Geometry (Part-5)

Total Questions: 50

11. In ∆АВС, АВ = 6 cm, BC = 9 cm and AC = 12 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then find DC. [SSC CGL 24/09/2024 (3rd Shift)]

1. (a) 9
2. (b) 6
3. (c) 3
4. (d) 7

Correct Answer: (b) 6

Solution:

12. A line cuts two concentric circles. The length of chords formed by this line on the circles is 6 cm and 18 cm. Find the difference in the squares of the radii of two circles. [SSC CGL 24/09/2024 (3rd Shift)]

1. (a) 90
2. (b) 120
3. (c) 60
4. (d) 72

Correct Answer: (d) 72

Solution:

13. It is always possible to draw a circle passing through_________non-collinear points in a plane. [SSC CGL 25/09/2024 (1st Shift)]

1. (a) 3
2. (b) 6
3. (c) 5
4. (d) 4

Correct Answer: (a) 3

Solution:It is always possible to draw a circle passing through 3 non-collinear points in a plane.

14. If the lengths of two sides of an isosceles triangle are 6 cm and 12 cm, then find the length of the third side. [SSC CGL 25/09/2024 (1st Shift)]

1. (a) 8 cm
2. (b) 6 cm
3. (c) 12cm
4. (d) 14 cm

Correct Answer: (c) 12cm

Solution:In triangle
Third side < 18(12 + 6)
Third side > 6(12 - 6)
For isosceles triangle side must be equal to 12 or 6 cm but third side should be greater than 6cm.
Hence, third side = 12cm

15. The centres of two circles are 36 cm apart. If the radii of these two circles are 15 cm and 9 cm, respectively, then what is the sum of the lengths (in cm) of direct a common tangent and a transverse common tangent of these two circles? [SSC CGL 25/09/2024 (1st Shift)]

1. (a) 6√5 (√7+2)
2. (b) 6√7 (√5+2)
3. (c) 6√5 (√5+2)
4. (d) 6√7 (√7+2)

Correct Answer: (a) 6√5 (√7+2)

Solution:

16. The side BC of ∆ABC is produced to a point D. If AC = BC and ∠BAC = 70º then find the value of ∠ACD - ∠ABC [SSC CGL 25/09/2024 (1st Shift)]

1. (a) 70°
2. (b) 60°
3. (c) 75°
4. (d) 45°

Correct Answer: (a) 70°

Solution:

17. In a quadrilateral ABCD, AB = BC, AD = DC, ∠ABD = 68º, ∠ADB = (2y - 7)º, ∠BDC = 33º ∠DBC = (3x + 2)º. Then the value of 2x + 3y is: [SSC CGL 25/09/2024 (2nd Shift)]

1. (a) 108º
2. (b) 144º
3. (c) 104º
4. (d) 118º

Correct Answer: (c) 104º

Solution:

18. The two circles intersect at two points P and Q. PR and PS are diameters of the two circles. What is ∠PQR ? [SSC CGL 25/09/2024 (2nd Shift)]

1. (a) 90º
2. (b) 0º
3. (c) 45º
4. (d) 60º

Correct Answer: (a) 90º

Solution:

19. A circular arc whose radius is 14 cm, makes an angle of 45° at the centre. Find the perimeter (in cm) of the sector. (Use π = 22/7 ) [SSC CGL 25/09/2024 (2nd Shift)]

1. (a) 38
2. (b) 28
3. (c) 39
4. (d) 34

Correct Answer: (c) 39

Solution:

20. In the figure shown above, quadrilateral PQRS has its vertices on the circumference of the circle with centre O. If m∠QOS = 20x° and m∠QRS = 26x°, then what is the value of 'x' ? [SSC CGL 25/09/2024 (3rd Shift)]

1. (a) 6
2. (b) 5
3. (c) 4
4. (d) 3

Correct Answer: (b) 5

Solution:

Submit Quiz