Geometry (Part-5)

Total Questions: 50

1. If the medians of a triangle are equal, then the triangle will be : [SSC CGL 23/09/2024 (2nd Shift)]

Correct Answer: (a) Equilateral triangle
Solution:If the medians of a triangle are equal, the triangle will be equileteral. This is because in any triangle, the medians are proportional to the sides. If all three medians are of equal length, it implies that all three sides of the triangle must also be equal. Hence, the triangle must be equilateral.

2. If in a circle a chord of length 14 cm is at a distance of 24 cm from its centre, then the length of the radius of the circle is: [SSC CGL 23/09/2024 (3rd Shift)]

Correct Answer: (d) 25 cm
Solution:

3. If each side of an equilateral triangle is 37√3 cm, then its altitude (in cm) is equal to [SSC CGL 23/09/2024 (3rd Shift)]

Correct Answer: (d) 55.5
Solution:

4. In ∆PQR, if 4 ∠P = 5 ∠Q = 20 ∠R, then the value of ∠Q is: [SSC CGL 23/09/2024 (3rd Shift)]

Correct Answer: (a) 72°
Solution:

5. Triangle XYZ is an isosceles triangle with sides XY = XZ If the measure of angle Y is 80°, what is the measure of angle X ? [SSC CGL 24/09/2024 (1st Shift)]

Correct Answer: (c) 20°
Solution:

6. PQ is the diameter of a circle with centre A. M is a point on the circumference of the circle. If m ∠MAP = 110°, then find the value of m∠MQA. [SSC CGL 24/09/2024 (1st Shift)]

Correct Answer: (a) 55°
Solution:

7. Let C be a circle with centre O and PQ be a minor arc on C. Let R and S be two points on the major arc of PQ on C. If PQ subtends an angle 80° at O, find ∠PRQ and ∠PSQ, respectively. [SSC CGL 24/09/2024 (2nd Shift)]

Correct Answer: (c) 40° and 40°
Solution:

8. In ∆DEF, DE = 12cm, EF =15cm, and ∠DEF = 90º. ∆DEF is congruent to ∆XYZ. If YZ = 15cm, then what is the length of XZ ? [SSC CGL 24/09/2024 (2nd Shift)]

Correct Answer: (a) 3√41 cm
Solution:

9. If two straight lines are coinciding with each other, then the number of points of intersection is/are: [SSC CGL 24/09/2024 (3rd Shift)]

Correct Answer: (a) infinitely many points of intersection
Solution:When two lines coincide with each other then there are infinitely many solution or points of intersection.

10. Let ABC be a triangle. If the mid-points of AB, BC and AC are D, E and F, respectively, then ∆DEF is NOT congruent to_______ . [SSC CGL 24/09/2024 (3rd Shift)]

Correct Answer: (d) ∆AВС
Solution: