9th Class Mathematics Geometry Question Bank

done Geometry Total Questions - 198

• question_answer1)
  Match List \[{{H}_{2}}\] with List \[{{H}_{1}}\] and select the correct answer using the codes given below the lists:

  List - I (Regular plane figure)	List - II (Measure of interior angles)
  I. Triangle	(A) \[30{}^\circ \]
  II. Square	(B) \[60{}^\circ \]
  III. Pentagon	(C) \[108{}^\circ \]
  IV. Hexagon	(D) \[90{}^\circ \]
  	(E) \[120{}^\circ \]

  Codes:
  A)
  I-D,     II-A,       III-B,        IV-E done clear
  B)
  I-B,     II-D,      III-C,       IV-E done clear
  C)
  I-A,     II-D,       III-C,        IV-B done clear
  D)
  I-B,     II-C,       III-A,        IV-D done clear
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• question_answer2)
  If an angle is eight times its complementary angle, then the measurement of the angle is
  A)
  \[10{}^\circ \]                    done clear
  B)
         \[20{}^\circ \] done clear
  C)
   \[80{}^\circ \]                     done clear
  D)
         \[160{}^\circ \] done clear
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• question_answer3)
  In the given figure, Z6 is less than one-third of a right angle, then
  A)
  \[\phi >150{}^\circ \] done clear
  B)
  \[\phi \ge 150{}^\circ \] done clear
  C)
  \[\phi \le 150{}^\circ \] done clear
  D)
  \[\phi <150{}^\circ \] done clear
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• question_answer4)
      The least number of non-collinear points required to determine a plane is
  A)
   one                       done clear
  B)
          two done clear
  C)
   three                      done clear
  D)
          infinite done clear
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• question_answer5)
  If A, B, C are three collinear points with coordinates \[x,y,z\] respectively, such that \[x<y<z\] then the order of the point is
  A)
  \[B-A-C\] done clear
  B)
  \[A-B-C\] done clear
  C)
  \[A-C-B\] done clear
  D)
  \[C-A-B\] done clear
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• question_answer6)
  Given a plane E and a line I contained in E, so that two half planes \[{{H}_{1}}\] and \[{{H}_{2}}\] are formed, then line \[l \] lies
  A)
   in \[{{H}_{1}}\] only done clear
  B)
   in \[{{H}_{2}}\] only done clear
  C)
   in both \[{{H}_{1}}\] and \[{{H}_{2}}\] done clear
  D)
   neither in \[{{H}_{1}}\] nor in \[{{H}_{2}}\]  done clear
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• question_answer7)
  At 4.24 pm, how many degrees has the hour hand of a clock moved from its position at noon?
  A)
  \[132{}^\circ \]   done clear
  B)
  \[135{}^\circ \] done clear
  C)
  \[140{}^\circ \] done clear
  D)
  \[145{}^\circ \] done clear
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• question_answer8)
  Two angles are called adjacent if
  A)
   they lie in the same plane and have a common vertex done clear
  B)
   they have a ray in common done clear
  C)
   the intersection of their interiors is empty done clear
  D)
   all the above   done clear
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• question_answer9)
  In the given figure, line RT is drawn parallel to \[SQ.\text{ }\,\text{If}~\,\angle QPS=100{}^\circ ,~\,\angle PQS=40{}^\circ ,\,\,\angle PSR=85{}^\circ \text{ }and\,\,\angle QRS~=70{}^\circ ,\text{ }then~\,\angle QRT\] is
  A)
  \[45{}^\circ \] done clear
  B)
         \[65{}^\circ \]   done clear
  C)
  \[85{}^\circ \] done clear
  D)
         \[90{}^\circ \] done clear
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• question_answer10)
  \[l,m,n\] are parallel lines. If p intersects them at A, B, C and q at D, E, F then
  A)
   AB= DE and BC = EF always done clear
  B)
   at least one of the pairs AB, DE and BC, EF are necessarily equal. done clear
  C)
   at least one of the pairs AB, BC and DE, EF are necessarily equal done clear
  D)
  \[\frac{AB}{BC}=\frac{DE}{EF}\] done clear
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• question_answer11)
  The internal bisectors of\[\text{I}\] and \[\text{II}\] of \[\text{III}\]meet at C. If \[\text{IV}\] = \[70{}^\circ \], then \[\text{I}\] is
  A)
  \[110{}^\circ \]                  done clear
  B)
  \[125{}^\circ \] done clear
  C)
  \[130{}^\circ \] done clear
  D)
  \[140{}^\circ \]   done clear
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• question_answer12)
  If two medians of a triangle are equal in length, then the triangle is
  A)
   right angled but not isosceles done clear
  B)
   isosceles but not right angle   done clear
  C)
   right angled isosceles done clear
  D)
   equilateral done clear
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• question_answer13)
  If two altitudes of a triangle are equal in length, then the triangle is
  A)
   right angled      done clear
  B)
          equilateral done clear
  C)
   isosceles            done clear
  D)
          scalene done clear
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• question_answer14)
  If \[\overline{\text{AC}}\] and \[\overline{\text{BD}}\] intersect at 0 such that AO = CO and BO = DO, then
  A)
   BC = AD done clear
  B)
  BC  | |  AD and BC = AD done clear
  C)
  BC  | |  AD done clear
  D)
   None of these done clear
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• question_answer15)
  The sum of the exterior angles of a hexagon is
  A)
  \[360{}^\circ \]   done clear
  B)
         \[540{}^\circ \] done clear
  C)
  \[720{}^\circ \] done clear
  D)
          None of these done clear
  View Solution play_arrow

• question_answer16)
  In any triangle the centroid divides the median in the ratio
  A)
   1 : 1                       done clear
  B)
          2 : 1   done clear
  C)
   3 : 1                       done clear
  D)
          3 : 2 done clear
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• question_answer17)
  The number of triangles with any three of the length 1, 4, 6 and 8 cms, as sides is
  A)
   4                             done clear
  B)
          2 done clear
  C)
   1                               done clear
  D)
          0 done clear
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• question_answer18)
  If two angles of a triangle are acute angles, the third angle
  A)
   is less than the sum of the two angles done clear
  B)
   is an acute angle done clear
  C)
   is the largest angle of the triangle done clear
  D)
   may be an obtuse angle   done clear
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• question_answer19)
  If one angle of a triangle equals the sum of the other two angles, the triangle must be
  A)
   scalene           done clear
  B)
          right angled   done clear
  C)
   obtuse angled     done clear
  D)
          acute angled done clear
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• question_answer20)
  ABC is a triangle. A line PQ intersects the sides AB and AC in points P and Q such that \[\frac{AP}{PB}=\frac{AQ}{QC}=\frac{m}{n}.\,\,\,m,\,\,n\] being positive integers. The line PQ will pass through the centre of gravity of the triangle if the value of m, n respectively is
  A)
    2, 3                      done clear
  B)
   1 , 2                   done clear
  C)
   1 , 3                 done clear
  D)
   2, 1                  done clear
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• question_answer21)
  The triangle ABC and PQR may not be congruent when
  A)
  \[AB=PQ,\text{ }AC=PR,~\text{ }\,\angle A\,=\,\angle P\] done clear
  B)
  AB = PQ, AC = PR, Altitude AD = Altitude PS done clear
  C)
  \[AB=PQ,\,\,AC=PR,~\text{ }\angle B\,\,=\,\,\angle Q\] done clear
  D)
  \[\angle A\,\,=\,\,\angle P,\,\,\angle B\,=\,\,\angle Q\,\,Altitude\,\,AD=Altitude\,\,PS\] done clear
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• question_answer22)
  The four triangle formed by joining the mid- points of the sides of a triangle respectively are
  A)
   similar, not necessarily congruent. done clear
  B)
   congruent.   done clear
  C)
   equilateral. done clear
  D)
   isosceles. done clear
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• question_answer23)
  If in triangles PQR and LMN, \[\angle P=\angle M=60{}^\circ \], \[\text{PQ}\,\,\text{:}\,\,\text{ML}\,\,\text{=}\,\,\text{PR}\,\,\text{:}\,\text{ MN}\] and \[\angle N=55{}^\circ \], then \[\angle \text{Q}\] is
  A)
  \[50{}^\circ \] done clear
  B)
  \[55{}^\circ \] done clear
  C)
  \[65{}^\circ \]   done clear
  D)
  \[75{}^\circ \] done clear
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• question_answer24)
  If in a triangles XYZ, P, Q are points on XY, YZ respectively such that XP = 2PY, XQ = 2QZ, then the ratio, area of\[\phi \]area of \[x,y,z\], is
  A)
   4 : 9                  done clear
  B)
          2 : 3 done clear
  C)
   3 : 2                done clear
  D)
          9 : 4 done clear
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• question_answer25)
  If D is any point on the side BC of \[\Delta ABC\] such that \[\Delta ADB\] and \[\Delta ADC\] are equal in area, then
  A)
   AD is the median   done clear
  B)
   AD is the altitude done clear
  C)
   AD is an angle bisector done clear
  D)
   AD is any line done clear
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• question_answer26)
  The sides of a triangle are 5 cm, 6 cm and 7 cm. One more \[\Delta \] is formed by joining the midpoints of the sides. The perimeter of the second \[\Delta \] is
  A)
  18 cm                   done clear
  B)
  12 cm done clear
  C)
  9 cm                        done clear
  D)
  6 cm done clear
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• question_answer27)
  The intercepts made by 3 parallel lines on a transverse line \[({{l}_{1}})\] are in the ratio 1:1. A second transverse line \[({{l}_{2}})\] making angle of \[30{}^\circ \] with \[{{l}_{1}}\] is drawn. The corresponding intercepts on \[{{l}_{2}}\] are in the ratio
  A)
   1 : 1                         done clear
  B)
   2 : 1 done clear
  C)
  1:2                         done clear
  D)
   1 : 3 done clear
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• question_answer28)
  At 2.15 o'clock the hour and minute hands of clock form an angle of
  A)
  \[30{}^\circ \] done clear
  B)
  \[22\frac{1{}^\circ }{2}\] done clear
  C)
  \[7\frac{1{}^\circ }{2}\] done clear
  D)
  \[5{}^\circ \] done clear
  View Solution play_arrow

