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.

351.

Chords AB and CD of a circle intersect at E. If AE = 9 cm, BE = 12 cm and CE = 3DE, then the length of DE (in cm) is

A. 9/4
B. 4
C. 6
D. 7
Answer» D. 7
Discussion
352.

Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the centre, then the distance between them is

A. 28 cm
B. 2 cm
C. 4 cm
D. 8 cm
Answer» C. 4 cm
Discussion
353.

In a circle, a chord, 52 cm long, makes a right angle at the centre. Then the length of the radius of the circle will be

A. 2.5 cm
B. 5 cm
C. 7.5 cm
D. 10 cm
Answer» C. 7.5 cm
Discussion
354.

Chords AB and CD of a circle intersect at E and are perpendicular to each other. Segments AE, EB and ED are of lengths 2 cm, 6 cm and 3 cm respectively. Then the length of the diameter of the circle (in cm) is

A.
B. <span style=" text-decoration: overline;">65</span>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> <span style=" text-decoration: overline;">65</span></td></tr><tr><td align="center">2</td></tr></table>
D. 65
E. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>65</center></td></tr><tr><td align="center">2</td></tr></table>
Answer» B. <span style=" text-decoration: overline;">65</span>
Discussion
355.

The length of the common chord of two circles of radii 30 cm and 40 cm whose centres are 50 cm apart, is (in cm)

A. 12
B. 24
C. 36
D. 48
Answer» E.
Discussion
356.

In a circle of radius 21 cm, an arc subtends an angle of 72 at the centre. The length of the arc is

A. 21.6 cm
B. 26.4 cm
C. 13.2 cm
D. 19.8 cm
Answer» C. 13.2 cm
Discussion
357.

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and distance between them is 17 cm, then the radius of the circle is :

A. 11 cm
B. 12 cm
C. 13 cm
D. 10 cm
Answer» D. 10 cm
Discussion
358.

AB and CD are two parallel chords on the opposite sides of the centre of the circle. If

A. 17 cm
B. 15 cm
C. 16 cm
D. 18 cm
Answer» B. 15 cm
Discussion
359.

AB is the chord of a circle with centre O and DOC is a line segment originating from a point D on the circle and intersecting AB produced at C such that BC = OD. If BCD = 20 , then AOD=?

A. 20
B. 30
C. 40
D. 60
Answer» D. 60
Discussion
360.

ABC is an isosceles triangle such that AB = AC and B = 35 . AD is the median to the base BC. Then BAD is:

A. 70
B. 35
C. 110
D. 55
Answer» E.
Discussion
361.

Two chords AB and CD of a circle with centre O, intersect each other at P. If AOD = 100 and BOC = 70 , then the value of APC is

A. 80
B. 75
C. 85
D. 95
Answer» E.
Discussion
362.

The three equal circles touch each other externally. If the centres of these circles be A, B, C then ABC is

A. a right angle triangle
B. an equilateral triangle
C. an isosceles triangle
D. a scalene triangle
Answer» C. an isosceles triangle
Discussion
363.

A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.

A. 600 m
B. 160 m
C. 60 m
D. 52 m
E. None of these
Answer» D. 52 m
Discussion
364.

If ABC is an isosceles triangle with C = 90 and AC = 5 cm, then AB is :

A. 5 cm
B. 10 cm
C. 52 cm
D. 2.5 cm
Answer» D. 2.5 cm
Discussion
365.

If PQRS is a rhombus and SPQ = 50 , then RSQ is

A. 55
B. 65
C. 75
D. 45
Answer» C. 75
Discussion
366.

If O is the orthocentre of a triangle ABC and BOC = 100 , the measure of BAC is

A. 100
B. 180
C. 80
D. 200
Answer» D. 200
Discussion
367.

In a ABC, if 4 A = 3 B = 12 C, find A.

A. 22.5
B. 90
C. 67.5
D. 112.5
Answer» D. 112.5
Discussion
368.

In a triangle ABC, A = 70 , B = 80 and D is the incentre of ABC. ACB = 2x and BDC = y . The values of x and y, respectively are

A. 15, 130
B. 15, 125
C. 35, 40
D. 30, 150
Answer» C. 35, 40
Discussion
369.

I is the incentre of ABC and if BAC =70 , then BIC is

A. 140
B. 55
C. 125
D. 35
Answer» D. 35
Discussion
370.

In ABC, if BAC = 90 and AB = AC, then ABC is :

A. 30
B. 60
C. 45
D. 25
Answer» D. 25
Discussion
371.

In a triangle XYZ, which of the following conditions is true?

