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.

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.

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.

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.

Find the equation of a line whose y-intercept is 6 and is parallel to x-axis. (a) y = 6 (b) x = 6 (c) x + y = 6 (d) y − x = 6

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).

If A = , then A² is equal to: (a) (b) (c) (d)

Statement 1: The point which is equidistant from three non-collinear points D, E and F is the circumcentre of △DEF. Statement 2: The incentre of a triangle is the point where the bisectors of the angles intersect. (a) Both statements are true. (b) Both statements are false. (c) Statement 1 is true and Statement 2 is false. (d) Statement 1 is false and Statement 2 is true.

Mr Anuj deposits ₹500 per month for 18 months in a recurring deposit account at a certain rate. If he earns ₹570 as interest at the time of maturity, then his matured amount is: (a) ₹(500 × 18 + 570) (b) ₹(500 × 19 + 570) (c) ₹(500 × 18 × 19 + 570) (d) ₹(500 × 9 × 19 + 570)

The marked price of an article is ₹1,375. If CGST is charged at the rate of 4%, then the price of the article including GST is: (a) ₹55 (b) ₹110 (c) ₹1,430 (d) ₹1,485