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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.
| 1. |
In a triangle ABC, ∠A = 90° and D is mid-point of AC. The value of BC2 - BD2 is equal to |
| A. | AD2 |
| B. | 2AD2 |
| C. | 3AD2 |
| D. | 4AD2 |
| Answer» B. 2AD2 | |
| 2. |
Let ΔABC be a triangle whose area is 10√3 units with side lengths |AB| = 8 units and |AC| = 5 units. Find possible values of the angle A. |
| A. | 60° or 120° |
| B. | 45° or 135° |
| C. | 30° only |
| D. | 90° only |
| Answer» B. 45° or 135° | |
| 3. |
In ΔABC, AB = 5 cm BC = 6 cm, and CA = 7 cm a transversal is drawn to cut the sides AB at F, BC produced at D and CA at E so that AF = 2 cm, AE = 4 cm applying Menelaus theorem the length of BD is: |
| A. | 12 cm |
| B. | 8 cm |
| C. | 10 cm |
| D. | 14 cm |
| Answer» C. 10 cm | |
| 4. |
If in a ΔABC, a = 8, b = 15 and c = 17, then the value of cos A will be |
| A. | \(\frac{{8}}{{15}}\) |
| B. | \(\frac{{15}}{{17}}\) |
| C. | \(\frac{8}{{17}}\) |
| D. | \(\frac{{17}}{{20}}\) |
| Answer» C. \(\frac{8}{{17}}\) | |
| 5. |
Consider the following statements in respect of the points (p, p - 3), (q + 3, q) and (6, 3):1. The points lie on a straight line.2. The points always lie in the first quadrant only for any value of p and q.Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 6. |
If perpendicular of a right angled triangle is 8 cm and its area is 20 cm2, the length of base is? |
| A. | 20 cm |
| B. | 05 cm |
| C. | 40 cm |
| D. | 08 cm |
| Answer» C. 40 cm | |
| 7. |
In a triangle ABC, AB = AC and the perimeter of ΔABC is 8(2 + √2) cm. If the length of BC is √2 times the length of AB, then find the area of ΔABC. |
| A. | 16 cm2 |
| B. | 32 cm2 |
| C. | 28 cm2 |
| D. | 36 cm2 |
| Answer» C. 28 cm2 | |
| 8. |
In a triangle ΔABC, if AB = 5, BC = 3 and CA = 4, then the value of \(\sin \frac A 2 + \tan \frac A 2\) is: |
| A. | \(3 + \sqrt {10}\) |
| B. | \(\frac {1 + \sqrt {10}} 9\) |
| C. | \(\frac {3 + \sqrt {10}} {3\sqrt {10}}\) |
| D. | \(\frac {9 + \sqrt {10}} 6\) |
| Answer» D. \(\frac {9 + \sqrt {10}} 6\) | |
| 9. |
In Δ ABC, the coordinates of B are (0, 0), AB = 2, ∠ABC = π/3 and the middle point of BC has the coordinates (2, 0). The centroid of triangle is: |
| A. | (1, -1) |
| B. | \(\left( {\frac{1}{2},\frac{{\sqrt 3 }}{2}} \right)\) |
| C. | \(\left( {\frac{5}{{ 3 }},\frac{1}{{\sqrt 3 }}} \right)\) |
| D. | \(\left( {\frac{{\sqrt 2 }}{3},\frac{1}{3}} \right)\) |
| Answer» D. \(\left( {\frac{{\sqrt 2 }}{3},\frac{1}{3}} \right)\) | |
| 10. |
In a lake, the tip of a bud of lotus is seen 10 cm above the surface of water. Forced by the wind, it gradually moved, and just submerged at a distance of 30 cm. The depth of water at the root of the lotus plant will be |
| A. | 40 cm |
| B. | 50 cm |
| C. | 60 cm |
| D. | 70 cm |
| Answer» B. 50 cm | |
| 11. |
