Q. 1. Given H.C.F (306, 657)= 9, find L.C.M (306, 657)
Q. 2. Prove that 3 + 2 √5 is irrational.
Q. 3. For which value of ‘P’ does the pair of equations have unique solutions.(p≠4)
4x + Py + 8 = 0
2x + 2y + 2 = 0
Q. 4. Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.(44/7 cm)
Q. 5. Find the co-ordinates of the centre of a circle whose end points of the diameter are ( 3, -10 ) and ( 1, 4). (2,3)
Q. 6. If tan 2A = cot (A – 180), where 2A is an acute angle, find the value of A.(360)
Q. 7. Use Euclid’s algorithm to find the H.C.F of 135 and 225.(45)
Q. 8. Show that any positive integer is of the form 6q + 1, or 6q + 3, 0r 6q + 5, where q Is some integer?
Q. 9. Draw the graphs of the equation x – y + 1 = 0 and 3x + 2y – 2 = 0.
Q. 10. Determine the coordinates of the vertices of the triangle formed by these lines and the x – axis, and shade the triangular region.
Q. 11. A train travels 360 km at a uniform speed. If the speed had been km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Q. 12. A motorboat whose speed is 18km/hr in still water takes 1 hour more to go 24km upstream than to return downstream to the same spot. Find the speed of the stream. (6km/h)
Q. 13. Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are ( 0, -1 ), ( 2, 1 ) and ( 0, 3 ). (4 sq unit)
Q. 14. In fig. AB and CD are two diameters of a circle (with centre O) perpendicular to each Other and OD is the diameter of the smaller circle. If OA = 7cm, find the area of the Shaded region.In a triangle, if the square of one side is equal to the sum of squares of the remaining two sides, prove that the angle opposite to the first side is a right angle. Using the above, do the following: ABC is an isosceles triangle with AB = BC. If AB2 = 2AC2, prove that ABC is a right Triangle.
Q. 15. As observed from the top of a 75m high lighthouse from the sea-level, the angles of Depression of two ships is 300 and 450. If one ship is exactly behind the other on the same side of the lighthouse fined the distance between the two ships.(75(√3 - 1))
Q. 16. A triangle ABC is drawn to circumscribe a circle of radius 4cm such that the segment BD And DC into which the point of contact D is of lengths 8cm and 6cm divides BC Respectively. Find the sides AB and AC. ( 15 , 13 )
Q. 17. The radii of the ends of a frustum of a cone 45cm high are 28cm and 7cm. Find its volume And total surface area.( 48510 cm3 , 8079.5 cm3 )
Q. 18. Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/hr. how much Area will it irrigate in 30 minutes, if 8cm-tanding water is needed?(450000m3)
Q. 19. In a flight of 600 Km, an aircraft was slowed down due to bad weather. The average speed for the trip was decreased by 200 Km/hr. and the time of flight increased by 30 minutes. Find the duration of the flight.(1 hour)
Q. 20. Solve the quadratic equation 6x2 + x -15 = 0( 3, -10/3 )
Q. 21. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle.(1056-252√3/7cm2)
Q. 22. If A and B are (1,4) and (5,2) respectively, find the coordinate of P when AP/PB=3/4.(19/7 , 22/7 )
Q. 23. Find the area of the shaded region in figure, ABCD is a square of side 4 cm.(24/7 cm3)
