Coordinate Geometry

A square is drawn on 1^st quadrant of XY plane having consecutive coordinates (counter - clockwise, starting from left bottom) as P(2,3), Q(7,3), R(7,8), S(2,8) respectively. Thereafter, each side of the square is doubled considering P as a fixed point and the new square becomes PQ'R'S'. Now this new square is mirrored with respect to X axis. What will be the coordinates for the image of R'?

The sum of the perpendicular distances from the origin to the planes 12x-3y+4z+26=0 and 2x-4y+4z+18=0 is

The points (a, 2), (0, b), (1, 1) are collinear. Then

The area bounded by the curve is

The value of for which the straight line (2x+3y+4)+ (6x-y+12)=0 is parallel to y-axis is

A point moves so that the sum of the squares of its distances from the six faces of a cube given by , , is 10 units. The locus of the point is:

Three cubes of side 2 cm are glued surface to surface horizontally such that it produces a cuboid. What is the surface area of the cuboid?

Area and perimeter of a rectangular field are 2000 sq.m. and 180 m respectively. What is the length and breadth?

A supporting element on a curved opening is called as

A circle of maximum possible size is cut from a square sheet. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be area of the final square?

Area bounded by and is

If the side of a square increases by 30% its area increases by:

If the points (2a, a),(a,2a), and (a, a) enclose a triangle of area 18 square units. Then the centroid of the triangle is:

The curved surface area of a cylindrical pillar is and its volume is Find the ratio of its diameter to its height

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

What is the percentage increase in the area of a rectangle, if each of its sides is increased by 20% ?

For the given tile pattern calculate the area shaded in BLUE colour if one of the length of the tile is 10 cm.

A man having height 1.68 m is standing near a pole. He casts a shadow 140 cm long. What is the length of the pole (in cm) if it gives a shadow 420 cm long ?

What is the length of the bridge (in m), which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds ?

All the rectangles are of equal area In the given figure a cube is inserted within a hemisphere such that the top four corners of the cube touch the inner surface of the hemisphere. Find the length of the green line which connects between the top center and bottom corner of the cube, if the radius of the hemisphere is 10cm.

Find the area of the Square given below, which is made up of 5 different rectangles all of equal areas. One of the sides of the rectangle is given as

A wire is in the form of a circle of radius 38cm. If it is bent into a square what will be the area of the square (in cm²) ?

Find the angle of "X" from the figure given below.

Which of the following solids may not be generated by revolving a planar surface along an axis ?

The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the center (in cm) is

A hyperbola has ____ vertices and ___foci.

Circle with center O and radius 25 cms has a chord AB of length of 14 cms in it. Find the area of triangle AOB.

Rhombus of side 6 cm has an angle equal to the external angle of a regular octagon. Find the area of the rhombus.

A (p,0), B (4,0), C (5,6) and D (1,4) are the vertices of a quadrilateral ABCD. If ADC is obtuse, what is the maximum integral value of p?

A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?

vertical pole 20 m long casts a shadow 10 m long on the ground. At the same time, a tower casts the shadow 50 m long on the ground. Find the height of the tower. (Answer to be provided in m)

ABC and BDE are two equilateral triangles such that D is the mid-point of BC. What is the ratio of the area of triangles ABC and BDE?

A well of depth 20 m with a radius 4 m is dug from the earth to form a platform of length 25 m and a breadth of 12 m. Find the height of the platform.

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same, which one of the following will not be affected?

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y. (Provide answer as x, y (in numerical). Any other format will not be accepted for marking)

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. (Answer to be provided in cm²)

A floor whose length and width is 50 m and 40 m respectively needs to be covered by rectangular tiles. The dimension of each tile is 1 m x 2 m. Find the total number of tiles that would be required to fully cover the floor.

A lady grows cabbage in her garden that is in the shape of a square. Each cabbage takes 1 square foot of area in her garden. This year, she has increased her output by 211 cabbages when compared to last year. The shape of the area used for growing the cabbage has remained a square in both these years. How many cabbages did she produce this year?

How many diagonals does a 63-sided convex polygon have?

The areas of two similar triangles are 100cm² and 49cm². If the altitude of the bigger triangle is 4 cm, then what will be the altitude of the corresponding smaller triangle?

A well of depth 20 m with a radius 4 m is dug from the earth to form a platform of length 25 m and a breadth of 12 m. Find the height of the platform.

Triangle ABC has angles A = 60° and B = 70°. The in-center of this triangle is at I. Find angle BIC. (Provide answer in degrees)