• question_answer29)
  If the diagonals of a quadrilateral bisect one another at right angles, then the quadrilateral is a
  A)
   Trapezium        done clear
  B)
          Rectangle done clear
  C)
   Rhombus         done clear
  D)
          None of these done clear
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• question_answer30)
  A, B, C and D are four angles at a point so that A+B+C+D=4 right angles, out of these A and B are acute angles while C and D are obtuse angles. Which of the following relations may be true?

  1. A+B=C+D

  2. A+C=B+D

  3. A+D=B+C

  A)
   2 and 3 only        done clear
  B)
   1 and 3 only done clear
  C)
  1 and 2 only      done clear
  D)
  3 only done clear
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• question_answer31)
  ABC is an isosceles triangle with AB = AC = 5 and BC = 6. If G is the centroid of \[\Delta \,ABC\], then AG is equal to
  A)
  \[\frac{1}{3}\] done clear
  B)
  \[\frac{2}{3}\] done clear
  C)
  \[\frac{4}{3}\] done clear
  D)
  \[\frac{8}{3}\] done clear
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• question_answer32)
  In the given figure, AD, BF and CE are medians of a triangle ABC and O is a point of concurrency of medians. If AD = 6 cm., then OD is equal to
  A)
   2 cm                            done clear
  B)
  3 cm                     done clear
  C)
  4 cm                      done clear
  D)
  \[\frac{2}{3}\,cm\] done clear
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• question_answer33)
  In the given figure, if PQRS is a rectangle which one is true?
  A)
  \[\text{Ar}\,\text{ }\!\!\Delta\!\!\text{ (APS)}\,\,\text{=}\,\,\text{Ar}\,\text{ }\!\!\Delta\!\!\text{ (QRB)}\] done clear
  B)
  \[\text{PA = RB}\] done clear
  C)
  \[\text{Ar}\,\text{(PQS)}\,\,\text{=}\,\,\text{Ar}\,\text{(QRS)}\] done clear
  D)
   All of the above   done clear
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• question_answer34)
  In the given figure, if E and F are the midpoint  of AB and CD of parallelogram ABCD, which one is true?
  A)
   CE trisects BD                    done clear
  B)
   AF trisects BD done clear
  C)
  \[\text{ }\!\!\Delta\!\!\text{ }\,\text{ADF}\,\,\text{=}\,\,\text{ }\!\!\Delta\!\!\text{ }\,\text{CBE}\] done clear
  D)
  All of these   done clear
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• question_answer35)
  The sum of all the angles of a pentagon are
  A)
  \[360{}^\circ \] done clear
  B)
         \[540{}^\circ \]   done clear
  C)
  \[720{}^\circ \] done clear
  D)
          None of these done clear
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• question_answer36)
  The angle that is three times as large as its complement is
  A)
  \[135{}^\circ \] done clear
  B)
         \[67.5{}^\circ \]   done clear
  C)
  \[50.5{}^\circ \] done clear
  D)
         \[45{}^\circ \] done clear
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• question_answer37)
  In the given figure, SO and PO are bisectors of two adjacent sides of quadrilateral, \[\angle \text{Q}+\,\angle \text{R}\,\] is
  A)
  \[2\angle \text{SOP}\] done clear
  B)
  \[\angle \text{OSP}\,\text{+}\,\angle \text{OPS}\] done clear
  C)
  \[\angle \text{SOP}\] done clear
  D)
  \[2(\angle \text{OSP}\,\text{+}\,\angle \text{OPS)}\] done clear
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• question_answer38)
  The measure of an angle which is four time its supplement is
  A)
  \[36{}^\circ \] done clear
  B)
  \[144{}^\circ \]   done clear
  C)
  \[180{}^\circ \] done clear
  D)
         \[150{}^\circ \] done clear
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• question_answer39)
  Two chords of lengths 16 cm and 17 cm are drawn perpendicular to each other in a circle of radius 10 cm. The distance of their point of intersection from the centre is approximately
  A)
   6.5 cm                  done clear
  B)
          7.2 cm done clear
  C)
   7.6 cm                                  done clear
  D)
   8 cm   done clear
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• question_answer40)
  In the diagram, 0 is the centre of the circle. The angles CBD is equal to
  A)
  \[25{}^\circ \]   done clear
  B)
   \[50{}^\circ \] done clear
  C)
  \[40{}^\circ \] done clear
  D)
  \[130{}^\circ \] done clear
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• question_answer41)
  In the given figure, \[\angle CAB\,\,=\,\,80{}^\circ \,,\angle ABC\,\,=\,\,40{}^\circ .\] The sum of \[\angle DAB\,+\,\,\angle ABD\] is equal to
  A)
  \[80{}^\circ \] done clear
  B)
  \[100{}^\circ \] done clear
  C)
  \[120{}^\circ \]   done clear
  D)
  \[140{}^\circ \] done clear
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• question_answer42)
       If one angle of the parallelogram is \[16{}^\circ \] less than three times the smallest angle, then the largest angle of the parallelogram is
  A)
  \[131{}^\circ \]                    done clear
  B)
         \[136{}^\circ \] done clear
  C)
  \[112{}^\circ \] done clear
  D)
         \[108{}^\circ \] done clear
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• question_answer43)
  In the given circle ABCD, O is the centre and \[\angle BDC\,=\,\,42{}^\circ .\]. The \[\angle ACB\] is equal to
  A)
  \[42{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[48{}^\circ \] done clear
  D)
  \[60{}^\circ \] done clear
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• question_answer44)
  In this Figure, QS and RS are bisectors of exterior angles Q and R. Then \[\angle QSR\,\,+\,\angle P/2\] is equal to
  A)
  \[270{}^\circ \] done clear
  B)
   \[180{}^\circ \] done clear
  C)
  \[90{}^\circ \]   done clear
  D)
   \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer45)
  The angle which is twice its supplement is
  A)
  \[120{}^\circ \]   done clear
  B)
         \[90{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
         \[30{}^\circ \] done clear
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• question_answer46)
  The angle which exceeds its complement by \[20{}^\circ \] is
  A)
  \[45{}^\circ \] done clear
  B)
  \[55{}^\circ \]   done clear
  C)
  \[70{}^\circ \] done clear
  D)
         \[110{}^\circ \] done clear
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• question_answer47)
  The sum of the acute angles of an obtuse triangle is \[70{}^\circ \] and their difference is \[10{}^\circ \]. The largest angle is
  A)
  \[110{}^\circ \]                    done clear
  B)
         \[105{}^\circ \] done clear
  C)
  \[100{}^\circ \] done clear
  D)
         \[95{}^\circ \] done clear
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• question_answer48)
  In a right angled triangle the square of the hypotenuse is twice the product of the square of the other sides. Then the triangle is
  A)
  equilateral        done clear
  B)
  isosceles   done clear
  C)
  \[\text{of }\angle s\,\,30{}^\circ ,\text{ 6}0{}^\circ ,\,\,90{}^\circ \] done clear
  D)
  \[\text{of }\angle s\,\,40{}^\circ ,\text{ }50{}^\circ ,\,\,90{}^\circ \] done clear
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• question_answer49)
  Find the approximate value of \[\angle \text{A}\] in \[\Delta \,\text{ABC}\] if \[8\angle \text{A}\,\text{=}\,\,\text{9}\,\,\angle B\,\text{=}\,4\,\angle C.\]
  A)
  \[70{}^\circ \] done clear
  B)
  \[74{}^\circ \]   done clear
  C)
  \[81{}^\circ \] done clear
  D)
  \[85{}^\circ \] done clear
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• question_answer50)
  PQRS is a parallelogram. If L, M are the mid- points of QR and PS respectively, and O is any point on LM, then the area of triangle OPQ is equal to
  A)
  \[\frac{1}{3}rd\] of the parallelogram PQRS done clear
  B)
  \[\frac{1}{4}th\] of the parallelogram PQRS  done clear
  C)
  \[\frac{1}{2}\] of the parallelogram PQRS done clear
  D)
   \[\frac{1}{6}th\] of the parallelogram PQRS done clear
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• question_answer51)
  In the given figure, if C is the centre of the circle and \[\angle PQC=25{}^\circ \] and \[\angle PRC=15{}^\circ \], then \[\angle QCR\] is equal to  
  A)
  \[40{}^\circ \] done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[80{}^\circ \]   done clear
  D)
  \[120{}^\circ \] done clear
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• question_answer52)
  Three wires of length\[{{l}_{1}}\]form a triangle surmounted by another circular wire, If \[{{l}_{2}}\] is the diameter and\[{{l}_{1}}\], then the angle between \[{{l}_{2}}\] and \[{{l}_{3}}\] will be
  A)
  \[30{}^\circ \] done clear
  B)
  \[60{}^\circ \]   done clear
  C)
  \[45{}^\circ \] done clear
  D)
   \[90{}^\circ \] done clear
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• question_answer53)
  Two circular wheels are rolling on a horizontal road. The loci of the centres will be
  A)
   two circles        done clear
  B)
          rectangle done clear
  C)
   two straight lines   done clear
  D)
         parallelogram done clear
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• question_answer54)
  A and B are two fixed points in a plane. If P is a moving point in the plane such that PA =PB, then the
  A)
   locus of P is the line AB itself. done clear
  B)
   locus of P is a line parallel to AB. done clear
  C)
   point P always makes equilateral triangles with A, B. done clear
  D)
   triangle PAB is isosceles for all positions of P.   done clear
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• question_answer55)
  If one angle of a \[\Delta \] is equal to the sum of the other two, the triangle is
  A)
   isosceles             done clear
  B)
   equilateral done clear
  C)
   right angled        done clear
  D)
  ordinary done clear
  View Solution play_arrow

