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MCQOPTIONS
This section includes 564 Mcqs, each offering curated multiple-choice questions to sharpen your Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
The length of a tangent from an external point to a circle is 5 3 unit. If radius of the circle is 5 units, then the distance of the point from the circle is |
| A. | 5 units |
| B. | 15 units |
| C. | -5 units |
| D. | -15 units |
| Answer» B. 15 units | |
| 52. |
A and B are centres of two circles of radii 11 cm and 6 cm, respectively. PQ is a direct common tangent to the circles. If AB = 13 cm, then length of PQ will be |
| A. | 8.5 cm |
| B. | 13 cm |
| C. | 12 cm |
| D. | 17 cm |
| Answer» D. 17 cm | |
| 53. |
O is the centre of a circle. P is an external point of it at a distance of 13 cm from O. The radius of the circle is 5 cm. Then the length of a tangent to the circle from P upto the point of contact is : |
| A. | |
| B. | cm. |
| C. | 10 cm. |
| D. | 12 cm. |
| E. | 8 cm. |
| Answer» D. 12 cm. | |
| 54. |
I and O are respectively the in-centre and circumcentre of a triangle ABC. The line AI produced intersects the circumcircle of ABC at the point D.
|
||||
| A. | 3 | ||||
| B. | 1 | ||||
| C. | 2 | ||||
| D. | 4 | ||||
| Answer» B. 1 | |||||
| 55. |
Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is |
| A. | 8.5 cm. |
| B. | 8 |
| C. | cm. |
| D. | 8 cm. |
| Answer» D. 8 cm. | |
| 56. |
For a triangle circumcentre lies on one of its sides. The triangleis
|
| A. | right angled |
| B. | obtused angled |
| C. | isosceles |
| D. | equilatera |
| Answer» B. obtused angled | |
| 57. |
ABC is an isosceles right angled triangle having C = 90 . If D is any point on AB, then AD2 + BD2 is equal to |
| A. | CD |
| B. | 2CD |
| C. | 3CD |
| D. | 4CD |
| Answer» C. 3CD | |
| 58. |
Chord PQ is the perpendicular bisector of radius OA of circle with centre O (A is a point on the edge of the circle). If the length of Arc PAQ = 2 /3 . What is the length of chord PQ ? |
| A. | 2 |
| B. | |
| C. | 2 |
| D. | |
| E. | 1 |
| Answer» C. 2 | |
| 59. |
Suppose ABC be a right-angled triangle where A = 90 and AD BC. If ABC = 40 cm , ACD = 10 cm and AC = 9 cm, then the length of BC is |
| A. | 12 cm |
| B. | 18 cm |
| C. | 4 cm |
| D. | 6 cm |
| Answer» C. 4 cm | |
| 60. |
In ABC, AB = BC = k, AC = 2k, then ABC is a : |
| A. | Isosceles triangle |
| B. | Right-angled triangle |
| C. | Equilateral triangle |
| D. | Right isosceles triangle |
| Answer» C. Equilateral triangle | |
| 61. |
A square is inscribed in a quarter-circle in such a manner that two of its adjacent vertices lie on the two radii at an equal distance from the centre, while the other two vertices lie on the circular arc. If the square has sides of length x, then the radius of the circle is |
| A. | |
| B. | x |
| C. | |
| Answer» E. | |
| 62. |
PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm. Then the length of the line joining the mid points of the sides AB and BC is |
| A. | 4 |
| B. | cm. |
| C. | 5 cm. |
| D. | 6 cm. |
| E. | 10 cm. |
| Answer» C. 5 cm. | |
| 63. |
If the measures of the sides of triangle are (x2 1), (x2 + 1) and 2x cm, then the triangle would be |
| A. | equilateral |
| B. | acute-angled |
| C. | isosceles |
| D. | right-angled |
| Answer» E. | |
| 64. |
The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 90 . Find the approximate length of side AC. |
| A. | 12 |
| B. | 9 |
| C. | 14 |
| D. | 16 |
| Answer» C. 14 | |
| 65. |
In a ABC, AD ,BE and CF are three medians. Then the ratio (AD + BE + CF) :
|
| A. | None of these |
| Answer» F. | |
| 66. |
In the given figure QPR = 90 , QR = 26 cm, PM = 6 cm, MR = 8 cm and PMR = 90 , find the area of PQR. |
| A. | 180 cm |
| B. | 240 cm |
| C. | 120 cm |
| D. | 150 cm |
| E. | None of these |
| Answer» D. 150 cm | |
| 67. |
ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12 5 cm and BC = 24 cm then the radius of circle is |
| A. | 10 cm. |
| B. | 15 cm. |
| C. | 12 cm. |
| D. | 14 cm. |
| Answer» C. 12 cm. | |
| 68. |
In a circle with centre O, AB and CD are two diameters perpendicular to each other. The length of chord AC is |
