Question Paper 

SECTIONA 

Q.1.  nth term of a sequence is given by 4n2 +2. Is this an A.P.? 
Q.2.  What is the probability that two friends have birthday on the same date? 
Q.3.  What is the distance between the points (4,0) and (5,0)? 
Q.4.  Find the area enclosed by two concentric circles of radius 4 cm and 3 cm (π =3.14) 
SECTIONB 

Q.5.  Comment on the nature of the roots of the equation 4x212x7=0. 
Q.6.  How many terms are there in the sequence 60,56,52,…….56. 
Q.7.  Find the area enclosed by two concentric sectors of radii 7 cm and 3.5 cm and central angle 45^{o} 
Q.8.  Diameter of a solid hemisphere is 14 cm. Find its surface area. 
Q.9.  A circle is inscribed in a right triangle. If the sides making right angle measure 5 cm and 12 cm, find the radius of the circle. 
Q.10.  Prove that a circle inscribed in an isosceles triangle bisects the base at the point of contact. 
SECTIONC 

Q.11.  A person saves Rs.100 in a month. There after he increases his savings every month by Rs.50.In how many months his savings would total to Rs. 29750? 
Q.12.  Solve for ‘x’: (x^{2}+5x)(x^{2} +5x3)18=0 
Q.13.  Prove that tangents drawn to a circle from an external point are equal. 
Q.14.  Draw line AB = 8cm and divide it in the ratio 3 : 5. 
Q.15.  A quadrilateral ABCD circumscribes a circle. Prove that AB + DC = AD + BC. 
Q.16.  A bag contains 15 balls 5 blue and rest red. By adding some more blue balls the probability of drawing blue balls becomes 3/2 times that of red ball. Find the number of blue balls added. 
Q.17.  If P(x,y) is equidistant from the points (5,2) and (4,5) find a relation between ‘x’ and ‘y’. 
Q.18.  Find the coordinates of the point that divides the line joining (3,7) and (7,5) in the ratio 3: 5. 
Q.19.  A spherical ball of diameter 7 cm is melted and drawn into a wire of diameter 3.5 mm. Find the length of the wire. 
Q.20.  A bucket is in the form of a frustum of a cone whose radii of top and bottom are 27 cm and 18 cm respectively. If the bucket is 40 cm high find the curved surface area of the bucket. 
SECTIOND 

Q.21.  A circus tent is cylindrical up to a height of 5 m and conical above it. If the diameter of the base is 35 m and slant height of conical part is 63 m find the cost of canvas used to make the tent at Rs. 30/m^{2}. 
Q.22.  Construct a triangle ABC given AB= 4 cm, BC = 5 cm and AC = 6 cm and construct a triangle AB’C similar to it with scale factor 4/5. Write steps of construction. 
Q.23.  Find the area of a quadrilateral whose vertices are A(4,6), B(5,5), C(6,3) and D(2,5). 
Q.24.  A flag staff on op of a building is ‘p’ metres high. From the point on he ground the angles of elevations of bottom and top of the flagstaff were found to be α and β respectively. Show that the height of the building h 
Q.25.  Angle of depression of a boat sailing towards a light house100 m high was found to be 30^{o}. After 8 minutes the angle of depression changes to 60^{o}.In how many more minutes the boat would reach the bottom of the light house? 
Q.26.  Fifty cards are numbered 1 –50. One card is drawn at random. What is the probability that the drawn card bears a (i) Prime number, (ii) Odd number, (iii) An even multiple of 7 (iv) A divisor of 72 on it? 
Q.27.  Four semi circles have been drawn using the sides of a square of side 14 cm touching each other. Find the area of the region between the semicircles. 
Q.28.  Find the sum of all 3digit numbers not divisible by 9. 
Q.29.  A plane left 45 minutes late due to bad weather. In order to reach its destination 4200 km away on time its speed had to be increased by 100 km/h. Find the original speed of the plane. 
Q.30.  A philanthropist wanted to donate Rs. 8000 equally among the inmates of a destitute home. Had there been 10 children less each would have got Rs.40 more. Find the number of inmates in the destitute home. What value does the person reflect? 
Q.31.  A rectangular park measures 80 m x 60 m. At each corner there is a circular flower bed of radius 10.5 m. Find the remaining area of the park and the cost of maintaining the flower beds at Rs. 45/m^{2}. 
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