Geometry (Part-11)

Total Questions: 50

1. A coconut tree swings with the wind in such a manner that the angle covered by its trunk is 18 degrees. If the topmost portion of the tree covers a distance of 44 meters, find the length of the tree. [SSC CGL 12/12/2022 (2nd Shift)]

Correct Answer: (c) 140 meters
Solution:

2. If C₁, C₂ be the centres of two circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents. [SSC CGL 12/12/2022 (2nd Shift)]

Correct Answer: (d) 3
Solution:

3. What is the ASA congruence rule of triangles, where A and S represent angle and side of triangle respectively? [SSC CGL 12/12/2022 (3rd Shift)]

Correct Answer: (b) Two triangles are said to be congruent if 2 angles and the included side of one triangle are equal to 2 angles and the included side of the other triangle.
Solution:ASA congruence rule of triangles : If two angles and their included side of one triangles are equal to two corresponding angles and included side of another triangle, then those triangles are congruent.

4. If the areas of two isosceles triangles are in the ratio of x²: y², then the ratio of their corresponding heights is: [SSC CGL 12/12/2022 (4th Shift)]

Correct Answer: (a) x:y
Solution:

5. The hour hand moves through 4 hours and has a length of 6 cm. Find the area (in cm², rounded off to two decimal places) of the sector covered by the hour hand. [SSC CGL 13/12/2022 (1st Shift)]

Correct Answer: (c) 37.71
Solution:

6. A triangle and a parallelogram have the same base 28 cm and the same area. If the height of the parallelogram is 12 cm, then find the length of the altitude of the triangle. [SSC CGL 13/12/2022 (2nd Shift)]

Correct Answer: (c) 24 cm

7. Select the INCORRECT statement with respect to the properties of a circle. [SSC CGL 13/12/2022 (2nd Shift)]

Correct Answer: (d) The perpendicular distance from the centre of a circle increases when the length of a chord increases.
Solution:

On observing the given options, we find that statements (d) is incorrect as it says that the perpendicular distance from the center of a circle increase when the length of a chord increases.

8. If ∆ABC ≅ ∆PQR and ∠ABC =(x+ 60)°, ∠PQR = (85 - 4x)º, and ∠RPQ =(3x + 65)°, then the value of ∠ABC in degree is: [SSC CGL 13/12/2022 (3rd Shift)]

Correct Answer: (d) 65
Solution:

9. In the given figure, if KI = IT and EK = ET then ∠TEI = _____ . [SSC CGL 13/12/2022 (4th Shift)]

Correct Answer: (c) 105°
Solution:

10. Find the area of the shaded portion of an equilateral triangle with 6 units shown in the following figure. A circle of radius 1 unit is centered at the midpoint of a side of the triangle. [SSC CGL 13/12/2022 (4th Shift)]

Correct Answer: (a)