Date:9-9-2014 MATHEMATICS TEST-3 Time:2 hrs Marks:50

You have to attempt all the questions.

Q1) In the diagramme PQR is tangent to circle at Q and "O" is the center of circle.Find the value of 'x'. [3 M]

Q2) An irrational number is [1 m]

a) terminating and non-repeating decimal

b)a non-terminating and non-repeating decimal

c) a terminating and repeating decimal

d)a non-terminating and repeating decimal.

Q3)If x + 1x

= 6 then find the value of x6 + 1

(x ³) ² . [3 m]

Q4)In the figure PQ is chord of circle with center O and PT is tangent at P such that <QPT =700.Find the measure of <PRQ. [2 M]

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Q5)AB and CD are two parallel chords of a circle such that AB = 10cm and CD =24cm.If the chords are on the opposite sides of center and distance between them is 17cm then find radius of circle. [4]

Q6) In the figure given below, if <AOP =750 and <AOB = 1200 then what is angle AQP where O is center of circle. [3m]

Q7) Two parallel chords of a circle whose diameter is 13 cm are respectively 5cm and 12 cm in length. If both chords lie in a semi-circle, then find the distance between the chord .[4 m]

Q8)In the figure <ABP = <ACQ ,<BAC = 680 then find meassure of <ABC .[2m]

Q9)If a and b are positive integers such that ab =125 then find the value of (a - b)a+ b - 4.[2m]

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Q10)A man has certain number of chickens and goats. Their head count is 30.If the total no. of legs is 84,what is ratio between number of chickens and goats. [4 m].

Q11)If (x -2) is common factor of x3 -4x2 +ax +b and x3 -ax2 + bx +8 then find values of a and b.[2 m]

Q12) The no. of common tangents which can be drawn to two concentric circle is x then x= ---- [1 m]

Q13)A circle is inscribed inside a trapezoid PQRS.If PS = QR = 25 cm, PQ = 18 cm and SR =32 cm.what is length of diameter of circle. [4 m]

Q14) The total surface area of a hollow metal cylinder open at both the ends of external radius 8cm and height 10 cm is 338 ᴨ cm2.Taking r to be inner radius write down an equation in r and use it to state the thickness of metal in the cylinder.[5M]

Q15) X and Y are the centres of circles of radii 9cm and 2 cm.XY=17cm.Z is the centre of circle of radius r cm,which touches the above circle externally.given that <XYZ=900.Write down an equation in r and solve it.[5]

Q16) IF (a-2b-3c+4d)(a+2b+3c+4d) = (a+2b-3c-4d)(a-2b+3c-4d) show that 2ad = 3bc. [3]

Q17) Find the values of k for the following quadratic equation so that they have two real equal roots: kx(x-2)+6= 0.[2]

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