MCQOPTIONS
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MCQOPTIONS
This section includes 192 Mcqs, each offering curated multiple-choice questions to sharpen your Arithmetic Ability knowledge and support exam preparation. Choose a topic below to get started.
| 151. |
Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is |
| A. | X = BY = CZ |
| B. | X ≠ BY = CZ |
| C. | X = BY ≠ CZ |
| D. | X ≠ BY ≠ CZ |
| Answer» B. X ≠ BY = CZ | |
| 152. |
The equidistant point from the vertices of a triangle is called its: |
| A. | entroid |
| B. | ncenter |
| C. | ircumcenter |
| D. | rthocenter |
| Answer» D. rthocenter | |
| 153. |
In a triangle ABC, the side BC is extended up to D such that CD = AC. If ∠BAD = 109° and ∠ACB = 72° then the value of ∠ABC is |
| A. | 5° |
| B. | 0° |
| C. | 0° |
| D. | 5° |
| Answer» B. 0° | |
| 154. |
An isosceles triangle ABC is right-angled 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 ΔABC. If AP = a cm, AQ = b cm and ∠BAD = 15°, sin 75° = ? |
| A. | $\frac{{2b}}{{\sqrt 3 a}}$$ |
| B. | $\frac{a}{{2b}}$$ |
| C. | $\frac{{\sqrt 3 a}}{{2b}}$$ |
| D. | $\frac{{2a}}{{\sqrt 3 b}}$$ |
| Answer» D. $\frac{{2a}}{{\sqrt 3 b}}$$ | |
| 155. |
In triangle PQR, points A, B and C are taken on PQ, PR and QR respectively such that QC = AC and CR = CB. If ∠QPR = 40°, then ∠ACB is equal to: |
| A. | 40° |
| B. | 0° |
| C. | 0° |
| D. | 00° |
| Answer» E. | |
| 156. |
In a right-angle ΔABC, ∠ABC = 90°, AB = 5 cm and BC = 12 cm. The radius of the circumcircle of the triangle ABC is |
| A. | .5 cm |
| B. | cm |
| C. | .5 cm |
| D. | cm |
| Answer» D. cm | |
| 157. |
If the length of the sides of a triangle are in the ratio 4 : 5 : 6 and the inradius of the triangle is 3 cm, then the altitude of the triangle corresponding to the largest side as base is : |
| A. | .5 cm |
| B. | cm |
| C. | 0 cm |
| D. | cm |
| Answer» B. cm | |
| 158. |
In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is |
| A. | 20° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 159. |
In a triangle, if three altitudes are equal, then the triangle is |
| A. | btuse |
| B. | quilateral |
| C. | ight |
| D. | sosceles |
| Answer» C. ight | |
| 160. |
I is the incentre of ΔABC. If ∠ABC = 60°, ∠BCA = 80°, then the ∠BIC is |
| A. | 0° |
| B. | 00° |
| C. | 10° |
| D. | 20° |
| Answer» D. 20° | |
| 161. |
If the median drawn on the base of a triangle is half of its base the triangle will be |
| A. | ight-angled |
| B. | cute-angled |
| C. | btuse-angled |
| D. | quilateral |
| Answer» B. cute-angled | |
| 162. |
ABC is an isosceles triangle with AB = AC, A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is: |
| A. | : 1 |
| B. | : 3 |
| C. | : 5 |
| D. | : 4 |
| Answer» E. | |
| 163. |
In ΔABC, D and E are points on AB and AC respectively such that DE || BC and DE divides the ΔABC into two parts of equal areas. Then ratio of AD and BD is |
| A. | : 1 |
| B. | : $$\sqrt 2 $$ - 1 |
| C. | : $$\sqrt 2 $$ |
| D. | : $$\sqrt 2 $$ + 1 |
| Answer» C. : $$\sqrt 2 $$ | |
| 164. |
In a triangle ABC,∠ A = 90°, AL is drawn perpendicular to BC, Then ∠BAL is equal to: |
| A. | ALC |
| B. | ACB |
| C. | BAC |
| D. | B - ∠BAL |
| Answer» C. BAC | |
| 165. |
AB and CDbisect each other at O. If AD = 6 cm. Then BC is : |
| A. | .9 cm |
| B. | .8 cm |
| C. | cm |
| D. | cm |
| Answer» D. cm | |
| 166. |
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is : |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | 0 cm |
| Answer» C. cm | |
| 167. |
If ABC and PQR are similar triangles in which∠A = 47° and ∠Q = 83°, then ∠C is: |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» B. 0° | |
| 168. |
If in a ΔABC, the mid-point of the BC is D, then the value of AB2 + AC2 is: |
| A. | AD2 + BD2 |
| B. | AD + BD |
| C. | 2(AD2 + BD2) |
| D. | AD - BD |
| Answer» D. AD - BD | |
| 169. |
If Δ ABC is an equilateral triangle whose side is 2a, then the length of its altitude is: |
| A. | a√2 |
| B. | a√3 |
| C. | a√5 |
| D. | a |
| Answer» C. a√5 | |
| 170. |
If a, b, c are in GP and log a - log 2b, log 2b - log 3c and log 3c - log a are in AP, then a, b, c are the lengths of the sides of a triangle which is |
| A. | Acute angle |
| B. | Obtuse angled |
| C. | Right angles |
| D. | Equilateral |
| Answer» C. Right angles | |
| 171. |
In which of the following cases, a triangle can not be formed with the given length of side? |
| A. | 4, 5, 6 |
| B. | 5, 8, 12 |
| C. | 10, 12, 15 |
| D. | 5, 9, 17 |
| Answer» E. | |
| 172. |
If r1, r2, r3 are ex-radii and r the in-radius of triangle ABC and r1 = r + r2 + r3, then triangle ABC is |
| A. | Isoscales triangle |
| B. | Equilateral triangle |
| C. | Right angled triangle |
| D. | None of these |
| Answer» D. None of these | |
| 173. |
In an equilateral triangle, the ratio of the radius of circumcircle to that of incircle is |
| A. | 3 : 1 |
| B. | 5 : 2 |
| C. | 3 : 2 |
| D. | 2 : 1 |
| Answer» E. | |
| 174. |
If (-4, 0) and (1, -1) are two vertices of a triangle of area 4 units, then its third vertex lie on: |
| A. | None of these |
| B. | x + 5y - 4 = 0 |
| C. | 5x + y + 12 = 0 |
| D. | y = x |
| Answer» C. 5x + y + 12 = 0 | |
| 175. |
In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is |
| A. | 45° |
| B. | 30° |
| C. | 15° |
| D. | None of these |
| Answer» D. None of these | |
| 176. |
A triangle cannot be drawn with the following three sides%! |
| A. | 2m, 3m, 4m |
| B. | 3m, 4m, 8m |
| C. | 4m, 6m, 9m |
| D. | 5m, 7m, 10m |
| Answer» C. 4m, 6m, 9m | |
| 177. |
*$_A triangle cannot be drawn with the following three sides? |
| A. | 2m, 3m, 4m |
| B. | 3m, 4m, 8m |
| C. | 4m, 6m, 9m |
| D. | 5m, 7m, 10m |
| Answer» C. 4m, 6m, 9m | |
| 178. |
*/*_In a triangle ABC,‚à †¬†A = 900, AL is drawn perpendicular to BC, Then ‚à †¬†BAL is equal to:? |
| A. | ‚Äö√ ‚Ä ALC |
| B. | ‚Äö√ ‚Ä ACB |
| C. | ‚Äö√ ‚Ä BAC |
| D. | ‚Äö√ ‚Ä B - ‚Äö√ ‚Ä BAL |
| Answer» C. ‚Äö√ ‚Ä BAC | |
| 179. |
%_In the adjoining figure AB, EF and CD are parallel lines. Given that GE = 5 cm, GC = 10 cm and DC = 18 cm, then EF is equal to:_% |
| A. | 11 cm |
| B. | 5 cm |
| C. | 6 cm |
| D. | 9 cm |
| Answer» E. | |
| 180. |
_ AB and CD bisect each other at O. If AD = 6 cm. Then BC is :$? |
| A. | 5.9 cm |
| B. | 4.8 cm |
| C. | 6 cm |
| D. | 7 cm |
| Answer» D. 7 cm | |
| 181. |
__In Δ ABC, AD ⊥ BC, then__ |
| A. | AB2 - BD2 = AC2 - CD2 |
