Mathematics
 Question Paper SECTION-A 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) SECTION-B Q.5. Comment on the nature of the roots of the equation 4x2-12x-7=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 45o 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. SECTION-C 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’: (x2+5x)(x2 +5x-3)-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. SECTION-D 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/m2. 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 30o. After 8 minutes the angle of depression changes to 60o.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 3-digit 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/m2. Download here Latest Sample Paper