A triangle with vertices (4, 0), (-1, -1) and (3, 5) is: |
| A. | isosceles and right angled |
| B. | isosceles but not right angled |
| C. | right angled but not isosceles |
| D. | neither right angled nor isosceles |
| Answer» B. isosceles but not right angled | |
| 12. |
If ΔABC and ΔDEF are similar and ∠A = 47°, ∠E = 83°, then ∠C is |
| A. | 80° |
| B. | 83° |
| C. | 47° |
| D. | 50° |
| Answer» E. | |
| 13. |
P(3, 1), Q(6, 5), and R(x, y) are three points such that the angle ∠PRQ is a right angle and the area ΔRQP = 7, then the number of such points R is |
| A. | 0 |
| B. | 2 |
| C. | 4 |
| D. | 1 |
| Answer» C. 4 | |
| 14. |
If three concurrent straight lines AD, BE and CF are drawn from the angular points of a triangle ΔABC to meet the opposite sides such that \(\dfrac{AF}{FB} = \dfrac{1}{2},\ \dfrac{BD}{DC} = \dfrac{2}{3}\), then by applying Ceva's theorem, \(\dfrac{EA}{EC}\) is equal to: |
| A. | 1/3 |
| B. | 3/2 |
| C. | 2/3 |
| D. | 1 |
| Answer» B. 3/2 | |
| 15. |
Let ABC be a triangle. If D(2, 5) and E(5, 9) are the mid-points of the sides AB and AC respectively, then what is the length of the side BC? |
| A. | 8 |
| B. | 10 |
| C. | 12 |
| D. | 14 |
| Answer» C. 12 | |
| 16. |
If ABC is an isosceles triangle and perpendicular AD is drawn from the vertex A to any point D on the base, then |
| A. | AB2 - AD2 = BD.DC |
| B. | AB2 + AD2 = BD.DC |
| C. | AB2 - AD2 = BD2 - DC2 |
| D. | AB2 + AD2 = BC2 - DC2 |
| Answer» B. AB2 + AD2 = BD.DC | |
| 17. |
In ΔABC, if a = 2, b = 4 and ∠C = 60°, then A and B are respectively equal to |
| A. | 90°, 30° |
| B. | 45°, 75° |
| C. | 60°, 60° |
| D. | 30°, 90° |
| Answer» E. | |
| 18. |
If a vertex of a triangle is (1, 1) and the midpoints of two sides of the triangle through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is |
| A. | \(\left( { - \frac{1}{3},\frac{7}{3}} \right)\) |
| B. | \(\left( { - 1,\frac{7}{3}} \right)\) |
| C. | \(\left( {\frac{1}{3},\frac{7}{3}} \right)\) |
| D. | \(\left( {1,\frac{7}{3}} \right)\) |
| Answer» E. | |
| 19. |
On the basis of angle, how many types of triangle are there? |
| A. | 2 |
| B. | 10 |
| C. | 9 |
| D. | 3 |
| Answer» E. | |
| 20. |
If I be the incentre of the triangle ABC, and a, b, c be the lengths of the sides BC, CA and AB respectively, then \(a\overrightarrow {IA} + b\overrightarrow {IB} + c\overrightarrow {IC} \) equals |
| A. | \(\overrightarrow 0 \) |
| B. | \(\overrightarrow {AB}\) |
| C. | \(\overrightarrow {AC}\) |
| D. | \(\overrightarrow {AD}\) |
| Answer» B. \(\overrightarrow {AB}\) | |
| 21. |
If the circumcentre of the triangle formed by the lines x + 2 = 0, y + 2 = 0 and kx + y + 2 = 0 is (-1, -1), then what is the value of k? |
| A. | -1 |
| B. | -2 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 22. |
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively: |
| A. | 30°, 30° |
| B. | 15°, 75° |
| C. | 30°, 60° |
