Geometry (Part-4)

Total Questions: 50

1. ∆EFG and ∆HIJ are similar. Also, ∠E = ∠H and ∠F = ∠l. If 3EF = HI and FG = 9 cm, then IJ is equal to ________ . [SSC CGL 10/09/2024 (2nd Shift)]

Correct Answer: (b) 27 cm
Solution:

2. If 45° and 65° are the angles of a triangle, then find the exterior angle of the third angle (remaining angle). [SSC CGL 10/09/2024 (2nd Shift)]

Correct Answer: (a) 110°
Solution:

3. In a circle of radius 5√13 cm, a chord is at a distance of 10 cm from the centre of the circle. Find the length (in cm) of the chord. [SSC CGL 10/09/2024 (2nd Shift)]

Correct Answer: (a) 30
Solution:

4. If ∆PQR ≅ ∆MON such that ∠PQR = 82º, ∠QRP = 47º, ∠RPQ = 51º, ∠MON = (5y - 8)º , QR = 24 and ON = 3x + y, then find (x + y). [SSC CGL 10/09/2024 (3rd Shift)]

Correct Answer: (d) 20
Solution:

5. In a circle, two chords MN and PQ intersect at O. If MO = 9cm, ON = 5 cm and OQ = 6 cm, then the value of OP (in cm) is: [SSC CGL 11/09/2024 (1st Shift)]

Correct Answer: (a) 7.5
Solution:

6. In a ∆ABC right-angled at C, if tan A = √3, then the value of sinA cosB cot(A + B) is: [SSC CGL 11/09/2024 (1st Shift)]

Correct Answer: (c) 0
Solution:

Since, the triangle is right angled at C, we know that A+B = 90º
⇒ cot(A+B) = 90º = 0
Hence, sinA cosB cot(A+B)
= sinA cosB × 0 = 0

7. In a rhombus ABCD, O is any interior point such that OA = OC. What is five-ninths of the degree measure of ∠DOB ? [SSC CGL 11/09/2024 (1st Shift)]

Correct Answer: (c) 100º
Solution:

8. In ∆PQR, M, N, and S are the mid-points of sides PQ, PR and QR, respectively. If the area of the ∆PQR is 46 cm², what is the area (in cm²) of the quadrilateral MNRQ? [SSC CGL 11/09/2024 (2nd Shift)]

Correct Answer: (d) 34.5
Solution:

9. In a triangle ΔΑΒC, the ∠ABC = 90°. If sin(A) = 1/2, then cos(C) is equal to: [SSC CGL 11/09/2024 (2nd Shift)]

Correct Answer: (d)
Solution:

10. In a triangle ΔΑΒC, AB = AC and ∠A = 80º, then find ∠B. [SSC CGL 11/09/2024 (2nd Shift)]

Correct Answer: (a) 50°
Solution: