11)

S is the incenter of \(\triangle PQR\) . If \(\angle PSR = 125^0\) , then the measure of \(\angle PQR\) is:

SSC CGL 2019

A)

\(75^0\)

B)

\(55^0\)

C)

\(80^0\)

D)

\(70^0\)

12)

If in \(\triangle ABC\), D and E are the points on AB and BC respectively such that \(DE \parallel AC ​\), and AD : AB = 3 : 8, then (area of \(\triangle BDE\) ) : ( area of quadrilateral DECA) = ?

SSC CGL 2019

A)

9 : 55

B)

9 : 64

C)

8 : 13

D)

25 : 39

Correct Option: D

25 : 39

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Let AB = 8 unit and AD = 3 unit, thus BD = 8 - 3 = 5 unit

since DE || AC therefore ΔBDE~ΔBAC

We know that if the triangles are similar, the ratio of areas of the triangles is equal to the square of their sides

Area of ΔBDE/area of ΔBAC = (BD/AB)²

Area of ΔBDE/area of ΔBAC = (5/8)² = 25/64

Let area of ΔBDE = 25 unit and area of ΔBAC = 64 unit

Area of quadrilateral DECA = area of ΔBAC – area of ΔBDE = 64 – 25 = 39 unit

Area of ΔBDE : Area of quadrilateral DECA = 25 : 39

13)

In \(\triangle ABC\), \(BE \perp AC\), \(CD \perp AB\) and BE and CD intersect each other at O. The bisectors of \(\angle OBC\) and \(\angle OCB\) meet at P. If \(\angle BPC = 148^0\), then what is the measure of \(\angle A\) ?

SSC CGL 2019

A)

\(56^0\)

B)

\(28^0\)

C)

\(32^0\)

D)

\(64^0\)

14)

In \(\triangle PQR \), \(\angle Q> \) \(\angle R\), PS is the bisector of \(\angle P\) and \(PT \perp QR\), If \(\angle SPT = 28^0\) and \(\angle R = 23^0\), then the measure of \(\angle Q\) is :

SSC CGL 2019

A)

\(74^0\)

B)

\(79^0\)

C)

\(82^0\)

D)

\(89^0\)

15)

In \(\triangle ABC\), D and E are the points on AB and AC respectively such that \(AD\times AC = \)\(AB\times AE\). If \(\angle ADE= \angle ACB+30^0\) and \(\angle ABC= 78^0\), then \(\angle A = ?\)

SSC CGL 2019

A)

\(56^0\)

B)

\(54^0\)

C)

\(68^0\)

D)

\(48^0\)

16)

If in \(\triangle PQR\), \(\angle P = 120^0\), \(PS \perp QR\) at S and PQ + QS = SR, then the measure of \(\angle Q\) is :

SSC CGL 2019

A)

\(20^0\)

B)

\(50^0\)

C)

\(40^0\)

D)

\(30^0\)

17)

The bisector of \(\angle A\) in \(\triangle ABC\) meets BC in D. If AB = 15cm, AC = 13cm and BC = 14cm,then DC = ?

SSC CGL 2019

A)

8.5 cm

B)

7.5 cm

C)

6.5 cm

D)

8 cm

18)

In \(\triangle ABD\), C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ?

SSC CGL 2019

A)

\(2\sqrt {41}\) cm.

B)

\(2\sqrt {10}\) cm.

C)

\(\sqrt {41}\) cm.

D)

\(\sqrt {10}\) cm.

19)

In \(\triangle ABC\), the medians AD, BE and CF meet at O. What is the ratio of the area of \(\triangle ABD\) to the area of \(\triangle AOE\)?

SSC CGL 2019

A)

2 : 1

B)

3 : 1

C)

5 : 2

D)

3 : 2

20)

The sides of a triangle are 56 cm, 90 cm and 106 cm. The circumference of its circumcircle is:

SSC CGL 2019

A)

\(106\pi\)

B)

\(109\pi\)

C)

\(108\pi\)

D)

\(112\pi\)