| D. | 30°, 120° |
| Answer» B. 15°, 75° | |
| 23. |
In a ΔABC, ∠A + ∠B = 75° and ∠B + ∠C = 140°, then ∠B is: |
| A. | 0° |
| B. | 5° |
| C. | 0° |
| D. | 5° |
| Answer» C. 0° | |
| 24. |
If ΔPQR and ΔLMN are similar and 3PQ = LM and MN = 9 cm, then QR is equal to: |
| A. | 2 cm |
| B. | cm |
| C. | cm |
| D. | cm |
| Answer» E. | |
| 25. |
An equilateral triangle of side 6 cm is inscribed in a circle. Then radius of the circle is: |
| A. | $2\sqrt 3 $$cm |
| B. | $3\sqrt 2 $$cm |
| C. | $4\sqrt 3 $$cm |
| D. | $\sqrt 3 $$cm |
| Answer» B. $3\sqrt 2 $$cm | |
| 26. |
In ΔABC, AC = BC and ∠ABC = 50°, the side BC is produced to D so that BC = CD then the value of ∠BAD is: |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» D. 0° | |
| 27. |
ΔABC is similar to ΔDEF is area of ΔABC is 9 sq. cm. and area of ΔDEF is 16 sq. cm. and BC = 21 cm. Then the length of EF will be: |
| A. | .6 cm |
| B. | .8 cm |
| C. | .7 cm |
| D. | .4 cm |
| Answer» C. .7 cm | |
| 28. |
Which of the following is a true statement |
| A. | wo similar triangles are always congruent |
| B. | wo similar triangles have equal areas |
| C. | wo triangles are similar if their corresponding sides are proportional |
| D. | wo polygons are similar if their corresponding sides are proportional |
| Answer» D. wo polygons are similar if their corresponding sides are proportional | |
| 29. |
ABC is a triangle, PQ is line segment intersecting AB is P and AC in Q and PQ || BC. The ratio of AP : BP = 3 : 5 and length of PQ is 18 cm. The length of BC is: |
| A. | 8 cm |
| B. | 8 cm |
| C. | 4 cm |
| D. | 2 cm |
| Answer» C. 4 cm | |
| 30. |
In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incenter of ΔABC, ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are: |
| A. | 5°, 130° |
| B. | 5°, 125° |
| C. | 5°, 40° |
| D. | 0°, 150° |
| Answer» C. 5°, 40° | |
| 31. |
If the measure of the angles of a triangle are in the ratio 1 : 2 : 3 and if the length of the smallest side of the triangle is 10 cm, then the length of the longest side is: |
| A. | 0 cm |
| B. | 5 cm |
| C. | 0 cm |
| D. | 5 cm |
| Answer» B. 5 cm | |
| 32. |
In case of an acute angled triangle, its orthocenter lies: |
| A. | nside the triangle |
| B. | utside the triangle |
| C. | n the triangle |
| D. | n one of the vertex of the triangle |
| Answer» B. utside the triangle | |
| 33. |
In an equilateral triangle ABC, G is the centroid. Each side of the triangle is 6 cm. The length of AG is: |
| A. | $2\sqrt 2 $$cm |
| B. | $3\sqrt 2 $$cm |
| C. | $2\sqrt 3 $$cm |
| D. | $3\sqrt 3 $$cm |
| Answer» D. $3\sqrt 3 $$cm | |
| 34. |
In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is: |
| A. | cm |
| B. | cm |
| C. | cm |
| D. | 2 cm |
| Answer» D. 2 cm | |
| 35. |
In ΔABC, AB = BC = K, AC = $$\sqrt 2 $$ k, then ΔABC is a : |
| A. | ight isosceles triangle |
| B. | sosceles triangle |
