Geometry (Part-6)

Total Questions: 50

21. Two triangles ABC and DEF are similar. The smallest side of ABC is equal to 15 units. If the sides of ABC are in the ratio 3 : 4 : 5, and the area of DEF is half of the area of ABC, then what is the largest side of DEF (in units) ? [SSC CHSL 08/07/2024 (4th Shift)]

Correct Answer: (b)
Solution:

22. The hypotenuse of a right triangle is 6m more than twice the shortest side. If the third side is 2 m less than the hypotenuse, find the area(in m²) of the triangle. [SSC CHSL 09/07/2024 (1st Shift)]

Correct Answer: (c) 120
Solution:

23. Find the length of the sides of a triangle, if its angles are in the ratio 2: 4: 6 and its circumradius is 12 cm. [SSC CHSL 09/07/2024 (1st Shift)]

Correct Answer: (d) 12 cm, 12√3 cm, 24 cm
Solution:

24. PQ is the diameter of a circle with centre O. PT is a tangent touching the circle at P. [SSC CHSL 09/07/2024 (2nd Shift)]

The secant QT intersects the circle at S. O and S are joined. If ∠SOP = 104º, what is the measure (in degrees) of ∠PTQ ?

Correct Answer: (d) 38
Solution:

25. ∆XYZ is similar to ∆PQR . If the ratio of the perimeter of ∆XYZ to the perimeter of ∆PQR is 16:9 and PQ = 3.6 cm, then what is the length (in cm) of XY? [SSC CHSL 09/07/2024 (2nd Shift)]

Correct Answer: (c)
Solution:

26. Consider AD is a tangent to a circle of radius 6 cm. AC is a secant meeting the circle at B and CD is a diameter. If AB is 7 cm, then the value of AC (in cm) is: [SSC CHSL 09/07/2024 (2nd Shift)]

Correct Answer: (a) 16
Solution:

27. The sides ST and TR and the median SU of the ∆STR are equal to the sides MN and NJ and the median MV of the ∆MNJ, respectively. If ∠TSU = 46º ∠NMJ = 79º and ∠MVN = 88º what is the degree measure of 7/11 ∠SRT? [SSC CHSL 09/07/2024 (3rd Shift)]

Correct Answer: (a) 35°
Solution:

28. The lengths of the three sides of a triangle are 19 cm, 25 cm and y cm. Which of the following options most accurately gives the possible values of 'y'? [SSC CHSL 09/07/2024 (4th Shift)]

Correct Answer: (b) 6 < y < 44
Solution:

29. By decreasing 17° from each angle of a triangle, the ratio of their angles is 3 : 4 : 7. The radian measure of the greatest angle is: [SSC CHSL 09/07/2024 (4th Shift)]

Correct Answer: (d)
Solution:

30. R wishes to use a stick of length 6 units as a common internal tangent to two circles of radius two units and three units. What can be the maximum distance (in units) between the centres of the circle? [SSC CHSL 10/07/2024 (1st Shift)]

Correct Answer: (d) √61
Solution: