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MCQOPTIONS
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 | |
| 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 | |
| 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. | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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. | |
| 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. | |
| 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 | |
| 111. |
The equidistant point from the vertices of a triangle is called its : |
| A. | Centroid |
| B. | Incentre |
| C. | Circumcentre |
| D. | Orthocentre |
| Answer» D. Orthocentre | |
| 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. | |
| 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 | |
| 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 | |
| 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 | |
| 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> | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 121. |
Angle between sss B is |
| A. | 50 |
| B. | 80 |
| C. | 40 |
| D. | 60 |
| Answer» E. | |
| 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 | |
| 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. | |
| 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 | |
| 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 | |
| 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 | |
| 127. |
|
|||||||
| A. | 60 | |||||||
| B. | 20 | |||||||
| C. | 30 | |||||||
| D. | 50 | |||||||
| Answer» D. 50 | ||||||||
| 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 | |
| 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. | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 134. |
O is the incentre of ABC and A = 30 , then BOC is |
| A. | 100 |
| B. | 105 |
| C. | 110 |
| D. | 90 |
| Answer» C. 110 | |
| 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. | |
| 136. |
|
||||
| A. | 60 | ||||
| B. | 30 | ||||
| C. | 45 | ||||
| D. | 15 | ||||
| Answer» C. 45 | |||||
| 137. |
In ABC, AB = a b, AC = |
| A. | 60 |
| B. | 30 |
| C. | 90 |
| D. | 45 |
| Answer» D. 45 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |
| 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. | |
| 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> | |
| 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 | |
| 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. | |
| 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 | |
| 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 | |
| 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 | |
| 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 | |