• question_answer56)
  What value of x will make AOB a straight line?
  A)
  \[30{}^\circ \] done clear
  B)
  \[50{}^\circ \]   done clear
  C)
  \[49{}^\circ \] done clear
  D)
   none of these       done clear
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• question_answer57)
  What value of \[x\] will make\[CD|\,|\,EF\], and \[AB|\,|\,CD\]?
  A)
  \[150{}^\circ \] done clear
  B)
  \[145{}^\circ \]   done clear
  C)
  \[140{}^\circ \] done clear
  D)
  \[135{}^\circ \] done clear
  View Solution play_arrow

• question_answer58)
  The value of \[x\] in the following Figure is
  A)
  \[30{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
      none of these        done clear
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• question_answer59)
  The measurement of each angle of a polygon is \[160{}^\circ \]. The number of its sides is
  A)
   15                          done clear
  B)
          18   done clear
  C)
   20                          done clear
  D)
          30 done clear
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• question_answer60)
  The sum of the interior angles of a polygon of n sides is equal to
  A)
   2n right angles done clear
  B)
   (2n - 2) right angles done clear
  C)
   2(n - 2) right angles   done clear
  D)
   2(n - 4) right angles done clear
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• question_answer61)
  If X is a point on the line AB, Y and Z are points outside such that \[\angle AXY=45{}^\circ \] and \[\angle YXZ=150{}^\circ \], then \[\angle AXZ\] is equal to  
  A)
  \[120{}^\circ \] done clear
  B)
  \[135{}^\circ \] done clear
  C)
  \[150{}^\circ \] done clear
  D)
  \[165{}^\circ \]   done clear
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• question_answer62)
  Lines PQ and RS intersect at O. If \[\angle POS=2\,\,\angle SOQ\] ,then the four angles at O are
  A)
  \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }120{}^\circ ,\text{ }180{}^\circ \] done clear
  B)
  \[60{}^\circ ,\text{ }60{}^\circ ,\text{ }120{}^\circ ,\text{ }120{}^\circ \]   done clear
  C)
  \[60{}^\circ ,\text{ }90{}^\circ ,\text{ }90{}^\circ ,\text{ }120{}^\circ \] done clear
  D)
  \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ ,\text{ }180{}^\circ \] done clear
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• question_answer63)
  In the given figure, \[AB|\,\,|\,CD\] , then \[\angle \text{EFD}\] is geometry equal to
  A)
  \[20{}^\circ \]                    done clear
  B)
  \[25{}^\circ \] done clear
  C)
  \[30{}^\circ \]   done clear
  D)
  \[35{}^\circ \] done clear
  View Solution play_arrow

• question_answer64)
  Find the value of x in the given figure.
  A)
  \[30{}^\circ \]   done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[40{}^\circ \] done clear
  D)
  \[45{}^\circ \] done clear
  View Solution play_arrow

• question_answer65)
  ABCDE is a regular pentagon. Alternate vertices are joined to make a fivepointed star ACEBDA. The sum of the 5 vertical angles of this star is
  A)
   1 rt. angle           done clear
  B)
   2 rt angle   done clear
  C)
  \[270{}^\circ \] done clear
  D)
  \[300{}^\circ \] done clear
  View Solution play_arrow

• question_answer66)
  Angle ABC in the following figure is a/an
  A)
   acute angle done clear
  B)
  obtuse angle done clear
  C)
   reflex angle          done clear
  D)
   straight angle     done clear
  View Solution play_arrow

• question_answer67)
  In the given figure, \[\angle \,\text{ADC}\] is
  A)
  \[30{}^\circ \] done clear
  B)
  \[60{}^\circ \]   done clear
  C)
  \[70{}^\circ \] done clear
  D)
  \[80{}^\circ \]                    done clear
  View Solution play_arrow

• question_answer68)
  The sum of the angles at appoint is
  A)
  \[0{}^\circ \] done clear
  B)
  \[90{}^\circ \] done clear
  C)
  \[180{}^\circ \] done clear
  D)
         \[360{}^\circ \]   done clear
  View Solution play_arrow

• question_answer69)
  In the figure if \[\text{BD}\,\text{ }\!\!|\!\!\text{ }\,\text{ }\!\!|\!\!\text{ }\,\text{EF}\], then \[\angle \,\text{CEF}\] is
  A)
  \[100{}^\circ \] done clear
  B)
   \[120{}^\circ \] done clear
  C)
  \[140{}^\circ \]   done clear
  D)
  \[160{}^\circ \] done clear
  View Solution play_arrow

• question_answer70)
  In the figure PQ II ST, then ZQRS is equal to
  A)
  \[30{}^\circ \] done clear
  B)
  \[40{}^\circ \] done clear
  C)
  \[50{}^\circ \] done clear
  D)
  \[60{}^\circ \]                         done clear
  View Solution play_arrow

• question_answer71)
  AB and CD are parallel line segments of lengths 8 cm and 7 cm respectively. If AD and BC intersect at O and AO = 16 cm, then OD is equal to
  A)
   14 cm   done clear
  B)
   15 cm done clear
  C)
   16cm done clear
  D)
   18 cm done clear
  View Solution play_arrow

• question_answer72)
    Consider the following statements relating to 3 lines \[{{L}_{1}},\,{{L}_{2}}\] and \[{{L}_{3}}\] in the same plane      

  1. If \[{{L}_{2}}\] and \[{{L}_{3}}\] are both parallel to \[{{L}_{1}}\], then they are parallel to each other.

  2. If \[{{L}_{2}}\] and \[{{L}_{3}}\]are both perpendicular to \[{{L}_{1}}\], then they are parallel to each other.

  3. If the acute angle between \[{{L}_{1}}\] and \[{{L}_{2}}\] is equal to te acute angle between \[{{L}_{1}}\] and \[{{L}_{3}}\], then \[{{L}_{2}}\] is parallel to\[{{L}_{3}}\]..

   
  A)
   1 and 2 are correct done clear
  B)
   1 and 3 are correct done clear
  C)
  2 and 3 are correct done clear
  D)
  1, 2 and 3 are correct   done clear
  View Solution play_arrow

• question_answer73)
  In the given figure, \[\angle \,\text{A}\,\text{+}\,\angle \,\text{B}\,\text{+}\,\angle \,\text{C}\,\text{+}\,\angle \,\text{D}\,\text{+}\,\angle \,\text{E}\] is equal to
  A)
  \[\frac{\pi }{2}\]\[\] done clear
  B)
  \[{\pi }\] done clear
  C)
  \[\frac{3\pi }{2}\] done clear
  D)
  \[{2\pi }\] done clear
  View Solution play_arrow

• question_answer74)
  Two beams of length \[{{l}_{1}}\] and \[{{l}_{2}}\] are leaning on opposite sides of a thin vertical wall meeting at the same point on the wall and making angles \[30{}^\circ \]and \[60{}^\circ \] with it respectively. Then \[{{l}_{2}}\] is equal to
  A)
  \[\frac{{{l}_{1}}}{2}\] done clear
  B)
  \[2{{l}_{1}}\] done clear
  C)
  \[{{l}_{1}}\sqrt{2}\] done clear
  D)
  \[{{l}_{1}}\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer75)
  A rectangle ABCD is inscribed in a circle with centre O. If AC is the diagonal and \[\angle \,\text{BAC}\,\text{= 30}{}^\circ \], then radius of the circle will be equal to
  A)
  \[\frac{\sqrt{3}}{2}BC\] done clear
  B)
  BC   done clear
  C)
  \[\sqrt{3}\,\,BC\] done clear
  D)
  2 BC done clear
  View Solution play_arrow

