The points A(x, y), B(3, −2) and C(4, −5) are collinear. Then y in terms of x is: (a) 3x − 11 (b) 11 − 3x (c) 3x − 7 (d) 7 − 3x

(a) If the lines kx − y + 4 = 0 and 2y = 6x + 7 are perpendicular to each other, find the value of k. (b) Find the equation of a line parallel to 2y = 6x + 7 and passing through (−1, 1).

In the given graph, P and Q are points such that PQ cuts off intercepts of 5 units and 3 units along the x-axis and y-axis respectively. Line RS is perpendicular to PQ and passes through the origin. Find: (a) the coordinates of P and Q. (b) the equation of RS.

Use the following graph and answer the given questions : (a) Write the co-ordinates of points A, B and C. (b) Find the equation of a line passing through the mid-point of AC and parallel to AB.

The equation of the line passing through the origin and parallel to the line 3x + 4y + 7 = 0 is: (a) 3x + 4y + 5 = 0 (b) 4x − 3y − 5 = 0 (c) 4x − 3y = 0 (d) 3x + 4y = 0

A and B are two points on the x-axis and y-axis respectively, as shown in the figure. (a) Write down the coordinates of A and B. (b) P is a point on AB such that AP : PB = 3 : 1. Using the section formula, find the coordinates of P. (c) Find the equation of a line passing through P and perpendicular to AB.

ABC is a triangle whose vertices are A(1, −1), B(0, 4) and C(−6, 4). D is the midpoint of BC. Find: (a) the coordinates of D (b) the equation of the median AD.

In the given graph, ABCD is a parallelogram. (a) Write the coordinates of A, B, C and D. (b) Calculate the coordinates of P, the intersection of diagonals AC and BD. (c) Find the slopes of CB and DA and verify that they are parallel. (d) Find the equation of diagonal AC.

The total surface area of a sphere S₁ of radius R and the total surface area of a solid hemisphere S₂ of radius r are equal. The ratio R : r is: (a) 1 : 1 (b) 2 : 1 (c) √3 : 2 (d) 2 : √3

In the given figure, AOB is a right-angled triangle and C is the midpoint of the hypotenuse AB. If the coordinates of C are (x, y), the point equidistant from A, O and B is: (a) (x, y) (b) (y, x) (c) (x/2, y/2) (d) (2x/3, 2y/3)

Assertion (A): The 9th term of the G.P. 6, −12, 24, −48, … is positive. Reason (R): (−2)⁸ is positive. (a) A is true and R is false. (b) A is false and R is true. (c) Both A and R are true and R is the correct explanation of A. (d) Both A and R are true but R is not the correct explanation of A.

What must be added to x³ + 7x² + 3x + 2 so that the resulting polynomial is exactly divisible by x + 2? (a) −40 (b) −16 (c) 16 (d) 40