A. XY YZ > ZX
B. XY + YZ < ZX
C. XY YZ < XZ
D. XY + ZX < YZ
Answer» D. XY + ZX < YZ
Discussion
372.

The length of the three sides of a right angled triangle are (x 2) cm, x cm and (x + 2) cm respectively. Then the value of x is

A. 10
B. 8
C. 4
D. 0
Answer» C. 4
Discussion
373.

If the length of the three sides of a triangle are 6 cm, 8 cm and 10 cm, then the length of the median to its greatest side is

A. 8 cm
B. 6 cm
C. 5 cm
D. 4.8 cm
Answer» D. 4.8 cm
Discussion
374.

Two medians AD and BE of ABC intersect at G at right angles. If AD = 9 cm and BE = 6 cm, then the length of BD (in cm) is

A. 10
B. 6
C. 5
D.
E. 3
Answer» D.
Discussion
375.

In a ABC, if A + B = 135 and C + 2 B = 180 , then the correct relation is :

A. CA > AB
B. CA = AB
C. CA < AB
D. CA + AB = CB
Answer» B. CA = AB
Discussion
376.

In ABC, DE || AC, where D and E are two points lying on AB and BC respectively. If AB = 5 cm and AD = 3 cm, then BE : EC is

A. 2 : 3
B. 3 : 2
C. 5 : 3
D. 3 : 5
Answer» B. 3 : 2
Discussion
377.

In ABC, the height CD intersects AB at D. The mid-points of AB and BC are P and Q respectively. If AD = 8 cm and CD = 6 cm, then the length of PQ is

A. 3 cm
B.
C. 7 cm
D. 9 cm
E. 5 cm
Answer» E. 5 cm
Discussion
378.

If the measures of the angles of a triangle are in the ratio. 1 : 2 : 3 and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is

A. 20 cm.
B. 25 cm.
C. 30 cm.
D. 35 cm.
Answer» B. 25 cm.
Discussion
379.

Three sides of a triangle are 5 cm, 9 cm and x cm. The minimum integral value of x is :

A. 2
B. 3
C. 4
D. 5
Answer» E.
Discussion
380.

In an acute angled triangle ABC if sin (B + C A) = 3 and tan (C + A B) = 1, then C is equal to 2

A. 37.5
B. 67.5
C. 52.5
D. 72.5
Answer» D. 72.5
Discussion
381.

In a ABC, DE || BC. D and E lie on AB and AC respectively. If AB = 7 cm and BD = 3 cm, then find BC : DE.

A. 2 : 3
B.
C. 3 : 2
D. 3.5 : 2
E. 7 : 2
Answer» D. 3.5 : 2
Discussion
382.

In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is

A. 2 : 3
B. 2 : 1
C. 1 : 2
D. 1 : 3
Answer» D. 1 : 3
Discussion
383.

In a ABC, D and E are points on AC and BC respectively, AB and DE are perpendicular to BC. If AB = 9 cm , DE = 3 cm and AC = 24 cm, then AD is :

A. 32cm
B. 16cm
C. 8 cm
D. 4 cm
Answer» C. 8 cm
Discussion
384.

In PQR, L and M are two points on the sides PQ and PR respectively such that LM is parallel to QR. If PL = 2cm. LQ = 6 cm and PM = 1.5 cm, then MR (in cm) is

A. 0.5
B. 4.5
C. 9
D. 8
Answer» C. 9
Discussion
385.

In ABC, AD BC and AD = BD.DC. The measure of BAC is:

A. 60
B. 75
C. 90
D. 45
Answer» D. 45
Discussion
386.

In a right angled triangle if hypotenuse is 20 cm and ratio of other two sides is 4 : 3, the lengths of the sides are

A. 4 cm. and 3 cm.
B. 8 cm. and 6 cm.
C. 12 cm. and 9 cm.
D. 16 cm. and 12 cm
Answer» E.
Discussion
387.

In ABC, B is right angle, D is the mid point of the side AC. If AB = 6 cm, BC = 8 cm, then the length of BD is

