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.
| 51. |
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. | : 3 |
| B. | : 1 |
| C. | : 2 |
| D. | : 3 |
| Answer» D. : 3 | |
| 52. |
For a triangle ABC, D and E are two points on AB and AC such that AD = $$\frac{1}{4}$$ AB, AE = $$\frac{1}{4}$$ AC. If BC = 12 cm, then DE is : |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | cm |
| Answer» D. cm | |
| 53. |
In a ΔABC, ∠A + ∠B = 118°, ∠A + ∠C = 96°. Find the value of ∠A. |
| A. | 6° |
| B. | 0° |
| C. | 0° |
| D. | 4° |
| Answer» E. | |
| 54. |
If in a triangle ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and $$\frac{{AD}}{{BD}}$$ = $$\frac{3}{5}$$. If AC = 4 cm, then AE is |
| A. | .5 cm |
| B. | .0 cm |
| C. | .8 cm |
| D. | .4 cm |
| Answer» B. .0 cm | |
| 55. |
If the three angles of a triangle are: $${\left(x + 15 \right)^ \circ },$$$${\left({\frac{{6x}}{5} + 6} \right)^ \circ }$$and $${\left({\frac{{2x}}{3} + 30} \right)^ \circ }$$then the triangle is: |
| A. | sosceles |
| B. | quilateral |
| C. | ight angled |
| D. | calene |
| Answer» C. ight angled | |
| 56. |
In ΔABC, 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. | : 3 |
| B. | : 5 |
| C. | : 2 |
| D. | : 2 |
| Answer» E. | |
| 57. |
Let ABC be an equilateral triangle and AX, BY, CZ be the altitude. Then the right statement out of the four give responses is : |
| A. | X = BY = CZ |
| B. | X ≠ BY = CZ |
| C. | X = BY ≠ CZ |
| D. | X ≠ BY ≠ CZ |
| Answer» B. X ≠ BY = CZ | |
| 58. |
In ΔABC, ∠C is an obtuse angle. The bisectors of the exterior angles at A and B meet BC and AC produced at D and E respectively. If AB = AD = BE, then ∠ACB = ? |
| A. | 05° |
| B. | 08° |
| C. | 10° |
| D. | 35° |
| Answer» C. 10° | |
| 59. |
If the measures of the sides of triangle are (x2 - 1), (x2 + 1) and 2x cm, then the triangle would be : |
| A. | quilateral |
| B. | cute-angled |
| C. | ight-Angled |
| D. | sosceles |
| Answer» D. sosceles | |
| 60. |
In ΔABC, ∠A + ∠B = 65°, ∠B + ∠C = 140°, then find ∠B. |
| A. | 0° |
| B. | 5° |
| C. | 5° |
| D. | 0° |
| Answer» C. 5° | |
| 61. |
If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then |
| A. | QR must be an equilateral triangle |
| B. | Q + QR = PQR + AB |
| C. | Q + QR = PR + 2AB |
| D. | QR must be a right angled |
| Answer» B. Q + QR = PQR + AB | |
| 62. |
In ΔABC, 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 ΔABC and ΔDBE are : |
| A. | imilar only if D lies outside the line segment AB |
| B. | ongruent only If D lies out side the line segment AB |
| C. | lways similar |
| D. | lways congruent |
| Answer» D. lways congruent | |
| 63. |
In a ΔABC, AB = AC and BA is produced to D such that AC = AD. Then the ∠BCD is : |
| A. | 00° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» E. | |
| 64. |
In ΔPQR, S and T are point 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. | cm |
| B. | cm |
| C. | $\frac{{31}}{3}$$ cm |
| D. | $\frac{{41}}{3}$$ cm |
| Answer» D. $\frac{{41}}{3}$$ cm | |
| 65. |
If two angles of a triangle are 21° and 38°, then the triangle is : |
| A. | ight-angled triangle |
| B. | cute-angled triangle |
| C. | btuse-angled triangle |
| D. | sosceles triangle |
| Answer» D. sosceles triangle | |
| 66. |
In a ΔABC, AB = BC, ∠B = x° and ∠A = (2x - 20)°, Then ∠B is : |
| A. | 4° |
| B. | 0° |
| C. | 0° |
| D. | 4° |
| Answer» E. | |
| 67. |
In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is: |
| A. | 1° |
| B. | 3° |
| C. | 5° |
| D. | 9° |