| A. | 2 AB |
| B. | |
| C. | AB |
| D. | |
| Answer» E. | |
| 69. |
For an equilateral triangle, the ratio of the in-radius and the ex-radius is |
| A. | 1 : 2 |
| B. | 1 : |
| C. | 1 : 3 |
| D. | 1 : |
| Answer» B. 1 : | |
| 70. |
The areas of two similar s are 81 cm2 and 144 cm2. If the largest side of the smaller is 27 cm, then the largest side of the larger is : |
| A. | 24 cm |
| B. | 48 cm |
| C. | 36 cm |
| D. | 88 cm |
| E. | None of these |
| Answer» D. 88 cm | |
| 71. |
In the given figure, |
| A. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">9</td></tr><tr><td style="text-align: center;">25</td></tr></table> |
| B. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">12</td></tr><tr><td style="text-align: center;">25</td></tr></table> |
| C. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">3</td></tr><tr><td style="text-align: center;">4</td></tr></table> |
| D. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">9</td></tr><tr><td style="text-align: center;">16</td></tr></table> |
| E. | None of these |
| Answer» E. None of these | |
| 72. |
The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the centre (in cm) is |
| A. | 13 |
| B. | 14 |
| C. | 15 |
| D. | 16 |
| Answer» C. 15 | |
| 73. |
One chord of a circle is known to be 10.1 cm. The radius of this circle must be: |
| A. | 5 cm |
| B. | greater than 5 cm |
| C. | greater than or equal to 5 cm |
| D. | less than 5 cm |
| Answer» C. greater than or equal to 5 cm | |
| 74. |
The side AB of a parallelogram ABCD is produced to E in such way that BE = AB. DE intersects BC at Q. The point Q divides BC in the ratio |
| A. | 1 : 2 |
| B. | 1 : 1 |
| C. | 2 : 3 |
| D. | 2 : 1 |
| Answer» C. 2 : 3 | |
| 75. |
If the ratio of an external angle and an internal angle of a regular polygon is 1 : 17, then the number of sides of the regular polygon is |
| A. | 20 |
| B. | 18 |
| C. | 36 |
| D. | 12 |
| Answer» D. 12 | |
| 76. |
Two circles touch externally at P. QR is a common tangent of the circles touching the circles at Q and R. Then measure of QPR is |
| A. | 60 |
| B. | 30 |
| C. | 90 |
| D. | 45 |
| Answer» D. 45 | |
| 77. |
If the chord of a circle is equal to the radius of the circle, then the angle subtended by the chord at a point on the minor arc is |
| A. | 150 |
| B. | 60 |
| C. | 120 |
| D. | 30 |
| Answer» C. 120 | |
| 78. |
N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is |
| A. | <table><tr><td rowspan="2">6</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td><td rowspan="2">cm.</td></tr><tr><td align="center">7</td></tr></table> |
| B. | <table><tr><td rowspan="2">12</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2">cm.</td></tr><tr><td align="center">7</td></tr></table> |
| C. | <table><tr><td rowspan="2">3</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td><td rowspan="2">cm.</td></tr><tr><td align="center">7</td></tr></table> |
| D. | <table><tr><td rowspan="2">10</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2">cm.</td></tr><tr><td align="center">7</td></tr></table> |
| Answer» E. | |
| 79. |
If the length of a chord of a circle is equal to that of the radius of the circle, then the angle subtended, in radians, at the centre of the circle by the chord is |
| A. | 1 |
| B. | /2 |
| C. | /3 |
| D. | /4 |
| Answer» D. /4 | |
| 80. |
Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Then the distance between their centres is |
| A. | 10 cm |
| B. | 8 cm |
| C. | 13.3 cm |
| D. | 15 cm |
| Answer» D. 15 cm | |
| 81. |
Two circles C |
| A. | 60 |
| B. | 80 |
| C. | 100 |
| D. | 120 |
| Answer» B. 80 | |
| 82. |
The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is |
| A. | 5 cm |
| B. | 6 cm |
| C. | 7 cm |
| D. | 8 cm |
| Answer» E. | |
| 83. |
In a triangle |
| A. | 2 cm |
| B. | 2.25 cm |
| C. | 2.5 cm |
| D. | 3 cm |
| E. | None of these |
| Answer» C. 2.5 cm | |
| 84. |
ABCD is a square, F is mid point of AB and E is a point on BC such that BE is one-third of BC. If area of FBE = 108 m |
| A. | 63 m |
| B. | 36 2 m |
| C. | 63 2 m |
| D. | 72 2 m |
| E. | None of these |
| Answer» C. 63 2 m | |
| 85. |
