Class: X SUB: Mathematics Topic :Real numbers Time : 30 Min. Part- A Marks: 5 X4 =20 1. If y = 3Ö3 + 1/3Ö3. Show that 3y3 -9y = 10 2. If lmn = 1 prove that 1/1 + l + m-1 + 1/1 + m + n -1 + 1/1 + n + l-1 =1. 3. If a 1/3 + b 1/3 + c 1/3 = 0 then show that (a + b + c) 3 = 27 abc. 4. If x = 0.1, find the value of [ 1 – { 1 – (1 –x 3) -1} -1 ] 1/3 5. If a + b + c = 0. Part –B Max Marks: 5 X2 =10 1. Show that Lt 6x - 5 = 3 . x ®0 2x + 5 2. Evaluate: Lt Öx +a - Ö2a x ®a x – a 3. Solve the inequation ½2x – 1½ £ 5. 5 4. If a = b3/y, b = c 4/x, c = a 5/z, then prove that xyz = 60. 5. Show that Lt x3 - 27 = 27. x ®3 x - 3 Topic : Analytical Geometry Part- A Marks: 5 X4 =20 1. A ( -1, 5), B (3, 1) and C (5, 7) are the vertices of triangle ABC. D, E, F are the mid points of the sides BC, CA, and AB respectively. Prove that the area of triangle ABC is 4 times the area of the triangle DEF. 2. Find the equations of the line passing through the point (5, -3) and whose sum of the intercepts on the coordinate axes is 5/6. 3. Find the area of triangle so formed by both the axes and a line passing through the points ( 8, -3) and ( -4, 12). 4. Find the equation of the line which passes through the point (1, -6) and whose product of the intercepts on the coordinate axes is one. 5. Find the equation of straight line passing through the point of intersection of lines Part- B Marks: 5 X4 =20 1. In what ratio is the segment joining the points (-3, 2) and (6, 1) divided by y-axis. 2. In what ratio does P (4, 6) divide the joining of A (-2, 3) and B (6, 7). 3. If the area of the triangle formed with the vertices (t, 2t), (-2, 6), and (3, 1) is 5 sq. cms, then find 't.' 4. Show that the points (1, 2) (-3, 4) and (7, -1) are collinear. 5. Find a point on X-axis, equidistant from (3, 2) and (6, 4).
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