TouchStone Test

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					Q. 1 If x + y = 4 and x – y = 8, then x =   and y =

Q. 2 A sum of Rs. 400 is to be used to give four cash prizes to
   students of a school for their overall performance. If each prize is
   Rs. 20 less than its preceding prize, find the value of each prize.
Q. 3 The product of two numbers is 108. If their H. C. F. is 3,
   then their LCM is       and GCF is

Q. 4 One card is drawn from a well shuffled deck of 52 cards.
   Find the probability of getting
   i) a king of red colour
   ii) a black card
Q. 5 Two dice are thrown simultaneously. Find the probability of
   i) the sum of the numbers appearing on the top of the two dice
   being 6.
   ii) the numbers appearing on the top of both dice being same.

Q. 6 Two vertical poles of heights 6m and 11m stand on a plane
   ground. The distance between their feet is 12m. A rope is tied
   tightly from the top of one pole to the top of the other. Find the
   length of the rope.
Q. 7 From the top of a 9 metres high building AB, the angle of
   elevation of the top of a tower CD is 30º C and the angle of
   depression of the foot of the tower is 60º. Find the height of the

Q. 8 The radius of a circle is 21 cms . Therefore its circumference is
Q. 9 A vessel is in the form of a hollow cylinder mounted on a
   hollow hemisphere. The diameter of the hemisphere is 14 cms,
   and the total height vessel is 13 cms. Find the outer surface area
   of the vessel

Q. 10 If cosec 18º = sec A, then the measure of A is ___________
Q. 11 A point A(x,y) divides the segment joining point B(5,-1) and
     C(-10,4) in the ratio 3:2. Find the value of x and y

Q. 12 A circle touches all the four sides of a quadrilateral PQRS.
   If PQ = 6 cms., QR = 7 cms., and RS = 4 cms. Find the length of

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