1. Given H.C.F (306, 657) = 9, find L.C.M (306, 657) (22335)
2. Prove that 3 + 2 √5 is irrational.
3. For which value of ‘P’ does the pair of equations have unique solutions.(p≠4)
4x + Py + 8 = 0
2x + 2y + 2 = 0
4. Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.(44/7 cm)
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)
6. If tan 2A = cot (A – 180), where 2A is an acute angle, find the value of A.(36◦)
6. Use Euclid’s algorithm to find the H.C.F of 135 and 225.(45)
7. Show that any positive integer is of the form 6q + 1, or 6q + 3, 0r 6q + 5, where q Is some integer?
8. Draw the graphs of the equation x – y + 1 = 0 and 3x + 2y – 2 = 0.
9. Determine the coordinates of the vertices of the triangle formed by these lines and the x – axis, and shade the triangular region.
10. 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.
2. Prove that 3 + 2 √5 is irrational.
3. For which value of ‘P’ does the pair of equations have unique solutions.(p≠4)
4x + Py + 8 = 0
2x + 2y + 2 = 0
4. Find the length of the arc of a circle with radius 6cm if the angle of sector is 600.(44/7 cm)
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)
6. If tan 2A = cot (A – 180), where 2A is an acute angle, find the value of A.(36◦)
6. Use Euclid’s algorithm to find the H.C.F of 135 and 225.(45)
7. Show that any positive integer is of the form 6q + 1, or 6q + 3, 0r 6q + 5, where q Is some integer?
8. Draw the graphs of the equation x – y + 1 = 0 and 3x + 2y – 2 = 0.
9. Determine the coordinates of the vertices of the triangle formed by these lines and the x – axis, and shade the triangular region.
10. 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.
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