| Answer» E. | |
| 68. |
If the sides of a right angled triangle are three consecutive integers, then the length of the smallest side is |
| A. | units |
| B. | units |
| C. | units |
| D. | units |
| Answer» B. units | |
| 69. |
If angle bisector of a triangle bisects the opposite side, then what type of triangle is it? |
| A. | ight angled |
| B. | quilateral |
| C. | sosceles and equilateral |
| D. | sosceles |
| Answer» D. sosceles | |
| 70. |
The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is : |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» B. 0° | |
| 71. |
In triangle ABC, ∠BAC = 75°, ∠ABC = 45°, $$\overline {BC} $$ is produced to D. If ∠ACD = x°, then $$\frac{x}{3}$$% of 60° is |
| A. | 0° |
| B. | 8° |
| C. | 5° |
| D. | 4° |
| Answer» E. | |
| 72. |
In ΔABC and ΔDEF, AB = DE and BC = EF, then one can infer that ΔABC ≅ ΔDEF, when |
| A. | BAC = ∠EFD |
| B. | ACB = ∠EDF |
| C. | ABC = 2∠DEF |
| D. | ABC = ∠DEF |
| Answer» E. | |
| 73. |
If each angle of a triangle is less than the sum of the other two, then the triangle is |
| A. | btuse angled |
| B. | cute or equilateral |
| C. | cute angled |
| D. | quilateral |
| Answer» C. cute angled | |
| 74. |
ABC is an equilateral triangle and CD is the internal bisector of ∠C. If DC is produced to E such that AC = CE, then ∠CAE is equal to |
| A. | 5° |
| B. | 5° |
| C. | 0° |
| D. | 5° |
| Answer» E. | |
| 75. |
ABC is an isosceles triangle inscribed in a circle. If AB = AC = 12$$\sqrt 5 $$ and BC = 24 cm then radius of circle is: |
| A. | 0 cm |
| B. | 5 cm |
| C. | 2 cm |
| D. | 4 cm |
| Answer» C. 2 cm | |
| 76. |
The centroid of a triangle is G. If area of ΔABC = 72 sq. unit, then the area of ΔBGC is? |
| A. | 6 sq. units |
| B. | 4 sq. units |
| C. | 6 sq. units |
| D. | 8 sq. units |
| Answer» C. 6 sq. units | |
| 77. |
Possible length of the sides of a triangle are: |
| A. | cm, 3cm, 6cm |
| B. | cm, 4cm, 5cm |
| C. | .5cm, 3.5cm, 6cm |
| D. | cm, 4cm, 9cm |
| Answer» C. .5cm, 3.5cm, 6cm | |
| 78. |
The orthocenter of a triangle is the point where? |
| A. | he medians meet |
| B. | he altitudes meet |
| C. | he right bisectors of the sides of |
| D. | he bisectors of the angles |
| Answer» C. he right bisectors of the sides of | |
| 79. |
In a triangle ABC, if ∠A + ∠C = 140° and ∠A + 3∠B = 180°, then ∠A is equal to: |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 80. |
In a ΔABC, BC is extended upto D; ∠ACD = 120°, ∠B = $$\frac{1}{2}$$ ∠A, then ∠A is: |
| A. | 0° |
| B. | 5° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 81. |
G is the centroid of ΔABC. If AB = BC = AC, then measure of ∠BGC is: |
| A. | 5° |
| B. | 0° |
| C. | 0° |
| D. | 20° |
| Answer» E. | |
| 82. |
Let ΔABC and ΔABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of triangles ABC and ABD will be |
| A. | ABD = $$\frac{1}{3}$$ ΔABC |
| B. | ABD = $$\frac{1}{2}$$ ΔABC |
| C. | ABC = $$\frac{1}{2}$$ ΔABD |
| D. | ABC = ΔABD |
| Answer» E. | |
| 83. |
In an isosceles triangle ΔABC, AB = AC and ∠A = 80°. The bisector of ∠B and ∠C meet at D. The ∠BDC is equal to. |
| A. | 0° |
| B. | 00° |
| C. | 30° |
| D. | 0° |
| Answer» D. 0° | |
| 84. |
If in ΔABC, DE || BC, AB = 7.5 cm BD = 6 cm and DE = 2 cm then the length of BC in cm is: |
| A. | cm |
| B. | cm |
| C. | 0 cm |
| D. | 0.5 cm |
| Answer» D. 0.5 cm | |
| 85. |
Incenter of ΔABC is I. ∠ABC = 90° and ∠ACB = 70°. ∠BIC is: |
| A. | 15° |
| B. | 00° |
| C. | 10° |
| D. | 05° |
| Answer» C. 10° | |
