Explore topic-wise MCQs in Aptitude.

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.

201.

In the following figure, B : C = 2 : 3, find B + C.

A. 120
B. 52
C. 78
D. 130
E. None of these
Answer» E. None of these
Discussion
202.

In ABC, the angle bisectors of B and C meet at O. If A = 70 , then BOC is equal to:

A. 135
B. 125
C. 115
D. 110
E. None of these
Answer» C. 115
Discussion
203.

D and E are the points on the sides AB and AC respectively of ABC such that AD = 8 cm, BD = 12 cm, AE = 6 cm and EC = 9 cm. Then find BC/ DE.

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">5</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;">2</td></tr><tr><td style="text-align: center;">5</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">5</td></tr><tr><td style="text-align: center;">7</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">5</td></tr><tr><td style="text-align: center;">3</td></tr></table>
E. None of these
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">2</td></tr><tr><td style="text-align: center;">5</td></tr></table>
Discussion
204.

In the given figure, AB || DC, find the value of x.

A. x = 8
B. x = 9
C. x = 8 or 9
D. x = 10
E. None of these
Answer» D. x = 10
Discussion
205.

If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:

A. Trapezium
B. Rectangle
C. Square
D. circle
E. None of these
Answer» C. Square
Discussion
206.

In the given figure, B = C = 55 and D = 25 . Then:

A. BC < CA < CD
B. BC > CA > CD
C. BC < CA, CA > CD
D. BC > CA, CA < CD
E. None of these
Answer» E. None of these
Discussion
207.

The area of two similar

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">11</td></tr><tr><td style="text-align: center;">9</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">22</td></tr><tr><td style="text-align: center;">9</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">11</td></tr><tr><td style="text-align: center;">18</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">33</td></tr><tr><td style="text-align: center;">6</td></tr></table>
E. None of these
Answer» B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">22</td></tr><tr><td style="text-align: center;">9</td></tr></table>
Discussion
208.

If the sides of a triangle are produced then the sum of the exterior angles i.e.,

A. 180
B. 90
C. 360
D. 270
E. None of these
Answer» D. 270
Discussion
209.

In the given figure, side

A. A - B
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( A + B)</td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. A + B
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( A - B)</td></tr><tr><td style="text-align: center;">2</td></tr></table>
E. None of these
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2">( A - B)</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
210.

In fig,

A. 1 : 2
B. 2 : 1
C. 3 : 1
D. 1 : 3
E. None of these
Answer» E. None of these
Discussion
211.

PQ is a chord of length 8 cm, of a circle with centre O and of radius 5 cm. The tangents at P and Q intersect at a point T. The length of TP is

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>20</center></td><td rowspan="2"> cm.</td></tr><tr><td style="text-align: center;">3</td></tr></table>
B.
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>21</center></td><td rowspan="2"> cm.</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;"><center>10</center></td><td rowspan="2"> cm.</td></tr><tr><td style="text-align: center;">3</td></tr></table>
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>15</center></td><td rowspan="2"> cm.</td></tr><tr><td style="text-align: center;">4</td></tr></table>
Answer» B.
Discussion
212.

The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D and the bigger circle at E. Point A is joined to D. The length of AD is

A. 20 cm
B. 19 cm
C. 18 cm
D. 17 cm
Answer» C. 18 cm
Discussion
213.

AB is a diameter of a circle. C is a point on the tangent drawn at A. If AB = 8 cm and AC = 6 cm, then the length of BC is :

A. 10 cm.
B. 14 cm.
C. 5 cm.
D. 7 cm.
Answer» B. 14 cm.
Discussion
214.

The distance between the centres of two circles having radii 8 cm and 3 cm, is 13 cm. The length (in cm) of the direct common tangent of the two circles is

A. 15
B. 16
C. 18
D. 12
Answer» E.
Discussion
215.

AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If CAB = 34 , then measure of CBA is

A. 56
B. 34
C. 68
D. 124
Answer» B. 34
Discussion
216.

If two circles of radii 9 cm and 4 cm touch externally, then the length of a common tangent is

A. 5 cm
B. 7 cm
C. 8 cm
D. 12 cm
Answer» E.
Discussion
217.

In a circle with centre O, AB is a chord, and AP is a tangent to the circle. If AOB = 140 , then the measure of PAB is

