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.

101.

In the accompanying figure, AB is one of the diameters of the circle and OC is perpendicular to it through the centre O. If AC is 7 2 cm, then what is the area of the circle in cm

A. 24.5
B. 49
C. 98
D. 154
E. None of these
Answer» E. None of these
Discussion
102.

If PA and PB are two tangents to a circle with centre O such that AOB = 110 , then APB is

A. 90
B. 70
C. 60
D. 55
Answer» C. 60
Discussion
103.

Two circles of diameters 10 cm and 6 cm have the same centre. A chord of the larger circle is a tangent of the smaller one. The length of the chord is

A. 4 cm.
B. 8 cm.
C. 6 cm.
D. 10 cm.
Answer» C. 6 cm.
Discussion
104.

Each interior angle of a regular polygon is 144 . The number of sides of the polygon is

A. 8
B. 9
C. 10
D. 11
Answer» D. 11
Discussion
105.

The minimum number of common tangents drawn to two circles when both the circles touch each other externally is

A. 1
B. 2
C. 3
D. 0
Answer» D. 0
Discussion
106.

Let P and Q be two points on a circle with centre O. If two tangents of the circle through P and Q meet at A with PAQ = 48 , then APQ is

A. 96
B. 48
C. 66
D. 60
Answer» D. 60
Discussion
107.

AB is a diameter of the circle with centre O, CD is chord of the circle. If BOC = 120 , then the value of ADC is

A. 42
B. 30
C. 60
D. 35
Answer» C. 60
Discussion
108.

In a triangle ABC, BAC = 90 and AD is perpendicular to BC. If AD = 6 cm and BD = 4 cm, then the length of BC is

A. 8 cm
B. 10 cm
C. 9 cm
D. 13 cm
Answer» E.
Discussion
109.

The points D and E are taken on the sides AB and AC of ABC such that AD = 1/3 AB, AE = 1/3 AC. If the length of BC is 15 cm, then the length of DE is :

A. 10 cm
B. 8 cm
C. 6 cm
D. 5 cm
Answer» E.
Discussion
110.

The external bisector of B and C of ABC (where AB and AC extended to E and F respectively) meet at point P. If BAC = 100 , then the measure of BPC is

A. 50
B. 80
C. 40
D. 100
Answer» D. 100
Discussion
111.

The equidistant point from the vertices of a triangle is called its :

A. Centroid
B. Incentre
C. Circumcentre
D. Orthocentre
Answer» D. Orthocentre
Discussion
112.

O is the in-centre of the ABC, if BOC = 116 , then BAC is

A. 42
B. 62
C. 58
D. 52
Answer» E.
Discussion
113.

In a triangle ABC, incentre is O and BOC = 110 , then the measure of BAC is :

A. 20
B. 40
C. 55
D. 110
Answer» C. 55
Discussion
114.

For a triangle ABC, D, E, F are the mid-points of its sides. If ABC = 24 sq. units then DEF is

A. 4 sq. units
B. 6 sq. units
C. 8 sq. units
D. 12 sq. units
Answer» C. 8 sq. units
Discussion
115.

If I be the incentre of ABC and B = 70 and C = 50 , then the magnitude of BIC is

A. 130
B. 60
C. 120
D. 105
Answer» D. 105
Discussion
116.

In a triangle ABC, AB + BC = 12 cm, BC + CA = 14 cm and CA + AB = 18 cm. Find the radius of the circle (in cm) which has the same perimeter as the triangle.

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>5</center></td></tr><td style="text-align: center;">2</td><td></td></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>7</center></td></tr><td style="text-align: center;">2</td><td></td></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>9</center></td></tr><td style="text-align: center;">2</td><td></td></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>11</center></td></tr><td style="text-align: center;">2</td><td></td></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>9</center></td></tr><td style="text-align: center;">2</td><td></td></table>
Discussion
117.

In ABC, PQ is parallel to BC. If AP : PB = 1 : 2 and AQ = 3 cm; AC is equal to

A. 6 cm
B. 9 cm
C. 12 cm
D. 8 cm
Answer» C. 12 cm
Discussion
118.

In a ABC, if 2 A = 3 B = 6 C, value of B is

A. 60
B. 30
C. 45
D. 90
Answer» B. 30
Discussion
119.

D is any point on side AC of ABC. If P, Q, X, Y are the midpoints of AB, BC, AD and DC respectively, then the ratio of PX and QY is

A. 1 : 2
B. 1 : 1
C. 2 : 1
D. 2 : 3
Answer» C. 2 : 1
Discussion
120.

In a ABC, A + B = 70 and B + C = 130 , value of A is

A. 20
B. 50
C. 110
D. 30
Answer» C. 110
Discussion
121.

Angle between sss B is

A. 50
B. 80
C. 40
D. 60
Answer» E.
Discussion
122.

In a regular polygon, the exterior and interior angles are in the ratio 1 : 4. The number of sides of the polygon is

A. 10
B. 12
C. 15
D. 16
Answer» B. 12
Discussion
123.

In ABC and DEF, AB = DE and BC = EF. Then one can infer that ABC DEF, when

A. BAC = EDF
B. ACB = EDF
C. ACB = DFE
D. ABC = DEF
Answer» E.
Discussion
124.

In a right-angled triangle ABC, ABC = 90 , AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is

A. 7.5 cm
B. 6 cm
C. 6.5 cm
D. 7 cm
Answer» D. 7 cm
Discussion
125.

ABC is a triangle and the sides AB, BC and CA are produced to E, F and G respectively. If CBE = ACF = 130 then the value of GAB is

A. 100
B. 130
C. 80
D. 90
Answer» B. 130
Discussion
126.

If O is the in-centre of ABC; if BOC = 120 , then the measure of BAC is

A. 30
B. 60
C. 150
D. 75
Answer» C. 150
Discussion
127.

In a ABC, AB = BD , B = 70 and C = 50 , thrn BAD = ?ACDC

A. 60
B. 20
C. 30
D. 50
Answer» D. 50
Discussion
128.

In ABC, D is the mid-point of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of ABC is equal to

A. 3 cm
B. 6 cm
C. 9 cm
D. 15 cm
Answer» B. 6 cm
Discussion
129.

In a ABC, the medians AD, BE and CF meet at G, then which of the following is true?

