MCQOPTIONS
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MCQOPTIONS
This section includes 21 Mcqs, each offering curated multiple-choice questions to sharpen your GEOMETRY knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In ΔABC, AB = AC, ∠B = 70°, ∠BAD = 80°, ∠ADE = ? |
| A. | 150° |
| B. | 135° |
| C. | 140° |
| D. | 120° |
| Answer» B. 135° | |
| 2. |
In a ∆ ABC, the sides AB and AC have been produced to D and E. Bisectors of ∠ CBD and ∠ BCE meet at O. If ∠ A = 64°, then ∠ BOC is : |
| A. | 52° |
| B. | 58° |
| C. | 26° |
| D. | 112° |
| Answer» C. 26° | |
| 3. |
Longest side of a triangle is 20 cm and another side is 10 cm. If area of the triangle is 80 cm2, then what is the length (in cm) of its third side? |
| A. | 260 |
| B. | 250 |
| C. | 256 |
| D. | 240 |
| Answer» B. 250 | |
| 4. |
In a equilateral triangle ABC, if AD ⊥ BC, then : |
| A. | 2 AB2 = 3 AD2 |
| B. | 4 AB2= 3 AD2 |
| C. | 3 AB2= 4 AD2 |
| D. | 3 AB2= 2 AD2 |
| Answer» D. 3 AB2= 2 AD2 | |
| 5. |
In a Δ ABC, if D and E are the points on the sides AB and AC respectively such that DE || BC and if AD = x , DB = x – 2 , AE = x + 2 and EC = x – 1. then find the value of x . |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» C. 3 | |
| 6. |
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° | |
| 7. |
If the hypotenuse of a right triangle is 41 cm and the sum of the other two sides is 49 cm, find the difference between the other sides. |
| A. | 30 cm |
| B. | 31 cm |
| C. | 32 cm |
| D. | 29 cm |
| Answer» C. 32 cm | |
| 8. |
The sides of a triangle are in the ratio 3 : 4 : 6 . The triangle is : |
| A. | acute-angled |
| B. | right-angled |
| C. | obtuse-angled |
| D. | either acute-angled or right-angled |
| Answer» D. either acute-angled or right-angled | |
| 9. |
If ΔABC is an isosceles triangle with ∠C = 90° and AC = 5 cm then AB is : |
| A. | 5 cm |
| B. | 10 cm |
| C. | 5 2 cm |
| D. | 2.5 cm |
| Answer» E. | |
| 10. |
The radius of the incircle of the equilateral triangle having each side 6 cm is |
| A. | 2√3cm |
| B. | √3 cm |
| C. | 6√3 cm |
| D. | 2 cm |
| Answer» C. 6√3 cm | |
| 11. |
G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is |
| A. | (5√3) / 3 cm |
| B. | (10√3) / 3 cm |
| C. | 5√3 cm |
| D. | 10√3 cm |
| Answer» C. 5√3 cm | |
| 12. |
If ABC is an equilateral triangle and D is a point on BC such that AD ⊥ BC, then |
| A. | AB : BD = 1 : 1 |
| B. | AB : BD = 1 : 2 |
| C. | AB : BD = 2 : 1 |
| D. | AB : BD = 3 : 2 |
| Answer» D. AB : BD = 3 : 2 | |
| 13. |
The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle? |
| A. | 6 cm2 |
| B. | 8 cm2 |
| C. | 10 cm2 |
| D. | 12 cm2 |
| Answer» B. 8 cm2 | |
| 14. |
Which one of the following is a Pythagorean triple in which one side differs from the hypotenuse by two units?Where, n is a positive real number. |
| A. | (2n+ 1, 4n, 2n2+ 2n) |
| B. | (2n, 4n,n2+ 1) |
| C. | (2n2, 2n, 2n+ 1) |
| D. | (2n,n2– 1,n2+ 1) |
| Answer» E. | |
| 15. |
AB is a straight line, C and D are points the same side of AB such that AC is perpendicular to AB and DB is perpendicular to AB. Let AD and BC meet at E. What is AE/AD + BE / BC equal to? |
| A. | 2 |
| B. | 1.5 |
| C. | 1 |
| D. | None of these |
| Answer» E. | |
| 16. |
Consider the following statements: (I). If G is the centroid of ΔABC, then GA = GB = GC. (II). If H is the orthocentre of ΔABC, then HA = HB = HC. Which of the statements given above is/are correct? |
| A. | Only I |
| B. | Only II |
| C. | Both I and II |
| D. | Neither I nor II |
| Answer» E. | |
| 17. |
The cordinates of the incentre of the triangle whose sides are 3x – 4y = 0, 5x + 12y = 0 and y – 15 = 0, are |
| A. | (1, 8) |
| B. | (–1, 8) |
| C. | (2, 8) |
| D. | (2, –8) |
| Answer» C. (2, 8) | |
| 18. |
The length of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The value of angle C is 59°. Find the length of side AC. |
| A. | 12 |
| B. | 10 |
| C. | 14 |
| D. | 16 |
| Answer» D. 16 | |
| 19. |
In the adjoining figure, if BC = a, AC = b, AB = c and ∠CAB = 120° , then the correct relation is: |
| A. | a2 = b2 + c2 + 2 bc |
| B. | a2 = b2 + c2 – 2 bc |
| C. | a2 = b2 + c2 + bc |
| D. | a2 = b2 + c2 – bc |
| Answer» D. a2 = b2 + c2 – bc | |
| 20. |
Two medians PS and RT of ΔPQR intersect at G at right angles. If PS = 9 cm and RT = 6 cm, then the length of RS in cm is |
| A. | 10 |
| B. | 6 |
| C. | 5 |
| D. | 3 |
| Answer» D. 3 | |
| 21. |
In the given figure, if area of triangle ABC is 64 sq. units, then find the area of triangle PQR, where D, E and F are mid points of sides of ΔABC and P, Q and R are midpoints of sides of ΔDEF. |
| A. | 4 sq units |
| B. | 6 sq units |
| C. | 8 sq units |
| D. | 16 sq units |
| Answer» B. 6 sq units | |