A. 35
B. 55
C. 70
D. 75
Answer» D. 75
Discussion
218.

Two circles with radii 25 cm and 9 cm touch each other externally. The length of the direct common tangent is

A. 34 cm
B. 30 cm
C. 36 cm
D. 32 cm
Answer» C. 36 cm
Discussion
219.

AC is transverse common tangent to two circles with centres P and Q and radii 6 cm and 3 cm at the point A and C respectively. If AC cuts PQ at the point B and AB = 8cm then the length of PQ is :

A. 13 cm
B. 12 cm
C. 10 cm
D. 15 cm
Answer» E.
Discussion
220.

XY and XZ are tangents to a circle, ST is another tangent to the circle at the point R on the circle, which intersects XY and XZ at S and T respectively. If XY = 15 cm and TX = 9 cm, then RT is

A. 4.5 cm
B. 7.5 cm
C. 6 cm
D. 3 cm
Answer» D. 3 cm
Discussion
221.

In the given figure, AM BC and AN is the bisector of A. What is the measure of MAN.

A. 17.5
B. 15.5
C. 20
D. 25
E. None of these
Answer» B. 15.5
Discussion
222.

Two circles of radii 5 cm and 3cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line joining the centers of the circles is:

A. 5 : 3
B. 3 : 5
C. 2.5 : 1.5
D. 1.5 : 2.5
Answer» B. 3 : 5
Discussion
223.

O is the centre of a circle and AB is the tangent to it touching at B. If OB = 3 cm. and OA = 5 cm, then the measure of AB in cm is

A.
B. <span style=" text-decoration: overline;">34</span>
C. 2
D. 8
E. 4
Answer» E. 4
Discussion
224.

AB and AC are tangents to a circle with centre O. A is the external point of the circle. The line AO intersect the chord BC at D. The measure of the BDO is

A. 60
B. 90
C. 45
D. 75
Answer» C. 45
Discussion
225.

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

A. 8.5 cm
B. 13 cm
C. 12 cm
D. 17 cm
Answer» D. 17 cm
Discussion
226.

A point Q is 13 cm from the centre of a circle. The length of the tangent drawn from Q to a circle is 12 cm. The distance of Q from the nearest point of the circle is

A. 7 cm
B. 8 cm
C. 5 cm
D. 12 cm
Answer» C. 5 cm
Discussion
227.

If PA and PB are two tangents to a circle with centre O such that APB = 80 , then, AOP = ?

A. 40
B. 50
C. 60
D. 70
Answer» C. 60
Discussion
228.

The distance between centres of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, then the length of the line segment PQ is :

A. 11.9 cm
B. 12 cm
C. 11.58 cm
D. 11.5 cm
Answer» C. 11.58 cm
Discussion
229.

How many common tangents can be drawn on two circles touching each other externally?

A. Infinity
B. 0
C. 2
D. 3
Answer» E.
Discussion
230.

If PQ and PR be the two tangents to a circle with centre O such that QPR = 120 , then POQ is :

A. 90
B. 45
C. 30
D. 60
Answer» D. 60
Discussion
231.

T is a point on the common tangents at P of two circles and if TA and TB are respectively the other tangents at A and B to the two circles drawn from the point T then

A. TA = 2 TB
B. TA = TB
C. <table><tr><td rowspan="2"> TA = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">TB</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. 3TA = TB
Answer» C. <table><tr><td rowspan="2"> TA = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">TB</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
232.

The radius of two concentric circles are 17cm and 10cm. A straight line ABCD intersects the larger circle at the point A and D and intersects the smaller circle at the points B and C. If BC = 12 cm, then the length of AD (in cm) is :

A. 20
B. 24
C.
D. 30
E. 34
Answer» D. 30
Discussion
233.

O is the circumcentre of triangle ABC. If BAC = 50 then OBC is

A. 50
B. 100
C.
D. 130
E. 40
Answer» E. 40
Discussion
234.

The radii of two concentric circles are 17 cm and 25 cm. A straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16 cm, then the length (in cm.) of PS is

A. 41
B. 32
C.
D. 33
E. 40
Answer» E. 40
Discussion
235.

The circumcentre of a triangle ABC is O. If BAC = 85 and BCA = 75 , then the value of OAC is

A. 40
B. 60
C. 70
D. 90
Answer» D. 90
Discussion
236.

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
Discussion
237.