A. 4 cm.
B. 5 cm.
C. 8 cm.
D. 12 cm.
Answer» C. 8 cm.
Discussion
388.

D and E are the points on the sides AB and AC respectively of a ABC and AD = 8 cm, DB = 12 cm, AE = 6 cm and EC = 9 cm, then BC is equal to :

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"> DE </td></tr><tr><td style="text-align: center;">5</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td><td rowspan="2"> DE </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>3</center></td><td rowspan="2"> DE </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>2</center></td><td rowspan="2"> DE </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>3</center></td><td rowspan="2"> DE </td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
389.

The sides of a right triangle ABC are a, b and c, where c is the hypotenuse. What will be the radius of the in circle of this triangle?

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>(a + b + c)</center></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;"><center>(a + b - c)</center></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>(b - c + a)</center></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>(a + c - b)</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>(b - c + a)</center></td></tr><tr><td style="text-align: center;">2</td></tr></table>
Discussion
390.

ABCD is a trapezium where AD|| BC. The diagonal AC and BD intersect each other at the point O. If AO = 3, CO = x 3, BO = 3x 19 and DO = x 5, the value of x is

A. 8, 9
B. 8, 9
C. 8, 9
D. 8, 9
Answer» E.
Discussion
391.

In a right angled triangle DEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

A. 3 cm.
B. 4 cm.
C. 6 cm.
D. 12 cm.
Answer» D. 12 cm.
Discussion
392.

In PQR, S and T are points on sides PR and PQ respectively such that PQR = PST. If PT = 5 cm, PS = 3 cm and TQ = 3 cm, then length of SR is

A. 5 cm
B. 6 cm
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>31</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>41</center></td><td rowspan="2">cm.</td></tr><tr><td style="text-align: center;">3</td></tr></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>41</center></td><td rowspan="2">cm.</td></tr><tr><td style="text-align: center;">3</td></tr></table>
Discussion
393.

In ABC, AB = BC = k, AC =

A. Isosceles triangle
B. Right-angled triangle
C. Equilateral triangle
D. Right isosceles triangle
Answer» C. Equilateral triangle
Discussion
394.

In ABC, B = 90 , AB = 8 cm and BC = 15 cm, then sinC = ?

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>15</center></td></tr><tr><td style="text-align: center;">17</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>8</center></td></tr><tr><td style="text-align: center;">17</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>15</center></td></tr><tr><td style="text-align: center;">8</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>8</center></td></tr><tr><td style="text-align: center;">15</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>15</center></td></tr><tr><td style="text-align: center;">8</td></tr></table>
Discussion
395.

In ABC, two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. Then ABC and DBE are

A. similar only if D lies outside the line segment AB
B. congruent only if D lies outside the line segment AB
C. always similar
D. always congruent
Answer» D. always congruent
Discussion
396.

The perimeters of two similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then AB is

A. 15 cm
B. 12 cm
C. 14 cm
D. 26 cm
Answer» B. 12 cm
Discussion
397.

XYZ is a right angled triangle and Y = 90 . If XY = 2.5 cm and YZ = 6 cm then the circumradius of XYZ is :

A. 6.5 cm
B. 3.25 cm
C. 3 cm
D. 2.5 cm
Answer» C. 3 cm
Discussion
398.

For a triangle ABC, D and E are two points on AB and AC such that AD = ( 1 / 4 )AB, AE = ( 1 / 4 )AC. If BC = 12 cm, then DE is

A. 5 cm
B. 4 cm
C. 3 cm
D. 6 cm
Answer» D. 6 cm
Discussion
399.

In ABC, DE || AC. D and E are two points on AB and CB respectively. If AB = 10 cm and AD = 4 cm, then BE : CE is

A. 2 : 3
B. 2 : 5
C. 5 : 2
D. 3 : 2
Answer» E.
Discussion
400.

Inside a triangle ABC, a straight line parallel to BC intersects AB and AC at the point P and Q respectively. If AB = 3 PB, then PQ : BC is

A. 1 : 3
B. 3 : 4
C. 1 : 2
D. 2 : 3
Answer» E.
Discussion