Geometry (Part-7)

Total Questions: 50

21. In ∆ABC, ∠A = 85º and ∠C = 58º. If ∆PQR is similar to ∆ABC , and in correspondence, then find ∠Q . [SSC CHSL Tier II (02/11/2023)]

Correct Answer: (a) 37º
Solution:

22. In ∆XYZ if XY = 5cm, XZ = 7cm and Q is a point on YZ such that XQ bisects ∠X then YQ : QZ is: [SSC CHSL Tier II (10/01/2024)]

Correct Answer: (a) 5 : 7
Solution:

23. The measures of two angles of a triangle are in the ratio 3 : 7. If the sum of these two measures is equal to the measure of the third angle, then find the smallest angle. [SSC CHSL Tier II (10/01/2024)]

Correct Answer: (a) 27º
Solution:

24. An equilateral triangle ABC surmounts a square BCDE. The value of ∠EAB + 3∠AEB is: [SSC CGL Tier II (26/10/2023)]

Correct Answer: (a) 60°
Solution:

25. One chord of a circle is given as 20.5 cm. Then the radius (r) of the circle must be: [SSC CGL Tier II (26/10/2023)]

Correct Answer: (d) r ≥ 10.25
Solution:

26. If the hypotenuse of a right-angled triangle is 29 cm and the sum of the other two sides is 41 cm, then the difference between the other two sides is: [SSC CPO 03/10/2023 (1st Shift)]

Correct Answer: (d) 1 cm
Solution:

27. For a triangle ABC, D and E are two points on AB and AC such that AD = 1/6 AB, AE = 1/6 AC. If BC = 22 cm, then DE is ______ .(Consider up to two decimals) [SSC CPO 03/10/2023 (2nd Shift)]

Correct Answer: (a) 3.67 cm
Solution:

28. A sector of a circle has a central angle of 45° and an arc length of 22 cm. Find the radius of the circle. (Use π = 22/7) [SSC CPO 03/10/2023 (2nd Shift)]

Correct Answer: (a) 28 cm
Solution:

29. In two circles centered at O and O', the distance between the centers of both circles is 17 cm. The points of contact of a direct common tangent between the circles are P and Q If the radii of both circles are 7 cm and 15 cm, respectively, then the length of PQ is equal to: [SSC CPO 03/10/2023 (3rd Shift)]

Correct Answer: (a) 15 cm
Solution:

30. PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at S. If ∠QSR = 40°, then ∠P is: [SSC CPO 04/10/2023 (1st Shift)]

Correct Answer: (a) 80°
Solution: