Mathematics
Topic :Real numbers
Time : 30 Min. Part- A
Marks: 5 X4 =20
1. If y = 33 + 1/33. 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 x +a - 2a
x a x – a
3. Solve the inequation 2x – 1 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
3x + 2y = 5 and y – 4x + 3 = 0 and parallel to x + 2y – 4 = 0.
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).
