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.

501.

In ABC, A = 90 , BP and CQ are two medians. Then the value of BP + CQ BC

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></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></tr><tr><td style="text-align: center;">4</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></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>3</center></td></tr><tr><td style="text-align: center;">5</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><tr><td style="text-align: center;">4</td></tr></table>
Discussion
502.

O is the orthocentre of ABC. Then BOC + BAC is equal to

A. 120
B. 135
C. 180
D. 90
Answer» D. 90
Discussion
503.

ABC is isosceles having AB = AC and A = 40 . Bisectors PO and OQ of the exterior angles ABD and &Ang;ACE formed by producing BC on both sides, meet at O. Then the value of BOC is

A. 70
B. 110
C. 80
D. 55
Answer» B. 110
Discussion
504.

In ABC, AB = AC, O is a point on BC such that BO = CO and OD is perpendicular to AB and OE is perpendicular to AC. If BOD = 30 then measure of AOE is

A. 45
B. 60
C. 75
D. 30
Answer» C. 75
Discussion
505.

Let AX BC of an equilateral triangle ABC. Then the sum of the perpendicular distances of the sides of ABC from any point inside the triangle is :

A. Equal to BC
B. Equal to AX
C. Less than AX
D. Greater than AX
Answer» C. Less than AX
Discussion
506.

If the three angles of a triangle are : (x + 15 ), [ (6x / 5) + 6 ] and [ (2x / 3) + 30 ] , then the triangle is:

A. isosceles
B. right angled
C. equilateral
D. scalene
Answer» D. scalene
Discussion
507.

O is the orthocentre of ABC, and if BOC = 110 , then BAC will be

A. 110
B. 70
C. 100
D. 90
Answer» C. 100
Discussion
508.

PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is

A. 3 cm
B. 6 cm
C. 12 cm
D. 4.5 cm
Answer» C. 12 cm
Discussion
509.

ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ABC = 30 , then BCD is equal to

A. 45
B. 90
C. 30
D. 60
Answer» C. 30
Discussion
510.

An isosceles triangle ABC is rightangled at B.D is a point inside the triangle ABC. P and Q are the feet of the perpendiculars drawn from D on the side AB and AC respectively of ABC. If AP = a cm, AQ = b cm and BAD = 15 , sin 75 =

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2b</center></td></tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span>a</td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>a</center></td></tr><td style="text-align: center;">2b</td><td></td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <span style=" text-decoration: overline;">3</span>a</center></td></tr><td style="text-align: center;">2b</td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2a</center></td></tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span>b</td></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2a</center></td></tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span>b</td></table>
Discussion
511.

The measure of the angle between the internal and external bisectors of an angle is

A. 60
B. 70
C. 80
D. 90
Answer» E.
Discussion
512.

The vertical angle A of an isosceles triangle ABC is three times the angle B of it. The measure of the angle A is

A. 90
B. 108
C. 100
D. 36
Answer» C. 100
Discussion
513.

In a ABC, BC is extended upto D. ACD = 120 , B = 1/2 A. Then A is

A. 60
B. 75
C. 80
D. 90
Answer» D. 90
Discussion
514.

BE and CF are two altitudes of a triangle ABC. If AB = 6 cm, AC = 5 cm and CF = 4 cm, then the length of BE is

A. 4.8 cm
B. 7.5 cm
C. 3.33 cm
D. 5.5 cm
Answer» B. 7.5 cm
Discussion
515.

In ABC, B = 70 and C = 60 . The internal bisectors of the two smallest angles of ABC meet at O. The angle so formed at O is

A. 125
B. 120
C. 115
D.
E. 110
Answer» B. 120
Discussion
516.

In a triangle PQR, the side QR is extended to S. QPR = 72 and PRS = 110 , then the value of PQR is :

A. 38
B. 32
C. 25
D. 29
Answer» B. 32
Discussion
517.

In case of an acute angled triangle, its orthocentre lies

A. inside the triangle
B. outside the triangle
C. on the traingle
D.
E. on one of the vertices of the triangle
Answer» B. outside the triangle
Discussion
518.

