10th Class Mathematics Related to Competitive Exam Question Bank

done Geometry Total Questions - 40

• question_answer1)
  In the shown figure, two line segments PQ and RS intersect each other at the point O such that PO = 4.8, OS = 4.2 cm, RO = 3.2 cm and \[\angle \]ORP = \[\mathbf{65}{}^\circ \], \[\angle \]POR = \[80{}^\circ \] and \[\angle \]OSQ = 35°, then find the value of OQ.
  A)
   3 cm      done clear
  B)
                                                          4.2 cm done clear
  C)
   2.8 cm              done clear
  D)
  3.6 cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer2)
  Find the value of x for which PQ || RS in shown figure.
  A)
   3                     done clear
  B)
                                  4             done clear
  C)
   5        done clear
  D)
                                                         6 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer3)
  From a point P, inside of an equilateral triangle ABC, the perpendicular istances of the three sides are 4 cm, 6 cm and 7 cm respectively. Find the perimeter of the triangle.
  A)
   56\[\sqrt{3}\]cm      done clear
  B)
                                                          24\[\sqrt{3}\]cm     done clear
  C)
   17\[\sqrt{3}\]                done clear
  D)
                                             34\[\sqrt{3}\]cm done clear
  E)
  None of these done clear
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• question_answer4)
  In a triangle ABC, P is a point on BC and from point P lines parallel to AB and AC are drawn which intersects AB and AC at R and Q respectively If RQ meets BC produced in S. Then \[\mathbf{S}{{\mathbf{P}}^{\mathbf{2}}}\] equals to _______
  A)
   3SB \[\times \] SC      done clear
  B)
                                              SB \[\times \] SC      done clear
  C)
   2SR \[\times \] RQ     done clear
  D)
                                             2SB \[\times \] SC done clear
  E)
  None of these done clear
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• question_answer5)
  Which one among the following statements is not true?
  A)
   In a triangle PQR, if S is a point on QR such that S divides QR in the ratio PQ : PR, then PS is the bisector of \[\angle \]P. done clear
  B)
   In a triangle PQR, if PS is the bisector of the exterior of angle P and meets QR produced in S, then \[\frac{QS}{RS}=\frac{PQ}{PR}\] done clear
  C)
   If a line through one vertex of a triangle divides the opposite sides in the ratio of other two sides, then the line bisects the angle at the vertex. done clear
  D)
  In a \[\Delta \]PQR, in which S is a point on QR such that \[\frac{QS}{QR}=\frac{PQ}{PR}\], then PS is bisector of \[\angle \]P. done clear
  E)
  None of these done clear
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• question_answer6)
  Find the length of altitude on the hypotenuse of a right angled triangle whose area is 60\[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\] and one of the sides containing the right angle is 15 cm.
  A)
   7.06 cm            done clear
  B)
                                  6.28 cm      done clear
  C)
   7.36 cm                        done clear
  D)
                                 6.88 cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer7)
  In a \[\Delta \] PQR, the bisector of \[\angle \] Q meets PR at T. If a line MN is drawn parallel to PR which meets PQ, QR and QT at M, N and 0 respectively, then ________
  A)
   MO.QN = QM.ON                    done clear
  B)
                      QP.NR = PM.QR done clear
  C)
   \[\frac{Area\text{ }of\text{ }\Delta QTP\text{ }}{Area\text{ }of\text{ }\Delta QTP\text{ }}=\frac{QR}{QP}\]       done clear
  D)
                                 All the above done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer8)
  In a triangle PQR (as shown below), \[\angle \]PQR = \[\mathbf{90}{}^\circ \] and QS is its bisector. If SM\[\bot \]QR then SM\[\times \](PQ + QR) is equal to _________
  A)
   PS \[\times \] SR                        done clear
  B)
                      PQ \[\times \] QR      done clear
  C)
   2PS \[\times \] SR    done clear
  D)
                                                         2PQ \[\times \] QR done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  In the shown figure, PQ || RS, find the value of x.
