SSC CGL Tier-2 9-March-2018 Maths-shift-1

If $$x^{y+z} = 1, y^{x+z} = 1024$$ and $$z^{x+y} =729$$(x, y and z are natural numbers), then what is the value of $$(z + 1)^{y+x+1}$$?

If $$x + y + z = 1, x^2 + y^2 + z^2 = 2$$ and $$x^3 + y^3 + z^3 = 3$$,then what is the value of $$xyz$$?

In triangle $$PQR$$, the internal bisector of $$\angle Q$$ and $$\angle R$$ meets at O. If $$\angle QPR$$ = 70°, then what is the value (in degrees) of $$\angle QOR$$?

$$PQR$$ is a triangle such that $$PQ = PR$$. $$RS$$ and $$QT$$ are the median to the sides $$PQ$$ and $$PR$$ respectively. If the medians $$RS$$ and $$QR$$ intersect at right angle, then what is the value of $$\left(\frac{PQ}{QR}\right)^2$$?

PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. Which of the following is TRUE?
I. Triangle PST is similar to triangle PQR.
II. ST = $$\frac{1}{2}$$(QR)
III. ST is parallel to QR.

ABC is a triangle in which $$\angle$$ABC = 90°. BD is perpendicular to AC. Which of the following is TRUE?
I. Triangle BAD is similar to triangle CBD.
II. Triangle BAD is similar to triangle CAB.
III. Triangle CBD is similar to triangle CAB.

Two parallel chords are one the one side of the centre of a circle. The length of the two chords is 24 cm and 32 cm. If the distance between the two chords is 8 cm, then what is the area (in cm$$^2$$) of the circle?

Two circles of radius 4 cm and 6 cm touch each other internally. What is the length (in cm) of the longest chord of the outer circle, which is also a tangent to inner circle?

In the given figure, PT is a common tangent to three circles at points A, B and C respectively. The radius of the small, medium and large circles is 4 cm, 6 cm and 9 cm. $$O_1, O_2$$ and $$O_3$$ are the centre of the three circles. What is the value (in cm) of PC?

PQRS is a cyclic quadrilateral. PR and QS intersect at T. If $$\angle$$SPR = 40° and $$\angle$$PQS = 80°, then what is the value (in degrees) of $$\angle$$PSR?