If the circumradius of an equilateral triangle ABC be 8 cm, then the height of the triangle is

A. 16 cm
B. 6 cm
C. 8 cm
D. 12 cm
Answer» E.
Discussion
238.

A tree of height h metres is broken by a storm in such a way that its top touches the ground at a distance of x metres from its root. Find the height at which the tree is broken. (Here h > x)

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h + x </center></td><td rowspan="2">metre</td></tr><tr><td style="text-align: center;">2h</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h - x </center></td><td rowspan="2">metre</td></tr><tr><td style="text-align: center;">2h</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h + x </center></td><td rowspan="2">metre</td></tr><tr><td style="text-align: center;">4h</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h - x </center></td><td rowspan="2">metre</td></tr><tr><td style="text-align: center;">4h</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>h + x </center></td><td rowspan="2">metre</td></tr><tr><td style="text-align: center;">4h</td></tr></table>
Discussion
239.

If O is the circumcentre of a triangle ABC lying inside the triangle, then OBC + BAC is equal to

A. 90
B. 60
C.
D. 110
E. 120
Answer» B. 60
Discussion
240.

O is the circumcentre of the triangle ABC and BAC = 85 , BCA = 75 , then the value of OAC is

A. 55
B. 150
C.
D. 20
E. 70
Answer» E. 70
Discussion
241.

O is the circumcentre of ABC. If BAC = 85 , BCA = 75 , then OAC is equal to :

A. 60
B.
C. 70
D. 50
E. 40
Answer» C. 70
Discussion
242.

ABC is a cyclic triangle and the bisectors of BAC, ABC and BCA meet the circle at P, Q, and R respectively. Then the angle RQP is

A. <table><tr><td rowspan="2">90 - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>B</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
B. <table><tr><td rowspan="2">90 + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>B</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td rowspan="2">90 + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>C</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td rowspan="2">90 - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>A</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» B. <table><tr><td rowspan="2">90 + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>B</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
243.

PQRS is a cyclic quadrilateral. The bisectors of the angles P and R meet the circle ABCD at A and B respectively. If the radius of the circle be r units, then AB = ?

A. r
B.
C. 2r
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2">r</td></tr><tr><td style="text-align: center;">3</td></tr></table>
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td><td rowspan="2">r</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» C. 2r
Discussion
244.

A, B, C are three angles of a triangle. If A B = 15 , B C = 30 , then A, B and C are

A. 80 , 60 , 40
B. 70 , 50 , 60
C.
D. 80 , 65 , 35
E. 80 , 55 , 45
Answer» D. 80 , 65 , 35
Discussion
245.

PQRS

A. 45
B. 90
C. 100
D. 60
E. None of these
Answer» B. 90
Discussion
246.

The two sides of a right triangle containing the right angle measure

A. 3.5 cm
B. 1.75 cm
C. 1 cm
D. 0.875 cm
E. None of these
Answer» D. 0.875 cm
Discussion
247.

If one of the diagonals of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio :

A. 3 : 1
B. 2 : 1
C. 3 : 1
D. 2 : 1
E. None of these
Answer» C. 3 : 1
Discussion
248.

O is the circumcentre of a triangle ABC. The point A and th chord BC are on the opposite side of O. If BOC = 150 . Then the angle BAC is :

A. 65
B. 60
C. 70
D.
E. 75
Answer» E. 75
Discussion
249.

In the fig.

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</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;"> 2 + 2</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;">1</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"> 2 - 2</td></tr><tr><td style="text-align: center;"> 2</td></tr></table>
E. None of these
Answer» E. None of these
Discussion
250.

In a

A. <table><tr><td rowspan="2">90 -</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> A</td></tr><tr><td style="text-align: center;">2</td></tr></table>
B. <table><tr><td rowspan="2">120 +</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> A</td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td rowspan="2">90 +</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> A</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td rowspan="2">120 -</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> A</td></tr><tr><td style="text-align: center;">2</td></tr></table>
E. None of these
Answer» D. <table><tr><td rowspan="2">120 -</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> A</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion