X MATHS SA II D SECTION SAMPLE PAPER 4

1.       The denominator of a fraction is one more  than  twice the numerator.  If the sum  of the fraction and  its reciprocal is     2-16/21 . Find  the  fraction.

2.       Prove  that  line joining centre of  the circle to pint of contact of a tangent is perpendicular .

3.       A two digit number is four times the sum of its digits.   It is also equal  to three  times the product of its digits.   Find  the number.

OR

The hypotenuse of a right  triangle is 3 root 5 cm.   If the  smaller  side  is tripled and  the larger  side is doubled, the new hypotenuse will be 15 cm.  Find the length  of each side.

4.       The surface  area of a solid metallic  sphere is 616 cm².  It is melted and recast into a cone of height  28 cm.  Find  the diameter of the base of the cone so formed.

5.       An aero plane flying  horizontally 1 km above  the ground is observed at an elevation of 60°.After  a flight  of 10 seconds, its angle  of elevation is observed to be 30° from  the same  point  on the ground.  Find  the speed of the aero plane in km/hour.

6.       A farmer connects a pipe  of internal diameter 20 cm from  a canal  into  a cylindrical tank  in his field, which  is 10 m in diameter and  2 m deep.   If water flows  through the pipe  at the rate  of 3 km/hour, in how  much  time  will the tank  be filled ?

OR

A container shaped like a circular cylinder having diameter 12 cm and  height  15 cm is full of ice-cream. The ice-cream  is filled  into  cones  of height  12 cm and  diameter 6 cm each having a hemispherical shape  on the top.   Find  the number of such  cones  which can be filled  with  ice-cream.