Two line segments PQ and RS intersect at X in such a way that XP = XR. If PSX = RQX, then one must have |
| A. | PR = QS |
| B. | PS = RQ |
| C. | |
| D. | XSQ = XRP |
| E. | ar( PXR) = ar( QXS) |
| Answer» C. | |
| 86. |
Let two chords AB and AC of the larger circle touch the smaller circle having same centre at X and Y. Then XY = ? |
| A. | BC |
| B. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">BC</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| C. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">BC</td></tr><tr><td style="text-align: center;">3</td></tr></table> |
| D. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">BC</td></tr><tr><td style="text-align: center;">4</td></tr></table> |
| Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">BC</td></tr><tr><td style="text-align: center;">3</td></tr></table> | |
| 87. |
If the ratio of the angles of a quadrilateral is 2 : 7 : 2 : 7, then it is a |
| A. | trapezium |
| B. | |
| C. | parallelogram |
| D. | square |
| E. | rhombus |
| Answer» C. parallelogram | |
| 88. |
In the given figure, In a |
| A. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( B + C)</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| B. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( C- B )</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| C. | B + C |
| D. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( B - C)</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| E. | None of these |
| Answer» E. None of these | |
| 89. |
The number of tangents that can be drawn to two non-intersecting circles : |
| A. | 4 |
| B. | 3 |
| C. | 2 |
| D. | 13 |
| E. | None of these |
| Answer» B. 3 | |
| 90. |
X, Y |
| A. | Rectangle |
| B. | Rhombus |
| C. | Parallelogram |
| D. | Square |
| E. | None of these |
| Answer» D. Square | |
| 91. |
The diagonals of a rectangle |
| A. | 90 |
| B. | 60 |
| C. | 100 |
| D. | 68 |
| E. | None of these |
| Answer» E. None of these | |
| 92. |
The circumcentre of a triangle is always the point of intersection of the : |
| A. | Medians |
| B. | Bisectors |
| C. | Perpendiculars |
| D. | Perpendiculars dropped from the, vertices on the opposite side of the triangle |
| E. | None these |
| Answer» C. Perpendiculars | |
| 93. |
In the following figure, If BC = 8 cm, AB = 6 cm, AC 9 cm, then DC is equal to : |
| A. | 7 cm |
| B. | 4.8 cm |
| C. | 7.2 cm |
| D. | 4.5 cm |
| E. | None of these |
| Answer» C. 7.2 cm | |
| 94. |
ABC |
| A. | BD = DC |
| B. | BD = BC |
| C. | BD = AB |
| D. | BD = AD |
| E. | None of these |
| Answer» C. BD = AB | |
| 95. |
ABC is a right angled triangle in which C = 90 . If BC = a, AB = c, CA = b and the length of perpendicular from C to AB be p, then, |
| A. | |
| B. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">p</td></tr></table> |
| C. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;">p </td></tr></table> |
| D. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">p </td></tr></table> |
| E. | None of these |
| Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">p </td></tr></table> | |
| 96. |
In center of a triangle lies in the interior of : |
| A. | an isosceles triangle only |
| B. | any triangle |
| C. | an equilateral triangle only |
| D. | a right triangle only |
| E. | None of these |
| Answer» C. an equilateral triangle only | |
| 97. |
In the given figure, which of the following is true : |
| A. | x = + + |
| B. | x + = + |
| C. | x + = + |
| D. | x + = + |
| E. | None of these |
| Answer» B. x + = + | |
| 98. |
In the given figure, the side |
| A. | A + 180 |
| B. | 180 A |
| C. | <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( A + 180 )</td></tr><tr><td style="text-align: center;">2</td></tr></table> |
| D. | A + 90 |
| E. | None of these |
| Answer» B. 180 A | |
| 99. |
If two diameters of a circle intersect each other at |
| A. | Rhombus |
| B. | Rectangle |
| C. | Square |
| D. | Parallelogram |
| E. | None of these |
| Answer» D. Parallelogram | |
| 100. |
If the sides of a right triangle are x, x + 1 and x 1, then the hypotenuse : |
| A. | 5 |
| B. | 4 |
| C. | 1 |
| D. | 0 |
| E. | None of these |
| Answer» B. 4 | |