SSC CGL 201911)S is the incenter of \(\triangle PQR\) . If \(\angle PSR = 125^0\) , then the measure of \(\angle PQR\) is:

Correct Option: D

\(70^0\)

SSC CGL 201912)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) = ?

Correct Option: D

25 : 39

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

SSC CGL 201913)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 \(\angle A\) ?

Correct Option: D

\(64^0\)

SSC CGL 201914)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 :

Correct Option: B

\(79^0\)

SSC CGL 201915)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 \(\angle A = ?\)

Correct Option: B

\(54^0\)

SSC CGL 201916)If in \(\triangle PQR\), \(\angle P = 120^0\), \(PS \perp QR\) at S and PQ + QS = SR, then the measure of \(\angle Q\) is :

Correct Option: C

\(40^0\)

SSC CGL 201917)The bisector of \(\angle A\) in \(\triangle ABC\) meets BC in D. If AB = 15cm, AC = 13cm and BC = 14cm,then DC = ?

Correct Option: C

6.5 cm

SSC CGL 201918)In \(\triangle ABD\), C is the midpoint of BD. If AB = 10 cm, AD = 12 cm and AC = 9 cm, then BD = ?

Correct Option: A

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

SSC CGL 201919)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 \(\triangle AOE\)?

Correct Option: B

3 : 1

SSC CGL 201920)The sides of a triangle are 56 cm, 90 cm and 106 cm. The circumference of its circumcircle is:

Correct Option: A

\(106\pi\)

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