  A)
   3              done clear
  B)
                                              7             done clear
  C)
   5                                 done clear
  D)
  8 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  In a trapezium PQRS, PQ || RS and RS = 2PQ. MN drawn parallel to PQ meets PS in M and QR in N such that \[\frac{\mathbf{QN}}{\mathbf{NR}}\]=\[\frac{\mathbf{3}}{\mathbf{4}}\]. If diagonal QS intersects MN at O, then the ratio of \[\frac{\mathbf{MN}}{\mathbf{PQ}}\] is equal to
  A)
   \[\frac{7}{10}\]      done clear
  B)
                                                          \[\frac{10}{7}\]           done clear
  C)
   \[\frac{4}{7}\]                                                              done clear
  D)
  \[\frac{7}{4}\] done clear
  E)
  None of these done clear
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• question_answer11)
  In the shown figure, if PS, UQ and RT are each perpendicular to PR, then _______
  A)
  \[\frac{1}{a}+\frac{1}{b}=\frac{1}{c}\]                                                             done clear
  B)
   \[\frac{1}{b}+\frac{1}{c}=\frac{1}{a}\]     done clear
  C)
   \[\frac{1}{a}+\frac{1}{c}=\frac{1}{b}\]            done clear
  D)
  \[\frac{1}{c}+\frac{1}{a}=\frac{2}{b}\] done clear
  E)
  None of these done clear
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• question_answer12)
  In the shown figure, if \[\Delta \]PQR is right angled at Q and TS \[\bot \] PR. Find the lengths of PS and ST respectively.
  A)
   \[\frac{30}{13}cm\,\,and\,\,\frac{36}{13}cm\]     done clear
  B)
                      \[\frac{20}{13}cm\,\,and\,\,\frac{26}{15}cm\] done clear
  C)
   \[\frac{15}{13}cm\,\,and\,\,\frac{17}{13}cm\]    done clear
  D)
                                            \[\frac{19}{13}cm\,\,and\,\,\frac{17}{13}cm\] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer13)
  Which one among the following statements is correct?
  A)
   The area of the equilateral triangle described on the side of a square is equal to the area of the equilateral triangle described on its diagonal. done clear
  B)
   If equilateral triangles are drawn on the sides of a right triangle then the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides. done clear
  C)
   The line segments joining the mid-points of the sides of a triangle form four triangles, each of which is similar to the original triangle. done clear
  D)
  both B and C done clear
  E)
  None of these done clear
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• question_answer14)
  In the shown figure, ST || PR and ST divides triangular region PQR into two parts of equal area. Find the ratio of \[\frac{PS}{PQ}\].
  A)
   \[\frac{2-\sqrt{2}}{3}\]              done clear
  B)
                                              \[\frac{\sqrt{2}\left( \sqrt{2}-2 \right)}{2}\]   done clear
  C)
   \[\sqrt{2}+1\]       done clear
  D)
                                                        \[2-\sqrt{2}\] done clear
  E)
  None of these done clear
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• question_answer15)
  In the shown figure, an equilateral triangle QRT surmounts square PQRS. Find the value of x + y.
  A)
   \[100{}^\circ \]        done clear
  B)
                                                          \[110{}^\circ \]  done clear
  C)
   \[120{}^\circ \]                                                            done clear
  D)
  \[120{}^\circ \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  In the shown figure, MN = QP and on producing MN & QP, they intersect at R. Also, MQ || NP. If \[\angle \]NMQ = 55°, then find \[\angle \] R.
  A)
   \[50{}^\circ \]      done clear
  B)
                                                          \[70{}^\circ \]       done clear
  C)
       \[60{}^\circ \]         done clear
  D)
                                                         \[80{}^\circ \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer17)
  PQR is a triangle in which\[\angle \]PQR = \[\mathbf{90}{}^\circ \] and a perpendicular is drawn from Q to PR which intersects PR at S. If PQ = a, QR = b, PR = c and QS = p, then which one of the following is true?
  A)
   \[cp=ab\]           done clear
  B)
                                             \[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}\] done clear
  C)
   \[\frac{1}{{{p}^{2}}}=\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}-\frac{1}{{{c}^{2}}}\]                done clear
  D)
                     both A and B done clear
  E)
  None of these done clear
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• question_answer18)
  In a right angled triangle PQR right angled at P, S and T are points on PQ and PR respectively, which divide these sides on the ratio 2 : 1, then which one of the following is correct?
  A)
   \[9(Q{{T}^{2}}+R{{S}^{2}})=13\,Q{{R}^{2}}\] done clear
  B)
                                  \[9\,QT=9P{{Q}^{2}}+4\,P{{R}^{2}}\] done clear
  C)
   \[9\,R{{S}^{2}}=4\,P{{Q}^{2}}+9\,P{{R}^{2}}\] done clear
  D)
  All the above done clear
  E)
  None of these done clear
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• question_answer19)
  Which among the following statements is incorrect?