• question_answer76)
  The angle which is one-fifth of its complement is
  A)
  \[15{}^\circ \]   done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
         \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer77)
  The angle which is one-fifth its supplement is
  A)
  \[15{}^\circ \] done clear
  B)
         \[30{}^\circ \]   done clear
  C)
  \[45{}^\circ \] done clear
  D)
         \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer78)
  The angles of a triangle, in ascending order are \[x,y,z\] and \[y-x=z-y=10{}^\circ \]. The smallest angle is
  A)
  \[40{}^\circ \] done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[50{}^\circ \]   done clear
  D)
         \[70{}^\circ \] done clear
  View Solution play_arrow

• question_answer79)
  In the adjoining figure, BD and CD are angle bisectors. Then, which of the following is true?
  A)
  \[\angle \,D=\frac{1}{2}\,\,\angle \,A\] done clear
  B)
  \[\angle \,x+\angle \,y=\angle \,A+\angle \,D\] done clear
  C)
  \[\angle \,D=\frac{\angle \,x+\angle \,y}{2}\] done clear
  D)
  All of above done clear
  View Solution play_arrow

• question_answer80)
  If two parallel lines are intersected by a transverse line, then the bisectors of the interior angles forms a
  A)
   square                 done clear
  B)
   rectangle   done clear
  C)
   parallelogram                   done clear
  D)
   trapezium done clear
  View Solution play_arrow

• question_answer81)
  In a \[\Delta \,ABC\], the sides AB, BC and CA are 10 cm, 8 cm and 7 cm respectively. In AB, a point P is taken such that AP = 4 cm. If PQ is drawn parallel to BC, then its length is equal to
  A)
   4.0 cm      done clear
  B)
  3.8 cm                  done clear
  C)
  3.5 cm                  done clear
  D)
  3.2 cm                   done clear
  View Solution play_arrow

• question_answer82)
  ABCD is a trapezium in which AB is parallel to DC. If the diagonals intersect at C, then which one of the following is correct?
  A)
  \[\frac{OA}{OC}=\frac{OB}{OD}\] done clear
  B)
  \[\frac{AD}{BC}=\frac{AB}{DC}\] done clear
  C)
  \[\frac{OB}{OD}=\frac{BC}{CD}\] done clear
  D)
  \[\frac{OA}{OC}=\frac{DA}{DC}\] done clear
  View Solution play_arrow

• question_answer83)
  In a trapezium \[\Delta \,BCD\], AB is parallel to DC and AB = 2 DC. If AC and BD meet at 0, then area of \[\Delta \,AOB\] is equal to
  A)
   the area of \[\Delta \,COD\] done clear
  B)
   twice the area of \[\Delta \,COD\] done clear
  C)
   thrice the area of \[\Delta \,COD\] done clear
  D)
   four times the area of \[\Delta \,COD\] done clear
  View Solution play_arrow

• question_answer84)
  If the three altitudes of a triangle are equal, then the triangle is
  A)
   isosceles done clear
  B)
   right angled triangle done clear
  C)
   equilateral   done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer85)
  If the angle in a major segment is x and in a minor segment is y, then
  A)
  \[x=y\] done clear
  B)
  \[x>y\] done clear
  C)
  \[x+y=180{}^\circ \] done clear
  D)
  \[x<y\] done clear
  View Solution play_arrow

• question_answer86)
  In \[\Delta \,ABC\], \[\angle \,B=90\], AB = 8 cm and BC = 6 cm. The length of the median BM is
  A)
   3 cm                                      done clear
  B)
  5 cm   done clear
  C)
  4 cm                      done clear
  D)
  7 cm done clear
  View Solution play_arrow

• question_answer87)
  In quadrilateral ABCD, the sides and diagonals are related as
  A)
   AB + BC + CD + DA > AC + BD   done clear
  B)
   AB + BC + CD + DA < AC + BD done clear
  C)
   AB + BC + CD + DA= AC + BD done clear
  D)
  AB + BC + CD + DA > AC\[\Delta \]BD done clear
  View Solution play_arrow

• question_answer88)
  What is the sum of \[\angle \,BAD+\angle \,BPR+\angle \,BCD+\angle \,BQR\] in the diagram
  A)
  \[540{}^\circ \] done clear
  B)
   \[360{}^\circ \]                    done clear
  C)
  \[240{}^\circ \] done clear
  D)
   None of the above   done clear
  View Solution play_arrow

• question_answer89)
          The number of lines of symmetry in    parallelogram is                          
  A)
   one                                       done clear
  B)
   zero                 done clear
  C)
   two                                       done clear
  D)
   four              done clear
  View Solution play_arrow

• question_answer90)
  If AD, BE and CF are the medians of \[\Delta \,ABC\] then which one of the following statements is correct?                                 
  A)
   (AD 4- BE + CF) = (AB + BC + CD)        done clear
  B)
   (AD + BE + CD) > -3 (AB + BC + CA)        done clear
  C)
   (AD + BE + CF) < 3- (AB + BC + CA)      done clear
  D)
   (AD + BE + CF) = - (AB + BC + CA) done clear
  View Solution play_arrow

• question_answer91)
  In a circle with centre O, \[OD\bot \]chord AB. If BC is the diameter, then
  A)
   AC = BC                               done clear
  B)
   OD = BD            done clear
  C)
   AC = 2OD         done clear
  D)
          None of these        done clear
  View Solution play_arrow

• question_answer92)
  If in a regular polygon, each exterior angle is twice the interior angle, then the number of sides will be                                         
  A)
   4                             done clear
  B)
          3                         done clear
  C)
   5                             done clear
  D)
          6 done clear
  View Solution play_arrow

• question_answer93)
  Any interior angle of a regular polygon exceeds the exterior angle by 100? The number of sides of the polygon is
  A)
   7                                             done clear
  B)
   8 done clear
  C)
   9                               done clear
  D)
          6 done clear
  View Solution play_arrow

• question_answer94)
  In the diagram two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. Find the length of the common chord.  
  A)
  \[2\sqrt{3}\,cm\] done clear
  B)
  \[4\sqrt{3}\,cm\] done clear
  C)
  \[4\sqrt{2}\,cm\] done clear
  D)
  \[8 cm\]           done clear
  View Solution play_arrow

• question_answer95)
  If in triangle XYZ, XY = XZ and M, N are the mid points of XY, YZ, then which one of the following is correct?
  A)
   MN = YZ                              done clear
  B)
   NY = NZ = MN done clear
  C)
   MX = MY = NY                  done clear
  D)
   MN = MX = MY   done clear
  View Solution play_arrow

• question_answer96)
  If O, G and H are the circumcentre, the centroid and the orthocentre of a triangle ABC, then
  A)
   O divides GH in the ratio 1 : 2 done clear
  B)
   G divides OH in the ratio 1 : 2   done clear
  C)
   H divides OG in the ratio 1 : 2 done clear
  D)
   O divides GH in the ratio 2 : 1 done clear
  View Solution play_arrow

• question_answer97)
  If the sum of the diagonal of a rhombus is 10 cm and its perimeter is \[4\sqrt{13}\,cm\], then the lengths of its diagonals are
  A)
   5, 5                                        done clear
  B)
   6, 4   done clear
  C)
   7,3                         done clear
  D)
   8,2 done clear
  View Solution play_arrow

• question_answer98)
  The sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at P, the sides AD and BC are produced to meet at Q. If \[\angle \,ADC=85{}^\circ \] and \[\angle \,BPC=40{}^\circ \], then \[\angle \,CQD\] equals
  A)
   \[30{}^\circ \]   done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
  \[75{}^\circ \] done clear
  View Solution play_arrow

• question_answer99)
  ABCD is a quadrilateral. If P, Q, R, S are the points of trisection of the sides AB, BC, CD and DA respectively and are adjacent to A and C, then PQRS is a
  A)
   square                 done clear
  B)
   rectangle done clear
  C)
   rhombus             done clear
  D)
   parallelogram   done clear
  View Solution play_arrow

• question_answer100)
  In the given figure, RS is a tangent, PQ = 12 cm and QR = 4 cm. Then RS is
  A)
   9 cm          done clear
  B)
   8 cm           done clear
  C)
   10 cm      done clear
  D)
   11 cm done clear
  View Solution play_arrow

• question_answer101)
  The number of sides of a regular polygon, if each of its interior angles is \[135{}^\circ \], is given by
  A)
   4                                             done clear
  B)
   6 done clear
  C)
   8                               done clear
  D)
          10 done clear
  View Solution play_arrow

• question_answer102)
  If each interior angle of a regular polygon is twice as large as the exterior angle, the number of sides is
  A)
   4                             done clear
  B)
          6   done clear
  C)
   10                          done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer103)
  The ratio of the sides of two regular polygons is 1 : 2 and their interior angles is 3 : 4, then the number of sides in each polygon is
  A)
   5, 10                        done clear
  B)
          9, 12 done clear
  C)
   10, 5                      done clear
  D)
          5, 12 done clear
  View Solution play_arrow

