HSC math

                                                COORDINATES

1.       Find  the distances of the point  (5,a) from the y axis and the point (7, 2) are equal .   [C.B.2007; J.B. 2006; R.B.2004; S.B.2003 ]

2.       Find the ratio in which the -axis divides the straight line joining the points and  find the abscissa of the point of division.      [S.B. 2007; R.B.2006, 2003; C.B.2005;c.B.2004; D.B.2002]

3.       Coordinates of the extremities of a diagonal of a parallelogram are (3, and  If the third vertex is find the coordinate of the fourth vertex of the parallelogram .     [D.b. 2007 ;C.B.2006, 2004; S.B.2003; C.B.2000]

4.    

                                         THE STRAIGHT LINE  

1.       If  and  cos  sin  represent the same straight line , express  in terms of and    [R.B.2007; D.B.2004; J.B.2003; S.B.2002 ]

2.       A straight  line passes through the point and intersects the  and -axes at the points A and  B respectively such that OA +2. OB = 0 where O is the origin. Find its equation.    [S.B.2007; D.B.2006,2001 J.B. 2006; C.B.206; R.B.2004 ]

3.       Find the coordinates of the middle point of the intercept of the straight line  between the axes. If this intercept be the side of a square, find its area.    [D.B.2007,2001 J.B. 2007; B.B.2005; S.B. 2003; R.B. 2003; C.B.2001 ]

4.        is a point on the straight line  and   is a point on the straight line  Find the equation of AB.    [R.B. 2007,2005,2001; B.B. 2004,2001; C.B. 2004,2000; D.B. 2002,2000; C.B.2002 ]

                                                 CIRCLE 

1.       A circle passes through the origin and cuts off intercepts  3 and  5 from the positive direction of the  and -axes respectively. Find the equation of the circle.   [S.B. 2007,2002; D.B.2006, 20032001; R.B.2006, 2001; C.B.2005,2001; B.B.2004 ]

2.       Find the equation of the circle whose centre is at the point  (4, 5) and which passes through the centre of the circle    [D.B.2007,2001; C.B.2006,2004,2002; C.B.2006,2004;S.B. 2005;B.B. 2005; R.B.2004, 2001; J.B.2000 ]

3.       A circle has its centre at the point  (1, 2) and it touches the -axis. Find its equation and the length of the intercept which it cuts off from the -axis.        [R.B.2007,2001 ; B.B.2007 ; C.B.2005; S.B. 2003 ; J.B.2002 ;D.B.2000 ]

4.       The circle  touches the -axis. Find  c and the coordinates of the point of contact.        [D.B. 2007, 2004, 2003; S.B. 2007; R.B. 2005; J.B. 2005 ; C.B.2005 ]

5.       The chord of the circle  is bisected at the point  (. Find the equation of the chord.     [D.B. 2007,2003 ; R.B. 2006, 2003 ; C.B.2006, 2001 ; C.B.2006, 2004; S.B. 2005,2003 ; J.B. 2003 ;B.B.2002 ]

                                                   VECTOR  

1.       Show that the diagonals of parallelogram bisect each other       [D.B.2007,2005 ; R.B.2007,2005, 2002 ; C.B.2007, 2005, 2003 ; J.B. 2007, 2002 ; Ch.B. 2006 ; S.B.2003 ; B.B. 2003 
                                                Mechanics

                                         CONCURRENT FORCES

 Two forces of magnitudes 3p , 2p have a resultant R. If the first force is doubled, the magnitude of the resultant is doubled. Find the angle between the forces. [B.B. 04, R.B. 03, J.B. 03]

 When two equal forces are inclined

 Forces P-Q, P, P +Q act at a point in directions parallel to the sides of an equilateral triangle taken in order. Find their resultant. [J.B. 04, D.B. 01]

 The resultant of two forces P and Q acting at a point is R ; the resolved part of R along P is Q show that the angle between the forces is 2 sin^(-1) (√(p/2Q)). [S.B. 02, Ct. B. 01]

 The resultant of forces P and Q (P>Q) trisects the angle between them. Show that the angle between them is 3 cos^(-1) P/2Q and the resultant is (p^2-Q^2)/Q [ B.B. 03, C.B. 01, R.B. 04, 01]

                       SYSTEM OF COPLANAR FORCES

 A straight uniform rod balances about a prop 1 metre from one end when a body of weight of 10 kg. is suspended at that end. If the pressure on the prop is 30 kg wt, find the length and weight of the rod.

 A force P acts along AO where O is the circumventer of the triangle ABC. Show that the parallel components of P acting at B and C are in the ratio sin 2B ; sin 2C. [J.B. 04, S.B. 03, Ct.B. 2000]

 P ,Q are two like parallel forces If P is moved parallel to itself through a distance x, show that the resultant of P and Q move through a distance Px/(P+Q) [ D.B. & Ct.B. 03, J.B. , D.B. 2000]

 Forces l. BC, m. CA, n.AB act along the sides of a triangle ABC taken in order. Show that their resultant passes through the centroid of the triangle if l+m+n=0 [C.B. 04, R.B. 02, D.B. 2000, S.B.01,04]

 A uniform plank of length 2a and weight W is supported horizontally on two vertical props at a distance b apart. The greatest weight that can be placed at the two ends in succession without hitting the plank are w_1 and w_2 respectively. Show that w_1/(w+w_1 )+w_2/(w+w_2 )=b/a [ S.B. 03, J.B. 01, B.B. 01, 04]

 Forces P. Q.R acting respectively along the sides BC, CA, AB of the triangle ABC. it the moments of the forces about A, B, C, are L, M, N, respectively , show that [R.B. 04, Ct. B. 01]