  A)
   Equal chords subtend equal angles at the centre of the circle. done clear
  B)
   The opposite angles of a cyclic quadrilateral are supplementary. done clear
  C)
   A line drawn through the end point of a radius of a circle and perpendicular to it is a tangent to the circle. done clear
  D)
  The number of common tangents to two circles touching externally is four. done clear
  E)
  None of these done clear
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• question_answer20)
  In the figure shown below, if PQ = 20 cm and \[\angle \]QPR =\[\angle \]SPR, then QR = ?    
  A)
  6 cm                 done clear
  B)
  8 cm done clear
  C)
  10 cm     done clear
  D)
  12 cm done clear
  E)
  None of these done clear
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• question_answer21)
  In the shown figure, if the angle between two chords PQ and PR is\[55{}^\circ \]then the angle between two tangents which are drawn at Q and R is ______
  A)
   \[50{}^\circ \]         done clear
  B)
                                                          \[60{}^\circ \]         done clear
  C)
     \[70{}^\circ \]          done clear
  D)
                                                         \[80{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer22)
  If PQRS is a trapezium, PR and QS are the diagonals intersecting each other at 0, then PR : QS = _______
  A)
   \[PO-RO:OQ-OS\]    done clear
  B)
                      \[PO+PS:SR+QR\] done clear
  C)
   \[P{{O}^{2}}:O{{Q}^{2}}\]      done clear
  D)
                                             \[PQ:RS\] done clear
  E)
  None of these done clear
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• question_answer23)
  In the shown figure, if PQR is an equilateral triangle and square ABCD is inscribed in it whose side is 6 cm, then by how many \[\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\] is the area of triangle more than that of the square?
  A)
   18\[\sqrt{3}\]                                        done clear
  B)
                      21           done clear
  C)
   21\[\sqrt{3}\]                done clear
  D)
                                             18 done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer24)
  If I is the in centre of a triangle PQR, where \[\angle \]PQR = \[\mathbf{65}{}^\circ \] and \[\angle \]PRQ = \[\mathbf{55}{}^\circ \], the \[\angle \]QIR is.
  A)
   \[140{}^\circ \]          done clear
  B)
                                                         \[120{}^\circ \]  done clear
  C)
           \[110{}^\circ \]    done clear
  D)
                                                         \[130{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer25)
  In a right angled triangle, the product of its two sides equals half of the square of the third side, where third side is the hypotenuse. One of the acute angles then must be
  A)
   \[15{}^\circ \]     done clear
  B)
                                                                      \[45{}^\circ \]     done clear
  C)
         \[30{}^\circ \]     done clear
  D)
                                                         \[60{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer26)
  The sum of the three altitudes of a triangle is ______
  A)
   more than the sum of three sides of the triangle. done clear
  B)
   equal to the half of the three sides of the triangle. done clear
  C)
   less than the sum of three sides of the triangle. done clear
  D)
  equal to the double of the three sides of the triangle. done clear
  E)
  None of these done clear
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• question_answer27)
  In an isosceles triangle PQR, PQ < 6 cm and PR = 12 cm, then
  A)
   QR = PR               done clear
  B)
                                             QR < PR done clear
  C)
   QR = PQ    done clear
  D)
                                                         QR > PR done clear
  E)
  None of these done clear
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• question_answer28)
  The lengths of 3 sides of a triangle are given as 12 cm, 9 cm and 15 cm. Find the length of the median to its greatest side.
  A)
   8.8 cm     done clear
  B)
                                                          8.6 cm done clear
  C)
   7.5 cm        done clear
  D)
                                                         8.2 cm done clear
  E)
  None of these done clear
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• question_answer29)
  Two equal circles of radius 14 cm intersect each other such that each passes through the centre of the other. The length of the common chord is
  A)
   12 cm   done clear
  B)
                                                          12\[\sqrt{3}\]cm done clear
  C)
   14\[\sqrt{3}\]cm     done clear
  D)
  15 cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer30)
  In a \[\Delta \]MMO, \[\angle \]MNO =\[\mathbf{90}{}^\circ \], MN: NP: PO = 3: 1: 3. If OM = 20 cm then what is the length of MP?
