The number of integer values of `m`, for which the x-coordiante of the point of intersection of the lines `3x+4y=9` and `y=mx+1` is also an integer, is
(a)   `2`    (b)  `0`
(c)   `4`    (d)  `1`

The acute angle between the lines y=3 and y=sqrt(3)x+k is (A)   30 °   (B)   60 °    (C)   45 °   (D)   90 °   

Find the volume in cubic decimetre of each of the cubes whose side is (i)1.5m          (ii)  75cm        (iii)  2dm 5cm

The number of solutions of z^2+bar z=0 is (a) 1           (b) 2 (c) 3           (d) 4

If the vertices of a triangle PQR are rational points, then which of the following points of this triangle may not be rational - (a)   Centroid     (b)   Incenter (c)    Circumcenter     (d)    Orthocenter

The measure of the angle between the internal and external bisectors of an angle is: (A)   60°     (B)   70°      (C)   80°      (D)   90°

The distance of the point (2,3) from the line x-2y+5=0 measured in a direction parallel to the line x -3y=0 is: (A)   2sqrt(10)     (B)   sqrt(10)     (C)   2sqrt(5)     (D)   None of these

How many diagonals does each of the following have? (i)A convex quadrilateral (ii)A regular hexagon             (iii)   A triangle

If alpha , beta and gamma are the zeroes of the cubic polynomial x^3-5x^2+2x-10 , then the value of (alpha + beta + gamma)(1/alpha + 1/beta +1/ gamma) is (1)    2     (2)   0 (3)    -1     (4)   1

The radical center of the circles x^2+y^2=a^2 , (x-c)^2+y^2=a^2 and x^2+(y-b)^2=a^2 is (A)   (a/2,b/2)   (B)   (b/2,c/2)   (C)   (c/2,b/2)   (D)   None of these

In an AP, S_p=q , S_q=p . Then S_(p+q) is equal to: a.     0 b.     -(p+q) c.     (p+q) d.     pq