| B. | AB2 + BD2 = AC2 - CD2 |
| C. | AB2 - BD2 = AC2 + CD2 |
| D. | AB2 - AC2 = BD2 + CD2 |
| Answer» B. AB2 + BD2 = AC2 - CD2 | |
| 182. |
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :$? |
| A. | 6 cm |
| B. | 8 cm |
| C. | 7 cm |
| D. | 10 cm |
| Answer» C. 7 cm | |
| 183. |
Consider the following statements :I. Three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.II. If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.Of these statements :$? |
| A. | I and II both are true |
| B. | I is true and II is false |
| C. | I is false and II is true |
| D. | None of these |
| Answer» C. I is false and II is true | |
| 184. |
Consider the following statements :I. Three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.II. If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.Of these statements :? |
| A. | I and II both are true |
| B. | I is true and II is false |
| C. | I is false and II is true |
| D. | None of these |
| Answer» C. I is false and II is true | |
| 185. |
In the following figure which of the following statements is true? |
| A. | AB = BD |
| B. | AC = CD |
| C. | BC + CD |
| D. | AD < Cd |
| Answer» C. BC + CD | |
| 186. |
Consider the following statements :I. Every equilateral triangle is necessarily an isosceles triangle.II. Every right-angled triangle is necessarily an isosceles triangle.III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle.The correct statements are: |
| A. | I and II |
| B. | II and III |
| C. | I and III |
| D. | I, II and III |
| Answer» D. I, II and III | |
| 187. |
If ABC and PQR are similar triangles in which ‚à †¬†A = 470 and ‚à †¬†Q = 830, then ‚à †C is:# |
| A. | 500 |
| B. | 700 |
| C. | 600 |
| D. | 800 |
| Answer» B. 700 | |
| 188. |
Two right angled triangles are congruent if :I.The hypotenuse of one triangle is equal to the hypotenuse of the other.II.a side for one triangle is equal to the corresponding side of the other.III.Sides of the triangles are equal.IV. An angle of the triangle are equal.Of these statements, the correct ones are combination of:$ |
| A. | I and II |
| B. | II and III |
| C. | I and III |
| D. | IV only |
| Answer» B. II and III | |
| 189. |
In Œî PQR, PS is the bisector of ‚à †¬†P and PT ‚ä• OR, then ‚à †¬†TPS is equal to:$ |
| A. | ‚Äö√ ‚Ä Q + ‚Äö√ ‚Ä R |
| B. | 900 + 1/2 ‚Äö√ ‚Ä Q |
| C. | 900 - 1/2 ‚Äö√ ‚Ä R |
| D. | 1/2 (‚Äö√ ‚Ä Q - ‚Äö√ ‚Ä R) |
| Answer» E. | |
| 190. |
The point of intersection of the altitudes of a triangle is called its: |
| A. | Incentre |
| B. | Excentre |
| C. | Orthocentre |
| D. | Centroid |
| Answer» D. Centroid | |
| 191. |
In a triangle ABC, the internal bisector of the angle A meets BC at D. If AB = 4, AC = 3 and ‚à †¬†A = 600, then length of AD is :$ |
| A. | 2‚à ö3 |
| B. | (12‚à ö3) / 7 |
| C. | (15‚à ö3) / 8 |
| D. | (6‚à ö3) / 7 |
| E. | None of these |
| Answer» C. (15‚Äö√ √∂3) / 8 | |
| 192. |
Consider the triangle shown in the figure where BC = 12 cm, Db = 9 cm, CD = 6 cm and What is the ratio of the perimeter of the triangle ADC to that of the triangle BDC ? |
| A. | 7 : 9 |
| B. | 8 : 9 |
| C. | 6 :9 |
| D. | 5 : 9 |
| E. | None of these |
| Answer» B. 8 : 9 | |