)
  None of these done clear
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• question_answer10)
  There are \[16\] points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points [RPET 1986; MP PET 1987]
  A)
  106 done clear
  B)
  105 done clear
  C)
  60 done clear
  D)
  55 done clear
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• question_answer11)
  The straight lines \[{{I}_{1}},\ {{I}_{2}},\ {{I}_{3}}\] are parallel and lie in the same plane. A total number of \[m\] points are taken on \[{{I}_{1}},\ n\] points on \[{{I}_{2}},\ k\] points on\[{{I}_{3}}\]. The maximum number of triangles formed with vertices at these points are [IIT Screening 1993; UPSEAT 2001]
  A)
  \[^{m+n+k}{{C}_{3}}\] done clear
  B)
  \[^{m+n+k}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}-{{}^{k}}{{C}_{3}}\] done clear
  C)
  \[^{m}{{C}_{3}}{{+}^{n}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\] done clear
  D)
  None of these done clear
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• question_answer12)
  The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is [WB JEE 1993; RPET 2001]
  A)
  6 done clear
  B)
  18 done clear
  C)
  12 done clear
  D)
  9 done clear
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• question_answer13)
  Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to
  A)
  105 done clear
  B)
  45 done clear
  C)
  51 done clear
  D)
  None of these done clear
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• question_answer14)
  There are \[m\] points on a straight line \[AB\] and \[n\] points on another line \[AC\], none of them being the point \[A\]. Triangles are formed from these points as vertices when (i) \[A\]is excluded (ii) \[A\] is included. Then the ratio of the number of triangles in the two cases is
  A)
  \[\frac{m+n-2}{m+n}\] done clear
  B)
  \[\frac{m+n-2}{2}\] done clear
  C)
  \[\frac{m+n-2}{m+n+2}\] done clear
  D)
  None of these done clear
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• question_answer15)
  There are \[n\] straight lines in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is
  A)
  \[\frac{n(n-1)(n-2)}{8}\] done clear
  B)
  \[\frac{n(n-1)(n-2)(n-3)}{6}\] done clear
  C)
  \[\frac{n(n-1)(n-2)(n-3)}{8}\] done clear
  D)
  None of these done clear
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• question_answer16)
  A parallelogram is cut by two sets of \[m\] lines parallel to its sides. The number of parallelograms thus formed is [Karnataka CET 1992]
  A)
  \[{{{{(}^{m}}{{C}_{2}})}^{2}}\] done clear
  B)
  \[{{\left( ^{m+1}{{C}_{2}} \right)}^{2}}\] done clear
  C)
  \[{{\left( ^{m+2}{{C}_{2}} \right)}^{2}}\] done clear
  D)
  None of these done clear
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• question_answer17)
  In a plane there are 37 straight lines of which 13 pass through the point \[A\] and 11 pass through the point \[B\]. Besides no three lines pass through one point, no line passes through both points \[A\]and \[B\] and no two are parallel. Then the number of intersection points the lines have is equal to
  A)
  535 done clear
  B)
  601 done clear
  C)
  728 done clear
  D)
  None of these done clear
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• question_answer18)
  The greatest possible number of points of intersection of 8 straight lines and 4 circles is
  A)
  32 done clear
  B)
  64 done clear
  C)
  76 done clear
  D)
  104 done clear
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• question_answer19)
  There are 16 points in a plane, no three of which are in a straight line except 8 which are all in a straight line. The number of triangles that can be formed by joining them equals                                  [Kurukshetra CEE 1996, 1998]
  A)
  504 done clear
  B)
  552 done clear
  C)
  560 done clear
  D)
  1120 done clear
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• question_answer20)
  Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of \[n\] sides. If \[{{T}_{n+1}}-{{T}_{n}}=21,\] then \[n\] equals [IIT Screening 2001]
  A)
  5 done clear
  B)
  7 done clear
  C)
  6 done clear
  D)
  4 done clear
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• question_answer21)
  Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining  these points are [RPET 2000]
  A)
  100 done clear
  B)
  150 done clear
  C)
  120 done clear
  D)
  None of these done clear
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• question_answer22)
  There are n points in a plane of which p points are collinear. How many lines can be formed from these points [Karnataka CET  2002]
  A)
  \[^{(n-p)}{{C}_{2}}\] done clear
  B)
  \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}\] done clear
  C)
    \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}+1\] done clear
  D)
  \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}-1\] done clear
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• question_answer23)
  Given six line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is [AMU 2002]
  A)
  \[^{6}{{C}_{3}}-7\] done clear
  B)
  \[^{6}{{C}_{3}}-6\] done clear
  C)
  \[^{6}{{C}_{3}}-5\] done clear
  D)
  \[^{6}{{C}_{3}}-4\] done clear
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• question_answer24)
  A polygon has 35 diagonals, then the number of its sides is [AMU 2002]
  A)
  8 done clear
  B)
  9 done clear
  C)
  10 done clear
  D)
  11 done clear
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• question_answer25)
  The number of straight lines that can be formed by joining 20 points no three of which are in the same straight line except 4 of them which are in the same line [Kerala (Engg.) 2002]
  A)
  183 done clear
  B)
  186 done clear
  C)
  197 done clear
  D)
  185 done clear
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