| 86. |
PQR is an equilateral triangle. MN is drawn parallel to QR such that M is on PQ and N is on PR. If PN = 6 cm, then the length of MN is: |
| A. | cm |
| B. | cm |
| C. | 2 cm |
| D. | .5 cm |
| Answer» C. 2 cm | |
| 87. |
Length of the sides of a triangle are a, b and c respectively. If a2 + b2 + c2 = ab + bc + ca then the triangle is: |
| A. | sosceles |
| B. | quilateral |
| C. | calene |
| D. | ight-angled |
| Answer» C. calene | |
| 88. |
In ΔPQR, straight line parallel to the base QR cuts PQ at X and PR at Y. If PX : XQ = 5 : 6, then XY : QR will be |
| A. | : 11 |
| B. | : 5 |
| C. | 1 : 6 |
| D. | 1 : 5 |
| Answer» B. : 5 | |
| 89. |
In a ΔPQR, ∠Q = 55° and ∠R = 35°. Find the ratio of angles subtended by side QR on circumcenter, incenter and orthocenter of the triangle. |
| A. | : 2 : 1 |
| B. | : 2 : 4 |
| C. | : 2 : 4 |
| D. | : 3 : 2 |
| Answer» E. | |
| 90. |
ΔABC is similar to ΔDEF. If the sides of ΔABC, that is AB, BC and CA, are 3, 4 and 5 cms respectively, what would be the perimeter of the ΔDEF, if the side DE measures 12 cms ? |
| A. | 4 cms |
| B. | 0 cms |
| C. | 6 cms |
| D. | 8 cms |
| Answer» E. | |
| 91. |
The side BC of a triangle ABC is proceed to D. If ∠ACD = 112° and ∠B = $$\frac{3}{4}$$ ∠A, then the measure of ∠B is: |
| A. | 4° |
| B. | 0° |
| C. | 8° |
| D. | 5° |
| Answer» D. 5° | |
| 92. |
ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, AC respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is: |
| A. | quilateral |
| B. | sosceles triangle |
| C. | ight angle triangle |
| D. | one of these |
| Answer» B. sosceles triangle | |
| 93. |
In ΔABC, the line parallel to BC intersect AB & AC at P & Q respectively. If AB : AP = 5 : 3, then AQ : QC is: |
| A. | : 2 |
| B. | : 2 |
| C. | : 5 |
| D. | : 3 |
| Answer» B. : 2 | |
| 94. |
In ΔABC, ∠B = 60° and ∠C = 40°; AD and AE are respectively the bisector of ∠A and perpendicular on BC. The measure of ∠EAD is: |
| A. | ° |
| B. | 1° |
| C. | 0° |
| D. | 2° |
| Answer» D. 2° | |
| 95. |
In ΔABC and ΔDEF, if ∠A = 50°, ∠B = 70°, ∠C = 60°, ∠D = 60°, ∠E = 70° and ∠F = 50°, then |
| A. | ABC ∼ ΔFED |
| B. | ABC ∼ ΔDFE |
| C. | ABC ∼ ΔEDF |
| D. | ABC ∼ ΔDEF |
| Answer» B. ABC ∼ ΔDFE | |
| 96. |
In ΔABC, ∠B = 70° and ∠C = 30°, AD and AE are respectively the perpendicular on side BC and bisector of ∠A. The measure of ∠DAE is: |
| A. | 4° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» E. | |
| 97. |
In ΔABC and ΔPQR, ∠B = ∠Q, ∠C = ∠R. M is the midpoint on QR, If AB : PQ = 7 : 4, then $$\frac{{{\text{area}}\,\left( {\vartriangle ABC} \right)}}{{{\text{area}}\,\left( {\vartriangle PMR} \right)}}$$is : |
| A. | $\frac{{35}}{8}$$ |
| B. | $\frac{{35}}{{16}}$$ |
| C. | $\frac{{49}}{{16}}$$ |
| D. | $\frac{{49}}{8}$$ |
| Answer» E. | |
| 98. |
A point D is taken on the side BC of a right-angled triangle ABC, where AB is hypotenuse. Then |
| A. | B2 + CD2 = AD2 + BC2 |
| B. | D2 + BD2 = 2AD2 |
| C. | B2 + AC2 = 2AD2 |
| D. | B2 = AD2 + BC2 |
| Answer» B. D2 + BD2 = 2AD2 | |
| 99. |
ABC is a right-angled triangle with AB = 6 cm and BC = 8 cm. A circle with center O has been inscribed inside ΔABC. The radius of the circle is |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | cm |
| Answer» C. cm | |
| 100. |
G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ? |
| A. | $\frac{{5\sqrt 3 }}{3}\,cm$$ |
| B. | $\frac{{10\sqrt 3 }}{3}\,cm$$ |
| C. | $5\sqrt 3 \,cm$$ |
| D. | $10\sqrt 3 \,cm$$ |
| Answer» C. $5\sqrt 3 \,cm$$ | |