In ABC if the median ( 1/2 ) AD = BC, then BAC is equal to

A. 90
B. 45
C. 60
D. 75
Answer» B. 45
Discussion
519.

In a triangle PQR, PQ = PR and Q is twice that of P. Then Q is equal to

A. 72
B.
C. 36
D. 144
E. 108
Answer» B.
Discussion
520.

In PQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be

A. 5 : 11
B. 6 : 5
C. 11 : 6
D. 11 : 5
Answer» B. 6 : 5
Discussion
521.

In a ABC, A + B = 75 and B + C = 140 , then B is

A. 40
B. 35
C. 55
D. 45
Answer» C. 55
Discussion
522.

An exterior angle of a triangle is 115 and one of the interior opposite angles is 45 . Then the other two angles are

A. 65 , 70
B. 60 , 75
C. 45 , 90
D. 50 , 85
Answer» B. 60 , 75
Discussion
523.

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

A. 12
B. 9
C. 14
D. 16
Answer» C. 14
Discussion
524.

In a triangle PQR, S and T are the points on PQ and PR respectively, such that ST || QR and PS / SQ = 3 / 5 , PR = 6 cm, then PT is

A. 2 cm
B. 2.25 cm
C. 3.5 cm
D. 4 cm
Answer» C. 3.5 cm
Discussion
525.

The mid-points of sides AB and AC of a triangle ABC are respectively X and Y. If (BC + XY) = 12 units, then the value of (BC XY) is :

A. 2 units
B. 6 units
C. 8 units
D. 4 units
Answer» E.
Discussion
526.

In ABC, A = 90 , AD BC and AD = BD = 2 cm. The length of CD is

A. 3 cm
B. 3.5 cm
C. 3.2 cm
D. 2 cm
Answer» E.
Discussion
527.

The mid points of AB and AC of the ABC are P and Q respectively. If PQ = 6 cm., then the side BC is

A. 10 cm.
B. 12 cm.
C. 8 cm.
D. 14 cm.
Answer» C. 8 cm.
Discussion
528.

ABC is a triangle, PQ is line segment intersecting AB in P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is

A. 28 cm.
B. 48 cm.
C.
D. 84 cm.
E. 42 cm.
Answer» C.
Discussion
529.

In ABC, AC = BC and ABC = 50 , the side BC is produced to D so that BC = CD then the value of BAD is

A. 80
B.
C. 40
D. 90
E. 50
Answer» D. 90
Discussion
530.

The difference between the largest and the smallest angles of a triangle whose angles are in the ratio of 5 : 3 : 10 is

A. 20
B. 30
C. 50
D.
E. 70
Answer» E. 70
Discussion
531.

In ABC, D is the mid point of BC and G is the centroid. If GD = 5 cm, then the length of AD is :

A. 10 cm
B.
C. 12 cm
D. 15 cm
E. 20 cm
Answer» D. 15 cm
Discussion
532.

ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12

A. 10 cm.
B. 15 cm.
C. 12 cm.
D. 14 cm.
Answer» C. 12 cm.
Discussion
533.

ABC is an isosceles triangle with AB = AC = 10 cm, AD = 8 cm is the median on BC from A. The length of BC is

A. 8 cm
B. 12 cm
C. 10 cm
D. 6 cm
Answer» C. 10 cm
Discussion
534.

In a triangle ABC, if A + C = 140 and A + B = 180 , then A is equal to

A. 80
B. 40
C. 60
D. 20
Answer» D. 20
Discussion
535.

The side BC of a triangle ABC is produced to D. If ACD = 112 and B = 3/4 A, then the measure of B is

A. 30
B. 48
C. 45
D. 64
Answer» C. 45
Discussion
536.

E is the mid-point of the median AD of ABC. BE is joined and produced to meet AC at F. F divides AC in the ratio :

