SSC CGL Tier-2 9-March-2018 Maths Shift-2
For the following questions answer them individually
If $$X^{y^z} = 1, Y^{z^x} = 125$$ and $$Z^{y^x} = 243$$ ($$X, Y$$ and $$Z$$ are natural numbers), then what is the value of $$9X + 10Y - 18Z$$?
If $$3x + 6y + 9z = \frac{20}{3}, 6x + 9y + 3z = \frac{17}{3}$$ and $$18x + 27y - z = \frac{113}{9}$$, then what is the value of $$75x + 113y$$?
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
In a triangle ABC, AB = 12, BC = 18 and AC = 15. The medians AX and BY intersect sides BC and AC at X and Y respectively. If AX and BX intersect each other at O, then what is the value of OX?
In a triangle PQR, PX bisects QR. PX is the angle bisector of angle P. If PQ =12 cm and QX = 3 cm, then what is the area (in cm$$^2$$) of triangle PQR?
In the given figure PT : TS : SR = 2 : 1 : 1 and SU is parallel to TQ. If RU = 10 cm. RS = 8 cm and SU = 6 cm, then what is the value (in cm) of PQ?
PQ and RS are two chords of a circle. PQ = 20 cm, RS = 48 cm and PQ is parallel to RS. If the distance between PQ and RS is 34 cm, then what is the area (in cm$$^2$$) of the circle?
Centre of two concentric circles is O. The area of two circles is 616 cm$$^2$$ and 154 cm$$^2$$ respectively. A tangent is drawn through point A on the larger circle to the smaller circle. This tangent touches small circle at B and intersects larger circle at C. What is the length (in cm) of AC?
PA and PB are two tangents drawn to two circles of radius 3 cm and 5 cm respectively. PA touches the smaller and larger circles at points X and Y respectively. PB touches the smaller and large circle at point U and V respectively. The centres of the smaller and larger circles O and N respectively. If ON =12 cm, then what is the value (in cm) of PY?
XR is a tangent to the circle. O is the centre of the circle. If $$\angle$$XRP = $$120^\circ$$, then what is the value (in degrees) of $$\angle$$QOR?