• question_answer104)
   Two poles of height 10 m and 15 m, stand on a plane ground. If the distance between their feet is 12m, the distance between their tops is
  A)
   12 m                                     done clear
  B)
   13 m   done clear
  C)
   12.5 m.            done clear
  D)
          13.5 m done clear
  View Solution play_arrow

• question_answer105)
  Any cyclic parallelogram is a
  A)
   rectangle           done clear
  B)
          rhombus done clear
  C)
   trapezium        done clear
  D)
          square done clear
  View Solution play_arrow

• question_answer106)
  In the given figure, AB = AC and \[\angle \,BAC\,=40{}^\circ \] Find the sum of angle ADC and angle DAC.
  A)
  \[55{}^\circ \]                        done clear
  B)
  \[65{}^\circ \] done clear
  C)
  \[70{}^\circ \]   done clear
  D)
  \[60{}^\circ \]                    done clear
  View Solution play_arrow

• question_answer107)
  The locus of the centres of all circles of given radius r, in the same planes, passing through a fixed point is
  A)
   A point           done clear
  B)
          A circle   done clear
  C)
   A straight line                   done clear
  D)
   Two straight lines done clear
  View Solution play_arrow

• question_answer108)
  In the given figure, ABC is a triangle in which D and E are the middle points of BC and AC respectively. If AO = 6 cm, find the length of OD.
  A)
   3 cm                              done clear
  B)
   6 cm                     done clear
  C)
        4 cm                      done clear
  D)
   2cm                   done clear
  View Solution play_arrow

• question_answer109)
  OA, OB are the radii of a circle with 0 as centre, the angle AOB = \[120{}^\circ \]. Tangents at A and B are drawn to meet in the point C. If OC intersects the circle in the point D, then D divides OC in the ratio of
  A)
   1 : 2                                       done clear
  B)
   1 : 3 done clear
  C)
   1:1                           done clear
  D)
          2 : 3 done clear
  View Solution play_arrow

• question_answer110)
  If ABCD is a parallelogram whose diagonals intersect at O and \[\Delta \,ABC\] is an equilateral triangle having each side of length 6 cm, then the length of diagonal AC is
  A)
  \[3\sqrt{3}\,\,cm\] done clear
  B)
  \[6\sqrt{3}\,\,cm\] done clear
  C)
  \[3\sqrt{6}\,\,cm\] done clear
  D)
  12 cm done clear
  View Solution play_arrow

• question_answer111)
  If two medians of a triangle are equal, the triangh is
  A)
   right angled       done clear
  B)
          isosceles   done clear
  C)
   equilateral       done clear
  D)
          scalene done clear
  View Solution play_arrow

• question_answer112)
  ABC is a triangle and AD is median. If E is any point on AD, then
  A)
   Ar(ABE) = Ar(ACE)   done clear
  B)
   BE = CE done clear
  C)
   AB + BE = AC + CE done clear
  D)
  \[AE=\frac{(BE+CE)}{2}\] done clear
  View Solution play_arrow

• question_answer113)
  If E and F are any two points lying on the sides DC and AD, respectively of a parallelogram ABCD, then
  A)
   BF + CF = AE + BE done clear
  B)
   AE = BF done clear
  C)
   Ar(AEB) = Ar(BFC)   done clear
  D)
   Ar(ADE) = Ar(BEC) done clear
  View Solution play_arrow

• question_answer114)
  The ratio of the areas of two similar triangles is equal to the
  A)
   ratio of corresponding medians done clear
  B)
   ratio of corresponding sides done clear
  C)
   ratio of the squares of corresponding sides   done clear
  D)
   none of these done clear
  View Solution play_arrow

• question_answer115)
  The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends on the longer segment of the circle is equal to
  A)
  \[30{}^\circ \]   done clear
  B)
                                         \[45{}^\circ \] done clear
  C)
  \[60{}^\circ \] done clear
  D)
         \[90{}^\circ \] done clear
  View Solution play_arrow

• question_answer116)
  In the figure, \[\angle \,B\] is equal to
  A)
  \[85{}^\circ \]  done clear
  B)
  \[95{}^\circ \]   done clear
  C)
  \[70{}^\circ \] done clear
  D)
  \[115{}^\circ \]              done clear
  View Solution play_arrow

• question_answer117)
  Two secants PAB and PCD are drawn to a circle from an outside point P. Then, which of the following is true?
  A)
   PA . PB = PC + CD done clear
  B)
   PA. PB = PC . PD   done clear
  C)
   PA + PB = PC + PD done clear
  D)
   PA - PB= PC.  CD done clear
  View Solution play_arrow

• question_answer118)
  If \[\angle \,P\] and \[\angle \,Q\] are complementary in a triangle PQR, then the measure of \[\angle \,R\] is
  A)
  \[45{}^\circ \] done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[75{}^\circ \] done clear
  D)
  \[90{}^\circ \]   done clear
  View Solution play_arrow

• question_answer119)
  The point O lies inside a triangle \[\text{PQR}\] such that \[\Delta \,\text{OPQ}\], \[\Delta \,\text{OQR}\]and \[\text{AORP}\] are equal in area. Then the point O is called as
  A)
   incentre              done clear
  B)
   centroid   done clear
  C)
   circumcentre                    done clear
  D)
   orthocenter done clear
  View Solution play_arrow

• question_answer120)
  In a right angled triangle, the square of the hypotenuse is equal to twice the product of the other two sides. One of the acute angles of the triangle is
  A)
  \[40{}^\circ \] done clear
  B)
  \[42{}^\circ \] done clear
  C)
  \[44{}^\circ \] done clear
  D)
  \[45{}^\circ \]   done clear
  View Solution play_arrow

• question_answer121)
  In \[\Delta \,\text{ABC}\], O is the orthocentre and \[\angle \,\text{BOC}\,\text{=}\,\,2\angle \,\text{A}\] then the measure of \[\angle \,\text{BOC}\] is equal to
  A)
  \[120{}^\circ \]   done clear
  B)
   \[100{}^\circ \] done clear
  C)
  \[80{}^\circ \] done clear
  D)
   \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer122)
  The external bisectors of \[\angle \,\text{B}\] and \[\angle \,\text{C}\] meet in O. If \[\angle \,\text{A}\] is equal to \[50{}^\circ \], then the magnitude of \[\angle \,\text{BOC}\] is
  A)
  \[140{}^\circ \] done clear
  B)
   \[105{}^\circ \] done clear
  C)
  \[65{}^\circ \]   done clear
  D)
   \[60{}^\circ \] done clear
  View Solution play_arrow

• question_answer123)
  Two isosceles triangles have equal vertical angles and their areas are in the ratio of 9 : 16. Then their heights are in the ratio of
  A)
   9 : 16                     done clear
  B)
          16 : 9 done clear
  C)
   4 : 3                done clear
  D)
          3 : 4   done clear
  View Solution play_arrow

• question_answer124)
  In the given figure, O is the centre of the circle and\[\ge \], then
  A)
  \[m+n=90{}^\circ \]            done clear
  B)
         \[m+n=180{}^\circ \] done clear
  C)
           \[m+n=120{}^\circ \] done clear
  D)
          \[m+n=150{}^\circ \]                done clear
  View Solution play_arrow

• question_answer125)
  If the difference of two supplementary angles is \[40{}^\circ \], then the measurement of the greater angle is
  A)
  \[65{}^\circ \] done clear
  B)
         \[110{}^\circ \]   done clear
  C)
  \[130{}^\circ \] done clear
  D)
         \[220{}^\circ \] done clear
  View Solution play_arrow

• question_answer126)
  In the given figure OA, OB are opposite rays and \[\angle \,\text{AOC}\,+\angle \,\text{BOD}\,\text{=}\,\text{90}{}^\circ \], then \[\angle \,\text{COD}\] is
  A)
  \[90{}^\circ \]   done clear
  B)
  \[60{}^\circ \] done clear
  C)
  \[45{}^\circ \] done clear
  D)
  \[30{}^\circ \] done clear
  View Solution play_arrow

• question_answer127)
  If ABCDE is a regular pentagon, then the angle BDE is equal to
  A)
  \[90{}^\circ \] done clear
  B)
  \[72{}^\circ \]   done clear
  C)
  \[60{}^\circ \] done clear
  D)
         \[54{}^\circ \] done clear
  View Solution play_arrow

• question_answer128)
  Consider a cube ABCD - PQRS, if 0 is the angle between diagonal BS and the plane PQRS, then  the value of tan 0 is equal to
  A)
  \[1\]              done clear
  B)
  \[\sqrt{2}\] done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer129)
             From an external point, K tangents can be drawn to a circle, then K is equal to
  A)
   0                                             done clear
  B)
   2   done clear
  C)
   1                                             done clear
  D)
   infinity done clear
  View Solution play_arrow

