Geometry (Part-10)

Total Questions: 50

31. ∆XYZ  ∼ ∆GST and XY : GS = 2:3 XV is the median to the side YZ,, and GD is the median to the side ST. The value of (YV/SD)² is_____ . [SSC CGL 03/12/2022 (2nd Shift)]

Correct Answer: (a) 4/9
Solution:

32. A,B,C are three angles of a triangle. If ∠A - ∠B = 45º and ∠B - ∠C = 15° then ∠A = ? [SSC CGL 03/12/2022 (3rd Shift)]

Correct Answer: (c) 95°
Solution:

33. Find the number of common tangents, if r₁ + r₂ = C₁ C₂ (With usual notations, r₁ & r₂ and C₁ & C₂ are the radii and centres of the two circles.) [SSC CGL 05/12/2022 (1st Shift)]

Correct Answer: (c) 3
Solution:

34. The perimeter of a triangle with sides of integer values are equal to 13. How many such triangles are possible? [SSC CGL 05/12/2022 (3rd Shift)]

Correct Answer: (a) 5
Solution:

Let, a, b and c be the sides of a triangle
Then :- (a + b) > c > (a - b)
Perimeter of the triangle is equal to 13.
Possible triangle are five having sides
(1,6,6) , (2,5,6) , (3,5,5) , (3,4,6) and (4,4,5)

35. In a ∆ABC, the internal bisectors of the angle B and the angle C intersect at an angle of 105°. What is the value of the angle A? [SSC CGL 05/12/2022 (3rd Shift)]

Correct Answer: (d) 30º
Solution:

36. Three circles of radius 4 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string? [SSC CGL 05/12/2022 (4th Shift)]

Correct Answer: (a) 24 + 8π cm
Solution:

37. The mid point of AB and AC of a triangle ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC - XY is: [SSC CGL 06/12/2022 (1st Shift)]

Correct Answer: (d) 8 cm
Solution:

38. The number of parallel tangents of a circle with a given tangent is: [SSC CGL 06/12/2022 (4th Shift)]

Correct Answer: (a) 1
Solution:

The number of parallel tangents of a circle with a given tangentsis always 1.

39. ∆PQR is an isosceles triangle and PQ = PR = 2a unit, QR a unit. Draw PX ⊥ QR, and find the length of PX. [SSC CGL 06/12/2022 (4th Shift)]

Correct Answer: (d)
Solution:

40. The height of an equilateral triangle is 9√3 cm. What is the area of this equilateral triangle? [SSC CGL 07/12/2022 (1st Shift)]

Correct Answer: (d) 81√3 cm²
Solution: