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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.

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