A. AD + BE + CF >1/2 (AB + BC + AC)
B. 2(AD + BE + CF) > (AB + BC + AC)
C. 3 (AD + BE + CF) > 4(AB + BC + AC)
D. AB + BC + AC > AD+BE + CF
Answer» E.
Discussion
130.

AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. Length of OD (in cm) is

A. 2
B. 4
C. 5
D. 7
Answer» D. 7
Discussion
131.

If in a triangle ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and AD / BD = 3 / 5 . If AC = 4 cm, then AE is

A. 1.5 cm
B. 2.0 cm
C. 1.8 cm
D. 2.4 cm
Answer» B. 2.0 cm
Discussion
132.

In ABC, the internal bisectors of ABC and ACB meet at I and BAC = 50 . The measure of BIC is

A. 105
B. 115
C. 125
D. 130
Answer» C. 125
Discussion
133.

Let O be the in-centre of a triangle ABC and D be a point on the side BC of ABC, such that OD BC. If BOD = 15 , then ABC =

A. 75
B. 45
C. 150
D. 90
Answer» D. 90
Discussion
134.

O is the incentre of ABC and A = 30 , then BOC is

A. 100
B. 105
C. 110
D. 90
Answer» C. 110
Discussion
135.

The measures of two angles of a triangle are in the ratio 4 : 5. If the sum of these two measures is equal to the measure of the third angle, find the smallest angle.

A. 10
B. 50
C. 90
D. 40
Answer» E.
Discussion
136.

In ABC, BAC = 90 and AB = 1BC.Then the measure of ACB is :2

A. 60
B. 30
C. 45
D. 15
Answer» C. 45
Discussion
137.

In ABC, AB = a b, AC =

A. 60
B. 30
C. 90
D. 45
Answer» D. 45
Discussion
138.

The side BC of ABC is extended to the point D. If ACD = 112 and B = 3/4 A, then the value of B is

A. 64
B. 48
C. 46
D. 50
Answer» C. 46
Discussion
139.

If the angles of a triangle are in the ratio of 2 : 3 : 4, then the difference of the measure of greatest angle and smallest angle is

A. 20
B. 30
C. 40
D. 50
Answer» D. 50
Discussion
140.

Suppose that the medians BD, CE and AF of a triangle ABC meet at G. Then AG : GF is

A. 1 : 2
B. 2 : 1
C. 1 : 3
D. 2 : 3
Answer» C. 1 : 3
Discussion
141.

Internal bisectors of Q and R of PQR intersect at O. If ROQ = 96 then the vlaue of RPQ is

A. 36
B. 24
C. 12
D. 6
Answer» D. 6
Discussion
142.

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then.

A. PQR must be an equilateral triangle
B. PQ + QR + PR = AB
C. PQ + QR + PR = 2 AB
D. PQR must be a right angled triangle
Answer» B. PQ + QR + PR = AB
Discussion
143.

What is the position of the circumcentre of an obtuse angled triangle?

A. It lies inside the triangle.
B.
C. It lies outside the triangle.
D. It is the mid point of the largest side.
E. It is the vertex opposite to the largest side.
Answer» C. It lies outside the triangle.
Discussion
144.

The centroid of an equilateral triangle ABC is G and AB = 10 cm. The length of AG (in cm) is :

A. <table><tr><td rowspan="2">3</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;">3</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>10</center></td></tr><tr><td style="text-align: center;"> <span style=" text-decoration: overline;">3</span></td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>10 <span style=" text-decoration: overline;">3</span></center></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> <span style=" text-decoration: overline;">3</span></center></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> <span style=" text-decoration: overline;">3</span></center></td></tr><tr><td style="text-align: center;">3</td></tr></table>
Discussion
145.

The exterior angles obtained on producing the base BC of a triangle ABC in both ways are 120 and 105 , then the vertical A of the triangle is of measure

A. 36
B. 40
C. 45
D. 55
Answer» D. 55
Discussion
146.

Let ABC be an equilateral triangle and AD perpendicular to BC. Then AB + BC + CA = ?

A. 2AD
B. 3AD
C. 4AD
D. 5AD
Answer» E.
Discussion
147.

The lengths of the sides of a triangle are a, b and c respectively. If a + b + c = ab + bc + ca, then the triangle is :

A. isosceles
B. equilateral
C. scalene
D. right-angled
Answer» C. scalene
Discussion
148.

If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is:

A. isosceles
B. scalene
C. equilateral
D. right angled
Answer» D. right angled
Discussion
149.

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

A. 35
B. 55
C. 70
D. 110
Answer» C. 70
Discussion
150.

In ABC, BD and CE are perpendicular to AC and AB respectively. If BD = CE, then ABC is

A. Equilateral
B. Isosceles
C. Right angled
D. Scalene
Answer» C. Right angled
Discussion