| C. | ight-angled triangle |
| D. | quilateral triangle |
| Answer» B. sosceles triangle | |
| 36. |
In ΔABC, AD ⊥ BC and AD2 = BD × DC. The measure of ∠BAC is : |
| A. | 5° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» C. 5° | |
| 37. |
In a ΔABC, If 2∠A = 3∠B = 6∠C, then the value of ∠B is: |
| A. | 0° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» B. 0° | |
| 38. |
Let ABC be an equilateral triangle and AD perpendicular to BC, then AB2 + BC2 + CA2 = ? |
| A. | AD2 |
| B. | AD2 |
| C. | AD2 |
| D. | AD2 |
| Answer» E. | |
| 39. |
In ΔABC, ∠BAC = 90° and AD ⊥ BC. If BD = 3 cm and CD = 4 cm, then length of AD is : |
| A. | $2\sqrt 3 $$ cm |
| B. | .5 cm |
| C. | cm |
| D. | cm |
| Answer» B. .5 cm | |
| 40. |
If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB = 19 cm and AC = 22 cm then the length of BC is : |
| A. | 0.5 cm |
| B. | 9.5 cm |
| C. | 6 cm |
| D. | 3 cm |
| Answer» E. | |
| 41. |
In ΔABC, if AD ⊥ BC, then AB2 + CD2 is equal to |
| A. | BD2 |
| B. | D2 + AC2 |
| C. | AC2 |
| D. | one of these |
| Answer» C. AC2 | |
| 42. |
If I be the incentre of ΔABC and ∠B = 70° and ∠C = 50°, then the magnitude of ∠BIC is |
| A. | 30° |
| B. | 0° |
| C. | 20° |
| D. | 05° |
| Answer» D. 05° | |
| 43. |
In ΔABC, the external bisectors of the angles ∠B and ∠C meet at the point O. If ∠A = 70°, then the measure of ∠BOC is : |
| A. | 5° |
| B. | 0° |
| C. | 5° |
| D. | 0° |
| Answer» D. 0° | |
| 44. |
Given that the ratio of altitudes of two triangles is 4 : 5, ratio of their areas is 3 : 2, the ratio of their corresponding bases is : |
| A. | : 8 |
| B. | 5 : 8 |
| C. | : 5 |
| D. | : 15 |
| Answer» C. : 5 | |
| 45. |
If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60°, BC = 8 cm, then area of the triangle ABC is: |
| A. | $96\sqrt 3 $$cm2 |
| B. | $48\sqrt 3 $$cm2 |
| C. | 8 cm2 |
| D. | $54\sqrt 3 $$cm2 |
| Answer» C. 8 cm2 | |
| 46. |
∠A + $$\frac{1}{2}$$ ∠B + ∠C = 140°, then ∠B is : |
| A. | 0° |
| B. | 0° |
| C. | 0° |
| D. | 0° |
| Answer» C. 0° | |
| 47. |
For a triangle ABC, D, E, F are the mid - point of its sides. If ΔABC = 24 sq. units then ΔDEF is : |
| A. | sq. units |
| B. | sq. units |
| C. | sq. units |
| D. | 2 sq. units |
| Answer» C. sq. units | |
| 48. |
∠A of ΔABC is a right angle. AD is perpendicular on BC. If BC = 14 and BD = 5 cm, then measure of AD is: |
| A. | $\sqrt 5 $$ cm |
| B. | $3\sqrt 5 $$ cm |
| C. | $3.5\sqrt 5 $$cm |
| D. | $2\sqrt 5 $$ cm |
| Answer» C. $3.5\sqrt 5 $$cm | |
| 49. |
ABC is a triangle in which ∠A = 90°. Let P be any point on side AC. If BC = 10 cm, AC = 8 cm and BP = 9 cm, then AP = ? |
| A. | $2\sqrt 5 $$ cm |
| B. | $3\sqrt 5 $$ cm |
| C. | $2\sqrt 3 $$ cm |
| D. | $3\sqrt 3 $$ cm |
| Answer» C. $2\sqrt 3 $$ cm | |
| 50. |
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. | 00° |
| B. | 0° |
| C. | 30° |
| D. | 0° |
| Answer» B. 0° | |