  A)
   \[2\sqrt{10}\]cm                                                            done clear
  B)
   \[4\sqrt{10}\]cm     done clear
  C)
   \[3\sqrt{5}\]cm              done clear
  D)
                                 \[4\sqrt{5}\]cm done clear
  E)
  None of these done clear
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• question_answer31)
  In the shown figure PQRS is a rectangle, where RQ = 24 cm, SU = 10 cm and RS = 15 cm, then PT + RT is equal to ________
  A)
   50 cm              done clear
  B)
                      48 cm       done clear
  C)
   51 cm              done clear
  D)
  38 cm done clear
  E)
  None of these done clear
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• question_answer32)
  PQR is an equilateral triangle of side 6 cm. If a circle of radius 1 cm is moving inside and along the sides of the triangle, then locus of the centre of the circle is an equilateral triangle of side _______
  A)
   5.5 cm             done clear
  B)
                                  \[(3-\sqrt{3)}\]cm   done clear
  C)
   \[(3+\sqrt{3)}\]cm         done clear
  D)
                                 \[\left( 6-2\sqrt{3} \right)\]cm done clear
  E)
  None of these done clear
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• question_answer33)
  An equilateral triangle ABC is constructed on a side AB of a square MNAB. The measure of \[\angle \] MCN can be ______
  A)
   \[30{}^\circ \]              done clear
  B)
          \[15{}^\circ \]           done clear
  C)
   \[45{}^\circ \]              done clear
  D)
         \[60{}^\circ \] done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer34)
  Diagonal PR of a rectangle PQRS is produced to the point E such that PR: RE = 2: 1. If PQ = 8 cm and QR = 6 cm, then the length of SE is ________
  A)
   \[2\sqrt{5}cm\]              done clear
  B)
   \[3\sqrt{17}cm\]    done clear
  C)
   \[3\sqrt{15}cm\]            done clear
  D)
  \[4\sqrt{19}cm\] done clear
  E)
  None of these done clear
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• question_answer35)
  In the shown figure, PQJ. RS and PS is the bisector of \[\angle \] QPM. If PQ = 3 cm and PR = 5 cm, then the length of RS is ______
  A)
   8 cm                done clear
  B)
                                              10 cm       done clear
  C)
   12 cm              done clear
  D)
                                             14 cm done clear
  E)
  None of these done clear
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• question_answer36)
  In the shown figure, AB is a tangent to the circle at A. If \[\angle \]BAC = \[\mathbf{40}{}^\circ \] and AC = BC, then \[\angle \]AED = ________
  A)
   \[{{60}^{o}}\]                        done clear
  B)
                      \[80{}^\circ \]           done clear
  C)
   \[100{}^\circ \]         done clear
  D)
                                             \[85{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer37)
  In the shown figure, two circles having centres P and Q respectively intersect at R and S. The radii PR and PS are tangents to the other Tele and radii RQ and QS are tangents to the first circle. Find \[\frac{3}{5}\angle \,PMR\].
  A)
   \[35{}^\circ \]              done clear
  B)
                                  \[70{}^\circ \]           done clear
  C)
   \[{{60}^{o}}\]            done clear
  D)
                                             \[54{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer38)
  Two sides of a triangle are 12 cm and 5 cm lone. lf the measure of third side is an integer is an obtuse triangle' then how many such triangle are possible?
  A)
   5                     done clear
  B)
                                  6            done clear
  C)
   7                     done clear
  D)
                                             8 done clear
  E)
  None of these done clear
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• question_answer39)
  In a \[\Delta \]ABC, P lies on AC such that BC = AP = BP. If \[\angle \]PBC = \[40{}^\circ \], then \[\angle \]P =?
  A)
   \[25{}^\circ \]              done clear
  B)
                                              \[30{}^\circ \]           done clear
  C)
   \[35{}^\circ \]              done clear
  D)
                                             \[40{}^\circ \] done clear
  E)
  None of these done clear
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• question_answer40)
  In the figure shown below, PQ is the diameter of the circle and \[\angle \]ORQ = \[\mathbf{30{}^\circ }\] then \[\angle \]SQR = ?
  A)
   \[{{72}^{o}}\]                        done clear
  B)
                                              \[62{}^\circ \]           done clear
  C)
   \[38{}^\circ \]              done clear
  D)
                                             \[68{}^\circ \] done clear
  E)
  None of these done clear
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