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.

251.

Two poles of ht.

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">a+b</td></tr><tr><td style="text-align: center;">ab</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">p</td></tr><tr><td style="text-align: center;">a+b</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">ab</td></tr><tr><td style="text-align: center;">a+b</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">a+b</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;">a+b</td></tr><tr><td style="text-align: center;">p</td></tr></table>
Discussion
252.

The centre of a circle of radius 5 cm is O . T is an external point where OT = 13 cm and OT intersects the circle at point E. AB is a tangent at point E. What is the length of AB ?

A. <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>
B. <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>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>40</center></td><td rowspan="2">cm</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>16</center></td><td rowspan="2">cm</td></tr><tr><td style="text-align: center;">3</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>40</center></td><td rowspan="2">cm</td></tr><tr><td style="text-align: center;">3</td></tr></table>
Discussion
253.

In a circular lawn, there is a

A. 16 m
B. 6 m
C. 10 m
D. 8 m
E. None of these
Answer» D. 8 m
Discussion
254.

Of all the chords of a circle passing through a given point in it, the smallest is that which :

A. Is trisected at the point
B. Is bisected at the point
C. Passes through the centre
D. None of these
Answer» E.
Discussion
255.

ABCD

A. parallelogram
B. rhombus
C. square
D. rectangle
E. None of these
Answer» B. rhombus
Discussion
256.

In the figure,

A. BAC
B. 2 BAC
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1</td><td rowspan="2"> BAC</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;">1</td><td rowspan="2"> BAC</td></tr><tr><td style="text-align: center;">3</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"> BAC</td></tr><tr><td style="text-align: center;">3</td></tr></table>
Discussion
257.

If, in the following figure, PA = 8 cm, PD = 4 cm, CD equal to 3 cm, then AB is :

A. 3.0 cm
B. 3.5 cm
C. 4.0 cm
D. 4.5 cm
E. None of these
Answer» E. None of these
Discussion
258.

In the given figure, what is the length of

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bc</center></td></tr><tr><td style="text-align: center;">b<sup>2</sup>+c<sup>2</sup></td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">b<sup>2</sup>+c<sup>2</sup></td></tr><tr><td style="text-align: center;">bc</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"> b<sup>2</sup>+c<sup>2</sup></td></tr><tr><td style="text-align: center;">bc</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>bc</center></td></tr><tr><td style="text-align: center;"> b<sup>2</sup>+c<sup>2</sup></td></tr></table>
E. None of these
Answer» E. None of these
Discussion
259.

In a triangle ABC, A = x , B = y and C = (y + 20) . If 4x y = 10, then the triangle is :

A. Right-angle
B. Obtuse-angled
C. Equilateral
D. None of these
Answer» B. Obtuse-angled
Discussion
260.

We have an angle of 2

A. <table><tr><td rowspan="2">2</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1 </td><td rowspan="2"> 4</td></tr><tr><td style="text-align: center;">2</td></tr></table>
B. <table><tr><td rowspan="2">2</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1 </td><td rowspan="2"> 3</td></tr><tr><td style="text-align: center;">2</td></tr></table>
C. <table><tr><td rowspan="2">2</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1 </td><td rowspan="2"> 2</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. <table><tr><td rowspan="2">2</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">1 </td><td rowspan="2"> 5</td></tr><tr><td style="text-align: center;">2</td></tr></table>
E. None of these
Answer» E. None of these
Discussion
261.

Two circles of unit radius touch each other and each of them touches internally a circle of radius two, as shown in the following figure. The radius of the circle which thouches all the three circles:

A. 5
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;">3</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;">2</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;">2</td></tr><tr><td style="text-align: center;">5</td></tr></table>
E. None of these
Answer» D. <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
262.

In a quadrilateral ABCD, B = 90 and AD

A. 90
B. 60
C. 30
D. 20
E. None of these
Answer» B. 60
Discussion
263.

In any triangle ABC the internal bisector of ABC and the external bisector of other base angle meet at point E. Then BEC = ?

A. A
B. 2 A
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> A</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;"><center>1</center></td><td rowspan="2"> B</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> B</td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
264.

PQRS is a rhombus in which SPQ = 64 . Equilateral triangles PXQ and QYR are drawn outside the rhombus on sides PQ and QR. Calculate the magnitude of the angle QXY.

