Quant mock(Speed test-18) for Govt. exams(10 qns) Geo.Special

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Q1.The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the larger circle and BD is a tangent to the smaller circle touching it at D and intersecting the larger circle at E. The length of line segment AD is,  

a.17 cm  b.19 cm  c.18 cm  d.20 cm

Q2.O and C are the Orthocenter and the Circumcenter of an acute angled triangle PQR respectively. The points P and O are joined and produced to meet the side QR at S. If <QCR = 130⁰ and <PQS = 60⁰ then angle RPS is, 

a.100⁰  b. 35⁰  c. 30  d. 60⁰

Q3.AD is a median of triangle ABC and O is the centroid such that AO = 10cm. Length of OD (in cm) is,  a.7  b.5  c.4  d.2

Q4.In a cyclic quadrilateral ABCD, side AB is extended to E so that BE = BC. If  angle ADC=70⁰ and angle BAD=95⁰ then angle DCE is, 

a.140⁰    b.165⁰  c.120⁰  d.110⁰

Q5.If the angle subtended by a chord at its center is 60⁰, the ratio between the lengths of the chord and the radius is,  

a.1 : 1  b.2 : 1  c.(2)^1/2 : 1  d.1 : 2

Q6.In a right triangle ABC,  angle A = 90⁰ and AD is perpendicular to BC. If areas of the triangles ABC = 40cm² and triangle ACD = 10cm² with AC = 9cm, the length of BC is,

a.4cm b.12cm  c.18cm  d.6cm

Q7.P and Q are centres of two circles of radii 9cm and 2cm respectively. PQ is 17cm and R is the centre of a third circle that touches the other two circles externally. If ∠PRQ=90⁰,then radius of the third circle is, a.7cm  b.4cm  c.8cm  d.6cm

Q8.In a circle with centre at O and radius 5 cm, the length of a chord AB is 8 cm. If two tangents at A and B meet at C length of tangent section AC is

a.20/3cm.  b.15/4cm  c.10/3  cm. d.21/4 cm.

Q9.The units digit of 2⁷⁹+7³⁵ is

a.1  b.3  c.5  d.7

Q10. A tank is losing water 50% per hour. The percentage of water left after 2 hour will be

a.50% b.0%  c.25%  d.75%