A. 2 : 3
B. 2 : 1
C. 1 : 3
D. 3 : 2
Answer» C. 1 : 3
Discussion
537.

In ABC, the external bisectors of the angles B and C meet at the point O. If A = 70 , then the measure of BOC is :

A. 55
B. 75
C. 60
D. 50
Answer» B. 75
Discussion
538.

AD is perpendicular to the internal bisector of ABC of ABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is

A. 3
B. 8
C. 4
D. 6
Answer» E.
Discussion
539.

O is the incentre of PQR and QPR = 50 , then the measure of QOR is :

A. 125
B. 100
C. 130
D. 115
Answer» E.
Discussion
540.

In ABC, D and E are two mid points of sides AB and AC respectively. If BAC = 40 and ABC = 65 then CED is :

A. 130
B. 75
C. 125
D. 105
Answer» E.
Discussion
541.

Astha cuts a triangle out of a cardboard and tries to balance the triangle horizontally at the tip of her finger. On what point will she be able to balance the shape for any kind of triangle?

A. Incentre
B. Circumcentre
C. Centroid
D. Orthocentre
Answer» D. Orthocentre
Discussion
542.

B

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">CC<sub>1</sub></td><td style="text-align: center;">AA<sub>1</sub></td><td style="text-align: center;">BB<sub>1</sub></td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><tr><td style="text-align: center;">CC<sub>1</sub></td><td style="text-align: center;">AA<sub>1</sub></td><td style="text-align: center;">BB<sub>1</sub></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"> + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;">BB<sub>1</sub></td><td style="text-align: center;">AA<sub>1</sub></td><td style="text-align: center;">CC<sub>1</sub></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"> + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;">AA<sub>1</sub></td><td style="text-align: center;">CC<sub>1</sub></td><td style="text-align: center;">BB<sub>1</sub></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"> + </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><tr><td style="text-align: center;">BB<sub>1</sub></td><td style="text-align: center;">AA<sub>1</sub></td><td style="text-align: center;">CC<sub>1</sub></td></tr></table>
Discussion
543.

Which of the set of three sides can t form a triangle?

A. 5 cm, 6 cm, 7 cm
B. 5 cm, 8 cm, 15 cm
C. 8 cm, 15 cm, 18 cm
D. 6 cm, 7 cm, 11 cm
Answer» C. 8 cm, 15 cm, 18 cm
Discussion
544.

G is the centroid of ABC. If AG = BC, then measure of BGC is

A. 45
B. 60
C. 90
D. 120
Answer» D. 120
Discussion
545.

The sides of a triangle are in the ratio of 7 : 9 : 12. The difference between the lengths of largest and smallest sides is 15 cm. The length of the largest side would be :

A. 36 cm
B. 12 cm
C. 60 cm
D. 24 cm
Answer» B. 12 cm
Discussion
546.

In ABC, the internal bisectors of B and C meet at point O. If A = 80 , then BOC is equal to :

A. 100
B. 120
C. 130
D. 140
Answer» D. 140
Discussion
547.

ABC is an isosceles right angled triangle having C = 90 . If D is any point on AB, then AD

A. CD
B. 2CD
C. 3CD
D. 4CD
Answer» C. 3CD
Discussion
548.

In ABC , B = 60 , and C = 40 , AD and AE are respectively the bisector of A and perpendicular on BC. The measure of EAD is :

A. 11
B. 10
C. 12
D. 9
Answer» C. 12
Discussion
549.

The ratio of circumradius and radius of an equilateral triangle is

A. 1 : 2
B. 3 : 1
C. 2 : 1
D. 1 : 3
Answer» D. 1 : 3
Discussion
550.

In ABC, the line parallel to BC intersects AB and AC at P and Q respectively. If AB : AP = 5 : 3, then AQ : QC is :

A. 3 : 2
B. 2 : 3
C. 3 : 5
D. 1 : 2
Answer» B. 2 : 3
Discussion