101)

A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R, respectively. If AB - BC = 4 cm, AB - AC = 2 cm, and the perimeter of ΔABC = 32 cm, then AC (in cm) = ?

SSC CGL 2022

A)

\(\frac{32}{3}\)

B)

\(\frac{38}{3}\)

C)

\(\frac{35}{3}\)

D)

\(\frac{26}{3}\)

102)

In a ΔABC, the bisector of ∠A meets BC at D. If AB = 9.6 cm, AC = 11.2 cm and BD = 4.8 cm, the perimeter (in cm) of ΔABC is:

SSC CGL 2022

A)

30.4

B)

28.6

C)

31.2

D)

32.8

103)

The sides AB and AC of ΔABC are produced to points D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 88°, the measure of ∠P is :

SSC CGL 2022

A)

51°

B)

56°

C)

46°

D)

61°

104)

In ΔABC, AB = 7 cm, BC = 10 cm, and AC = 8 cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then \( \frac{DC}{4}\) (in cm) is equal to:

SSC CGL 2022

A)

\(11\over 3\)

B)

\(4\over 3\)

C)

\(14\over 3\)

D)

\(7\over 3\)

105)

The area of similar triangles PQR and MNT are 196 cm² and 169 cm² respectively. If the longest side of the larger Δ PQR be 28 cm then what is the length (in cm) of the longest side of the smaller Δ MNT?

SSC CGL 2022

A)

25

B)

24

C)

26

D)

27

106)

In Δ PQR, S is a point on the side QR such that PS is the bisector of ∠QPR. If PQ = 12 cm, QS = 3 cm and QR = 7 cm, then what is the length of side PR?

SSC CGL 2022

A)

15 cm

B)

14 cm

C)

18 cm

D)

16 cm

107)

In a ΔABC, D, E and F are the mid-points of side BC, CA and AB respectively. If BC = 14.4 cm, CA = 15.2 cm and AB = 12.4 cm, what is the perimeter (in cm) of the ΔDEF?

SSC CGL 2022

A)

35

B)

42

C)

28

D)

21

108)

Let ΔABC ~ ΔQPR and (Area of ΔABC) : (Area of ΔPQR) = 121 : 64. If QP = 14.4 cm, PR = 12 cm and AC = 18 cm, then what is the length of AB?

SSC CGL 2022

A)

21.6 cm

B)

16.2 cm

C)

19.8 cm

D)

32.4 cm

109)

The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?

SSC CGL 2022

A)

6.4

B)

7.2

C)

9.6

D)

12.8

110)

In ΔABC, ∠A = 66°, BD ⊥ AC and CE ⊥ AB. BD and EC intersect at P. The bisectors ∠PBC and ∠PCB meet at Q. What is the measure of ∠BQC?

SSC CGL 2022

A)

143°

B)

132°

C)

127°

D)

147°