• question_answer130)
  Tangents at the end points of the diameter of a circle intersect at angle Q. Q is equal to
  A)
   \[90{}^\circ \] done clear
  B)
         \[60{}^\circ \] done clear
  C)
  \[0{}^\circ \]   done clear
  D)
         \[30{}^\circ \] done clear
  View Solution play_arrow

• question_answer131)
  In the given figure (PQ is diameter), x is equal to
  A)
  \[30{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[70{}^\circ \] done clear
  D)
  \[60{}^\circ \]   done clear
  View Solution play_arrow

• question_answer132)
  In the given figure, \[\angle \,\text{MON}\,=\,\,8\text{0}{}^\circ ,\,\,\angle \,\text{MQO}\,\text{=}\,\text{20}{}^\circ \], then the measure of \[\angle \,\text{MOP}\] is
  A)
  \[40{}^\circ \]   done clear
  B)
  \[45{}^\circ \]  done clear
  C)
  \[50{}^\circ \] done clear
  D)
  \[55{}^\circ \]                       done clear
  View Solution play_arrow

• question_answer133)
  Which one of the following statements is not correct?
  A)
   If the exterior angle of a regular polygon is \[30{}^\circ \], it has 12 sides. done clear
  B)
   If the enterior and exterior angle of a regular polygon are all equal, it is a rectangle. done clear
  C)
   If the exterior angle of a regular polygon is greater than its interior angle, then it is an equilateral triangle. done clear
  D)
   In a regular pentagon, the exterior angle is half of the interior angle.   done clear
  View Solution play_arrow

• question_answer134)
  In the given figure, \[\angle \,\text{QPB}\] is
  A)
  \[60{}^\circ \] done clear
  B)
  \[45{}^\circ \] done clear
  C)
  \[30{}^\circ \] done clear
  D)
  \[15{}^\circ \]                        done clear
  View Solution play_arrow

• question_answer135)
  If the straight lines AB and XY intersect at the point O and \[\angle \,\text{AOX}\,=\,\,8\,\,\angle \,\text{XOB}\], then the four angles formed at 0 are
  A)
  \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }90{}^\circ ,\text{ }210{}^\circ \] done clear
  B)
  \[30{}^\circ ,\text{ }30{}^\circ ,\text{ }150{}^\circ ,\text{ }150{}^\circ \] done clear
  C)
  \[45{}^\circ ,\text{ }135{}^\circ ,\text{ }90{}^\circ ,\text{ }90{}^\circ \] done clear
  D)
  \[45{}^\circ ,\text{ }45{}^\circ ,\text{ }135{}^\circ ,\text{ }135{}^\circ \]   done clear
  View Solution play_arrow

• question_answer136)
  In the given diagram CE is parallel to AD and the measures of two angles at B and C have been indicated. Then \[\angle \,\text{DAB}\] is equal to
  A)
  \[30{}^\circ \]                  done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[40{}^\circ \]   done clear
  D)
   Cannot be determined        done clear
  View Solution play_arrow

• question_answer137)
  If \[l,m,n\] are three parallel lines and the transversals \[{{t}_{1}}\] and \[{{t}_{2}}\] cut the lines \[l,m,n\] at the points A, B, C and P, Q, R as shown in the figure, then
  A)
  \[\frac{AB}{BC}=\frac{PQ}{QR}\] done clear
  B)
  \[\frac{AB}{QR}=\frac{BC}{PQ}\] done clear
  C)
  \[\frac{AP}{BQ}=\frac{BQ}{CR}\] done clear
  D)
  \[\frac{AB}{PQ}=\frac{AP}{BQ}\] done clear
  View Solution play_arrow

• question_answer138)
  In the following figure, \[AE\bot BC,\,\,D\] is the mid-point of BC, then \[x\] is equal to
  A)
  \[\frac{1}{\alpha }\left[ {{b}^{2}}-{{d}^{2}}-\frac{{{a}^{2}}}{4} \right]\] done clear
  B)
  \[\frac{h+d}{3}\] done clear
  C)
  \[\frac{c+d-h}{2}\] done clear
  D)
  \[\frac{{{a}^{2}}+{{b}^{2}}+{{d}^{2}}-{{c}^{2}}}{4}\] done clear
  View Solution play_arrow

• question_answer139)
  One angle of a cyclic trapezium is double the other. What is the measure of the larger angle?
  A)
  \[60{}^\circ \] done clear
  B)
         \[80{}^\circ \] done clear
  C)
  \[75{}^\circ \] done clear
  D)
          \[120{}^\circ \]   done clear
  View Solution play_arrow

• question_answer140)
  In the given figure, \[\angle \,\text{B}\,\text{=}\angle \,\text{C}\,=\,65{}^\circ \] and \[\angle \,D\,=\,30{}^\circ \]. Then.
  A)
  BC < CA < CD done clear
  B)
  BC > CA > CD done clear
  C)
  BC < CA, CA > CD done clear
  D)
  BC > CA, CA < CD done clear
  View Solution play_arrow

• question_answer141)
  Two non-intersecting circles, one lying inside another, are of radii a and b (a > b). The minimum distance between their circumference is c. The distance between their centres is
  A)
  a - b done clear
  B)
  a - b + c done clear
  C)
  a + b - c done clear
  D)
  a - b - c done clear
  View Solution play_arrow

• question_answer142)
  Given inside a circle, whose radius is equal to 13 cm, is a point M at a distance 5 cm from the centre of the circle. A chord AB = 25 cm is drawn through M. The lengths of the segments into which the chord AB is divided by the point M in CM are
  A)
   12, 13 done clear
  B)
   14, 11 done clear
  C)
   15, 10 done clear
  D)
   16, 9   done clear
  View Solution play_arrow

• question_answer143)
  Each angle of a regular polygon of n sides contains
  A)
   4n right angles done clear
  B)
  \[\frac{2(n+1)}{n}\] right angles done clear
  C)
  \[\frac{2(n-1)}{n}\]right angles done clear
  D)
  \[\frac{2(n-2)}{n}\] right angles  done clear
  View Solution play_arrow

• question_answer144)
  The parallel sides of a trapezium are x and y in length. The length of the line segement joining the mid points of the non parallel sides is
  A)
  \[\frac{x+y}{2}\] done clear
  B)
  \[x+y\] done clear
  C)
  \[\frac{2x+3y}{2}\] done clear
  D)
  \[\frac{xy}{2}\] done clear
  View Solution play_arrow

• question_answer145)
  If O is the orthocentre of the \[\Delta \,ABC\], then
  A)
  \[\angle \,BOC=2\,\,\angle \,BAC\] done clear
  B)
  \[\angle \,BOC\,\,and\,\,\angle \,BAC\] are supplementary  done clear
  C)
  \[\angle \,BOC\,=\,\angle \,BAC\] done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer146)
  In the given figure, if AB = AC, CH = CB and \[HK\,|\,|\,BC\] , then value of \[\angle \,HCK\] is
  A)
  \[30{}^\circ \]   done clear
  B)
  \[35{}^\circ \] done clear
  C)
  \[40{}^\circ \]                                    done clear
  D)
  \[45{}^\circ \] done clear
  View Solution play_arrow

• question_answer147)
  ABODE is a regular pentagon. If AD is joined, then
  A)
   ABCD is a parallelogram. done clear
  B)
   ABCD is a rhombus. done clear
  C)
   ABCD is a cyclic trapezium.   done clear
  D)
   ABCD is not cyclic quadrilateral. done clear
  View Solution play_arrow

• question_answer148)
  Two triangles ABC and PQR are similar, if BC : CA : AB = 1 : 2 : 3, then \[\frac{\text{QR}}{\text{PR}}\] is
  A)
  \[\frac{2}{3}\] done clear
  B)
  \[\frac{1}{2}\] done clear
  C)
  \[\frac{1}{\sqrt{2}}\] done clear
  D)
  \[\frac{2}{3}\] done clear
  View Solution play_arrow

• question_answer149)
  In a triangle ABC, if angle B = \[90{}^\circ \] and D is the point in BC such that BD = 2 DC, then
  A)
  \[A{{C}^{2}}=\,A{{D}^{2}}+3C{{D}^{2}}\] done clear
  B)
  \[A{{C}^{2}}=\,A{{D}^{2}}+5C{{D}^{2}}\] done clear
  C)
  \[A{{C}^{2}}=\,A{{D}^{2}}+7C{{D}^{2}}\] done clear
  D)
  \[A{{C}^{2}}=\,A{{B}^{2}}+5B{{D}^{2}}\] done clear
  View Solution play_arrow

• question_answer150)
  If the area of two similar triangles are equal, then they are
  A)
   equilateral done clear
  B)
   isosceles done clear
  C)
   congruent   done clear
  D)
   not congruent done clear
  View Solution play_arrow

• question_answer151)
  If the given diagram, BD is the bisector of,if, then which one of the statements is not correct?
  A)
   Triangles ABD and DBE are similar done clear
  B)
  \[Area\text{ }ABD\text{ }:\text{ }Area\text{ }DBE=A{{B}^{2}}:B{{D}^{2}}\] done clear
  C)
  \[AB\times BE=B{{D}^{2}}\] done clear
  D)
  \[AB\times DE=AD\times BE\] done clear
  View Solution play_arrow

• question_answer152)
  In a triangle ABC, D and E are the midpoints of AB and AC. If the area of AABC = 60 sq cm. then the area of the A ADE is equal to
  A)
   15 sq cm           done clear
  B)
          20 sq cm done clear
  C)
   25 sq cm         done clear
  D)
          30 sq cm done clear
  View Solution play_arrow

• question_answer153)
  In \[\Delta \,ABC,D\] is drawn such that \[\Delta \,ABD\] and \[\Delta \,ACD\] are equal in area then, the AD is
  A)
   any segment drawn from A to BC done clear
  B)
   the bisector of \[\angle \,BAC\] done clear
  C)
   A median of \[\Delta \,ABC\] done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer154)
   The measure of an angle which is five times its supplement is
  A)
  \[36{}^\circ \] done clear
  B)
  \[30{}^\circ \] done clear
  C)
  \[150{}^\circ \]   done clear
  D)
         \[180{}^\circ \] done clear
  View Solution play_arrow

• question_answer155)
  A trapezium has its non parallel sides congruent, then its opposite angles are
  A)
   congruent          done clear
  B)
   supplementary   done clear
  C)
   complementary               done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer156)
  In a triangle ABC, a straight line parallel to BC intersects AB and AC at point D and E respectively. If the area of ADE is one-fifth of the area of ABC and BC = 10 cm, then DE equals
  A)
   2 cm                      done clear
  B)
          2/5 cm   done clear
  C)
   4 cm                      done clear
  D)
          4/5 cm done clear
  View Solution play_arrow

• question_answer157)
  AX, BY and CZ are the medians of \[\Delta \,ABC\] intersecting at O. If CK is drawn parallel to BY to meet AX in K, then AO is
  A)
  \[\frac{1}{4}\,AK\] done clear
  B)
  \[\frac{1}{2}\,AK\] done clear
  C)
  \[\frac{1}{3}\,AK\] done clear
  D)
  \[\frac{2}{3}\,AK\] done clear
  View Solution play_arrow

• question_answer158)
  In \[\Delta \,PQR\], if O is the orthocentre and \[\angle \,QOR\,=\,2\,\angle P\] , then \[\angle \,QOR\] is equal to
  A)
  \[90{}^\circ \] done clear
  B)
  \[120{}^\circ \]   done clear
  C)
  \[150{}^\circ \] done clear
  D)
  \[160{}^\circ \] done clear
  View Solution play_arrow

• question_answer159)
  In a quadrilateral ABCD, if the diagonals AC,BD intersect at right angles, then
  A)
  \[A{{B}^{2}}+B{{C}^{2}}=D{{C}^{2}}+D{{A}^{2}}\] done clear
  B)
  \[A{{B}^{2}}+C{{D}^{2}}=B{{C}^{2}}+D{{A}^{2}}\] done clear
  C)
  \[A{{B}^{2}}+A{{D}^{2}}=C{{B}^{2}}+C{{D}^{2}}\] done clear
  D)
  \[A{{B}^{2}}+B{{C}^{2}}=2(D{{C}^{2}}+D{{A}^{2}})\] done clear
  View Solution play_arrow

• question_answer160)
  The diagram shows two squares. If square I is transformed into square II by reflection what is the image of P?        
  A)
  A                            done clear
  B)
  B   done clear
  C)
  Q                       done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer161)
  The two diagonals of a rhombus are 24 cm and 10 cm long. The length of each side of the rhombus is
  A)
   17 cm                                   done clear
  B)
   16 cm done clear
  C)
   14 cm                                   done clear
  D)
   13 cm   done clear
  View Solution play_arrow

• question_answer162)
  A, B, C are three points on a circle such that AB is the chord and CP is perpendicular to OP, where O is the centre and P is any point on AB. The radius r of the circle is given by
  A)
  \[{{r}^{2}}=O{{P}^{2}}+AP\times CP\] done clear
  B)
  \[{{r}^{2}}=O{{P}^{2}}+AP\times PB\] done clear
  C)
  \[{{r}^{2}}=O{{P}^{2}}+PB\times PC\] done clear
  D)
  \[{{r}^{2}}=O{{P}^{2}}+P{{B}^{2}}\] done clear
  View Solution play_arrow

• question_answer163)
  ABCD is a parallelogram. All the angles of the parallelogram are bisected. If these bisectors enclose a figure PQRS, then enclosed figure is a
  A)
   parallelogram     done clear
  B)
          rectangle   done clear
  C)
   square                 done clear
  D)
          rhombus done clear
  View Solution play_arrow

• question_answer164)
  ED is chord parallel to the diameter AC of a circle. A point B is on the perimeter of the circle such that angle CBE =\[63{}^\circ \]. The angle DEC is equal to
  A)
  \[63{}^\circ \] done clear
  B)
  \[42{}^\circ \] done clear
  C)
  \[31.5{}^\circ \] done clear
  D)
         \[27{}^\circ \]   done clear
  View Solution play_arrow

• question_answer165)
  Three circles have the centres at A, B, C and each circle touches the other two externally. If AB = 5 cm, BC = 7 cm and CA = 6 cm, then the radii of three circles respectively are
  A)
   2, 3, 4                     done clear
  B)
          3, 4, 5 done clear
  C)
   2, 4, 5                                   done clear
  D)
   2, 3, 5 done clear
  View Solution play_arrow

• question_answer166)
  If P is (-3, 4) and My  Mx (P) shows the reflectior of the point P in the x-axis and then the reflectior of the image in the y-axis, then My Mx (P) is
  A)
  (3, 4)                     done clear
  B)
  (-3, -4) done clear
  C)
  (-3, 4) done clear
  D)
  (3, -4) done clear
  View Solution play_arrow

• question_answer167)
  Two equal circles in the same plane can have at the most the following numbers of common tangents
  A)
   3                                             done clear
  B)
   2 done clear
  C)
   4                               done clear
  D)
          1 done clear
  View Solution play_arrow

• question_answer168)
  If P= (8, 6) and R is the rotation through \[-90{}^\circ \] about O, then \[{{R}_{-90}}O(P)\] is
  A)
   (6,-8)                                      done clear
  B)
   (-8, -6) done clear
  C)
   (8, 6)                                     done clear
  D)
  (-8, 6) done clear
  View Solution play_arrow

• question_answer169)
  The straight lines which join the middle points of opposite sides of a quadrilateral
  A)
   Are parallel to one another done clear
  B)
   Bisect one another   done clear
  C)
   Trisect one another done clear
  D)
   None of these done clear
  View Solution play_arrow

• question_answer170)
  For a regular polygon the sum of the interior angles is twice the sum of the exterior angles, then the number of sides of the regular polygon is
  A)
   4                             done clear
  B)
          5 done clear
  C)
   6                               done clear
  D)
          8 done clear
  View Solution play_arrow

• question_answer171)
  In a parallelogram PQRS, PQ = 4.5 cm, PR = 6 cm, QS = 7.8 cm and the diagonals PR and QS intersect each other at 0, then to draw a parallelogram we have to draw first
  A)
   APQR                                   done clear
  B)
   AROS   done clear
  C)
   AQOR                                   done clear
  D)
   APRS done clear
  View Solution play_arrow

• question_answer172)
  The direct common tangents of two congruent circles are
  A)
   equal done clear
  B)
   parallel done clear
  C)
   parallel and equal   done clear
  D)
   parallel and unequal done clear
  View Solution play_arrow

• question_answer173)
  In the trapezium PQRS, PQ is parallel to RS and the diagonals intersect at O. If OP . SR=m(OR . PQ), then the value of m is
  A)
  \[\frac{1}{4}\] done clear
  B)
  \[\frac{1}{3}\] done clear
  C)
   \[1\]                        done clear
  D)
  \[\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer174)
  The sides of a triangle are in the ratio 4 : 6 : 7 Then                                   
  A)
   The triangle is obtuse-angled done clear
  B)
   The triangle is acute-angled   done clear
  C)
   The triangle is right-angled done clear
  D)
   The triangle is impossible done clear
  View Solution play_arrow

• question_answer175)
  A circle has two equal chords AB and AC. Chord AD cuts BC in E. If AC = 12 cm. and AE = 8 cm., then AD is equal to
  A)
   27                          done clear
  B)
          24 done clear
  C)
   21                          done clear
  D)
          18   done clear
  View Solution play_arrow

• question_answer176)
  If X, Y, Z, P are points on a line, X, Y have coordinates -7,11 with respect to an origin 0 on the line and XZ = ZY = PY = 9, ZP = 18, then which one of the following is the correct sequence ?
  A)
  \[X-Z-P-Y\] done clear
  B)
  \[Y-Z-X-P\] done clear
  C)
  \[P-Z-X-Y\] done clear
  D)
  \[P-Y-Z-X\] done clear
  View Solution play_arrow

• question_answer177)
  A, B, C, D are four points in a straight line. Distance from A to B is 10, B to C is 5, C to D is 4 and A to D is 1. Which one of the following is the correct sequence of the points?
  A)
  \[A-B-C-D\] done clear
  B)
  \[A-C-B-D\] done clear
  C)
  \[A-D-C-B\] done clear
  D)
  \[A-C-D-B\] done clear
  View Solution play_arrow

• question_answer178)
  If the sum of all interior angles of a convex polygon is 1440., then the number of sides of the polygon is
  A)
   8                             done clear
  B)
          10 done clear
  C)
   11                          done clear
  D)
          12   done clear
  View Solution play_arrow

• question_answer179)
  One angle of a seven-sided polygon is 114. And each of the other six angles is \[x{}^\circ \]. The value of \[x\] is
  A)
  \[114{}^\circ \] done clear
  B)
  \[121{}^\circ \] done clear
  C)
  \[131{}^\circ \]   done clear
  D)
   \[151{}^\circ \] done clear
  View Solution play_arrow

• question_answer180)
  Given AB, CD and EF straight lines intersecting at the point O. If \[a=c<45\], then
  A)
   EF bisects \[\angle \,BOD\] done clear
  B)
   CD bisects \[\angle \,AOF\] done clear
  C)
   AB bisects \[\angle \,COD\]            done clear
  D)
   CD bisects \[\angle \,EOB\] done clear
  View Solution play_arrow

• question_answer181)
  The angle between the internal bisector and the external of an angle is
  A)
  \[60{}^\circ \] done clear
  B)
  \[90{}^\circ \]   done clear
  C)
  \[120{}^\circ \] done clear
  D)
  \[135{}^\circ \] done clear
  View Solution play_arrow

• question_answer182)
  AB and CD are parallel straight lines. EG intersects the lines AB and CD at F and G respectively If \[\angle \,AFE=60{}^\circ \] and the straight line HI bisects \[\angle \,EGD\], then \[\angle DGI\] is  
  A)
  \[60{}^\circ \] done clear
  B)
  \[120{}^\circ \]   done clear
  C)
  \[130{}^\circ \] done clear
  D)
  \[140{}^\circ \]                           done clear
  View Solution play_arrow

• question_answer183)
  BD is a median of a triangle ABC. F is a point on AB such that CF intersects BD at E and BE = ED. If BF = 5 cm. BA is equal to
  A)
   10                                          done clear
  B)
   12 done clear
  C)
   15                            done clear
  D)
          17 done clear
  View Solution play_arrow

• question_answer184)
  M is a point on an arc BC of a circle which circumscribes an equilateral triangle ABC. Then AM is
  A)
   equal to BM + CM   done clear
  B)
   less than BM + CM done clear
  C)
   greater than BM + CM done clear
  D)
   equal to BM + MC done clear
  View Solution play_arrow

• question_answer185)
  The perimeter of a triangle is
  A)
   greater than the sum of its altitudes   done clear
  B)
   less than the sum of its altitudes done clear
  C)
   equal to the sum of its altitudes done clear
  D)
   none of these done clear
  View Solution play_arrow

• question_answer186)
  In a right-angled triangle \[ABC,\,\,\angle BCA=90{}^\circ \]. CD is perpendicular from C to AB. By using the concept of area or areas of triangles, which one of the following relationships holds good?
  A)
  \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}-\frac{1}{C{{A}^{2}}}\] done clear
  B)
  \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}+\frac{1}{C{{A}^{2}}}\] done clear
  C)
  \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}-\frac{1}{C{{A}^{2}}}\] done clear
  D)
  \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}+\frac{1}{C{{A}^{2}}}\] done clear
  View Solution play_arrow

• question_answer187)
  In a quadrilateral PQSR, with a diagonal PS, if QS = SR and \[\angle \,\text{QSP = }\angle \,\text{RSP}\], then consider the following statements:  

  Assertion (A): \[\angle \,\text{QPS = }\angle \,\text{RPS}\]

  Reason (R): Triangles QPS and RPS are congruent.

    Of these statements:
  A)
   both A and R are true and R is the correct explanation of A   done clear
  B)
   both A and R are true but R is not a correct explanation of A done clear
  C)
   A is true, but R is false done clear
  D)
   A is false, but R is true done clear
  View Solution play_arrow

• question_answer188)
  \[\Delta \,ABC\] is congruent of \[\Delta \,DEF\], if
  A)
  \[AB=4=DE,\,AC=6=DF,\,\,\angle A=\angle D\,\] done clear
  B)
  \[AB=4=DE,\,AC=6=DF,\,\,\angle B=\angle E\,\] done clear
  C)
  \[AB=6=DE,\,AC=4=DF,\,\,\angle C=\angle F\,\] done clear
  D)
  \[AB=4=DE,\,AC=6=DF,\,\,\angle C=\angle F\,\] done clear
  View Solution play_arrow

• question_answer189)
  The triangle ABC has AB = 5 cms, AC = 8 cms and BC = 9 cms. Then
  A)
   the triangle ABC is obtuse angled done clear
  B)
   the triangle ABC is not obtuse angled   done clear
  C)
   the triangle ABC is right-angled done clear
  D)
   none of the above statements is correct done clear
  View Solution play_arrow

• question_answer190)
  Three sides of a triangle are 6 cm, 12 cm and 13 cm; then
  A)
   all three angles are acute   done clear
  B)
   one angle is a right angle and others acute done clear
  C)
   one angle is obtuse and others acute done clear
  D)
   one angle is obtuse, one acute and one right angle done clear
  View Solution play_arrow

• question_answer191)
  ABCD is a quadrilateral with unequal sides, unequal diagonals and unequal angles. E, F, G, H are the middle points of the four sides, then EFGH is a
  A)
   quadrilateral with unequal sides done clear
  B)
   parallelogram   done clear
  C)
   rhombus done clear
  D)
   rectangle done clear
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• question_answer192)
  P and Q are the mid points of the sides AB and BC respectively of the triangle ABC, right-angled at B, then
  A)
  \[\text{A}{{\text{Q}}^{\text{2}}}\text{ + C}{{\text{P}}^{\text{2}}}\text{ = A}{{\text{C}}^{\text{2}}}\] done clear
  B)
  \[\text{A}{{\text{Q}}^{\text{2}}}\text{ + C}{{\text{P}}^{\text{2}}}\text{ = }\frac{4}{5}\,\,\text{A}{{\text{C}}^{\text{2}}}\] done clear
  C)
  \[\text{A}{{\text{Q}}^{\text{2}}}-\text{C}{{\text{P}}^{\text{2}}}\text{ = }\frac{4}{5}\,\,\text{A}{{\text{C}}^{\text{2}}}\] done clear
  D)
  \[\text{A}{{\text{Q}}^{\text{2}}}\text{+ C}{{\text{P}}^{\text{2}}}\text{ = }\frac{5}{4}\,\,\text{A}{{\text{C}}^{\text{2}}}\] done clear
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• question_answer193)
  If in a quadrilateral, the diagonals bisect each other, then which one of the following conclusions about the quadrilateral is the most appropriate one?
  A)
   It is a parallelogram   done clear
  B)
   It is a square done clear
  C)
   It is a rectangle done clear
  D)
   None of these done clear
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• question_answer194)
  In the given figure, if AL is the bisector of \[\Delta \,ABC\], then AB is a
  A)
  7 cm                      done clear
  B)
  10  cm                      done clear
  C)
  15 cm                   done clear
  D)
  22.50 cm                     done clear
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• question_answer195)
  If D, E, F are the midpoints of the sides BC, CA, AB respectively of \[\Delta \,ABC\], then the ratio area \[\Delta \,DEF\]: area \[\Delta \,ABC\] is equal to
  A)
  1 : 2 done clear
  B)
  1 : 3 done clear
  C)
  2 : 3 done clear
  D)
  1 : 4 done clear
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• question_answer196)
  Match List-I with List-II and select the correct answer using the codes given below the lists:  

  List-I (Set of lines)	List-II (Intersection points of the set of lines)
  A. Median lines	1. circumcentre
  B. Altitude lines	2. incentre
  C. Bisectors of angles	3. orthocentre
  D. Perpendicular bisectors of the sides	4. centroid

  A)
  A-3         B-4         C-1         D-2 done clear
  B)
  A-4         B-3         C-2         D-1 done clear
  C)
  A-1         B-2         C-3         D-4 done clear
  D)
  A-2         B-1         C-4         D-3 done clear
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• question_answer197)
  The medians AL, BM and CN of a \[\Delta \,ABC\] intersect at P. If AL = 5, then the length of AP is
  A)
  \[\frac{5}{13}\] done clear
  B)
  \[\frac{5}{4}\] done clear
  C)
  \[\frac{15}{2}\] done clear
  D)
  \[\frac{10}{3}\] done clear
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• question_answer198)
  In \[\Delta \,ABC\], \[AB=AC\] and AD is the median. Find which of the points lies on AD.  

  (i) Centroid

  (ii) Incentre

  (iii) Circumcentre

  (iv) Orthocentre

    Correct answer is
  A)
   (i), (ii), (iii)         done clear
  B)
  (i), (ii), (iv) done clear
  C)
  (ii) (iii), (iv)        done clear
  D)
  (i), (ii) (iii) (iv)   done clear
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