A. 26
B. 28
C. 30
D.
E. 45
Answer» C. 30
Discussion
265.

In any triangle PQR, PS is the internal bisector of QPR and PT QR then TPS = ?

A. Q R
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">( Q + R)</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">( Q R)</td></tr><tr><td style="text-align: center;">2</td></tr></table>
D. Q + R
Answer» D. Q + R
Discussion
266.

AC is the diameter of a circumcircle of ABC. Chord ED is parallel to the diameter AC. If CBE = 50 , then the measure of DEC is

A. 50
B. 90
C. 60
D.
E. 40
Answer» E. 40
Discussion
267.

Two concentric circles are drawn with radii 12 cm and 13 cm. What will be the length of any chord of the larger circle that is tangent to the smaller circle?

A. 5 cm
B. 8 cm
C. 10 cm
D. 25 cm
Answer» D. 25 cm
Discussion
268.

If PA and PB are tangents to the circle with centre O such that APB = 50 , then OAB is equal to

A. 25
B. 30
C. 40
D. 50
Answer» B. 30
Discussion
269.

A, B and C are three points on a circle with centre O. The tangent at C meets BA produced to T. If ATC = 30 and ACT = 48 , then what is the value of AOB ?

A. 78
B. 96
C. 102
D. 108
Answer» E.
Discussion
270.

The chord AB of a circle of centre O subtends an angle with the tangent at A to the circle. Then measure of ABO is :

A.
B. 90
C. 90 +
D. 2 (180 )
Answer» C. 90 +
Discussion
271.

A circle has its centre at O. A tangent drawn from a point P, which is situated outside the circle, touches the circle at A. If PA = 4 cm and PO = 5 cm, then the length of the radius of the circle is

A. 1 cm.
B. 2 cm.
C. 3 cm.
D. 4 cm.
Answer» D. 4 cm.
Discussion
272.

PT is a tangent to a circle with centre O and radius 6 cm. If PT is 8 cm then length of OP is

A. 10 cm.
B. 12 cm.
C. 16 cm.
D. 9 cm.
Answer» B. 12 cm.
Discussion
273.

From an external point two tangents to a circle are drawn. The chord passing through the points of contact subtends an angle 72 at the centre. The angle between the tangents is

A. 36
B. 72
C. 108
D. 144
Answer» D. 144
Discussion
274.

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and RST = 65 , the PTS = ?

A. 65
B. 130
C. 115
D. 55
Answer» D. 55
Discussion
275.

ABC is inscribed in a circle so that BC is diameter. The tangent at a point C intersects BA when produced at a point D. If ABC = 36 then the value of ADC is

A. 36
B. 44
C. 48
D. 54
Answer» E.
Discussion
276.

There are two equal circles of radius 3 cm each and distance between their centres is 10 cm. The length of one of their transverse common tangents is

A. 7 cm
B. 9 cm
C. 10 cm
D. 8 cm
Answer» E.
Discussion
277.

A and B are the centres of two circles with radii 11 cm and 6 cm respectively. A common tangent touches these circles at P and Q respectively. If AB = 13 cm., then the length of PQ is

A. 13 cm.
B. 17 cm.
C. 8.5 cm.
D. 12 cm.
Answer» E.
Discussion
278.

2 equal tangents PA and PB are drawn from an external point P on a circle with centre O. What is the length of each tangent, if P is 12 cm from the centre and the angle between the tangents is 120 ?

A. 24 cm.
B. 6 cm.
C. 8 cm.
D. Cannot be determined
Answer» C. 8 cm.
Discussion
279.

The length of a tangent from an external point to a circle is 5

A. 5 units
B. 15 units
C. -5 units
D. -15 units
Answer» B. 15 units
Discussion
280.

Two circles are of radii 7 cm and 2 cm their centres being 13cm apart. Then the length of direct common tangent to the circles between the points of contact is

A. 12 cm
B. 15 cm
C. 10 cm
D. 5 cm
Answer» B. 15 cm
Discussion
281.

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to diameter of the circle, then APB is

A. 45
B. 90
C. 30
D. 60
Answer» E.
Discussion
282.

ST is a tangent to the circle at P and QR is a diameter of the circle. If RPT = 50 , then the value of SPQ is

A. 40
B. 60
C. 80
D. 100
Answer» B. 60
Discussion
283.

The distance between the centres of two circles with radii 9 cm and 16 cm is 25 cm. The length of the segment of the tangent between them is

A. 24 cm
B. 25 cm
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>50</center></td><td rowspan="2"> cm.</td></tr><tr><td style="text-align: center;">3</td></tr></table>
D. 12 cm
Answer» B. 25 cm
Discussion
284.

DE is a tangent to the circumcircle of ABC at the vertex A such that DE|| BC. If AB = 17 cm, then the length of AC is equalto

A. 16.0 cm
B. 16.8 cm
C. 17.3 cm
D. 17 cm
Answer» E.
Discussion
285.

If ABCD be a rhombus, AC is its smallest diagonal and ABC = 60 , find length of a side of the rhombus when AC = 6 cm.

A. 6 cm.
B. 3 cm.
C. 62cm.
D. 33 cm.
Answer» B. 3 cm.
Discussion
286.

ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If ABC = 75 then the measure of BCD is :

A. 75
B. 95
C. 45
D. 105
Answer» B. 95
Discussion
287.

If the parallel sides of a trapezium are 8 cm. and 4 cm., M and N are the mid-points of the diagonals of the trapezium, then length of MN is

A. 12 cm.
B. 6 cm.
C. 1 cm.
D. 2 cm.
Answer» E.
Discussion
288.

AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If BAP = ABQ, then ABQP is a :

A. cyclic square
B. cyclic trapezium
C. cyclic rhombus
D. cyclic rectangle
Answer» C. cyclic rhombus
Discussion
289.

The length of two chords AB and AC of a circle are 8 cm and 6 cm and BAC = 90 , then the radius of circle is

A. 25 cm
B. 20 cm
C. 4 cm
D. 5 cm
Answer» F.
Discussion
290.

The length of a chord of a circle is equal to the radius of the circle. The angle which this chord subtends in the major segment of the circle is equal to

A. 30
B. 45
C. 60
D. 90
Answer» B. 45
Discussion
291.

ABCD is a cyclic trapezium in which AD || BC. If ABC = 70 , then BCD is

A. 110
B. 80
C. 70
D. 90
Answer» D. 90
Discussion
292.

ABCD is a cyclic trapezium with AD || BC. If A = 105 , then other three angles are

A. B = 75 , C = 75 , D = 105
B. B = 105 , C = 75 , D = 75
C. B = 75 , C = 105 , D = 75
D. B = 105 , C = 105 , D = 75
Answer» B. B = 105 , C = 75 , D = 75
Discussion
293.

The length of the chord of a circle is 8 cm and perpendicular distance between centre and the chord is 3 cm. Then the radius of the circle is equal to :

A. 4 cm
B. 5 cm
C. 6 cm
D. 8 cm
Answer» C. 6 cm
Discussion
294.

Each of the circles of equal radii with centres A and B pass through the centre of one another circle they cut at C and D then DBC is equal to

A. 60
B. 100
C. 120
D. 140
Answer» D. 140
Discussion
295.

If two equal circles whose centres are O and O', intersect each other at the point A and B, OO' = 12 cm and AB = 16 cm, then the radius of the circle is

A. 10 cm
B. 8 cm
C. 12 cm
D. 14 cm
Answer» B. 8 cm
Discussion
296.

Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is

A. 10 cm
B. 18 cm
C. 12 cm
D. 16 cm
Answer» C. 12 cm
Discussion
297.

A, B, C are three points on the circumference of a circle and if

A. 10 cm
B. 5 cm
C. 20 cm
D. 15 cm
Answer» C. 20 cm
Discussion
298.

In ABC, ABC = 70 , BCA = 40 . O is the point of intersection of the perpendicular bisectors of the sides, then the angle BOC is

A. 100
B. 120
C. 130
D. 140
Answer» E.
Discussion
299.

O is the centre of the circle, AB is a chord of the circle, OM AB. If AB = 20 cm, OM = 2 11 cm, then radius of the cir-cle is

A. 15 cm
B. 12 cm
C. 10 cm
D. 11 cm
Answer» C. 10 cm
Discussion
300.

In a right angled triangle, the circumcentre of the triangle lies

A. inside the triangle
B. outside the triangle
C. on midpoint of the hypotenuse
D. on one vertex
Answer» D. on one vertex
Discussion