Question Bank  Geometry  Hemant Malhotra

Q10) 2x + 3y + 5 = 0 and 6x – 4y + 9 = 0 are two lines. If a point is at a distance of 1 unit from each of the two given lines, then how many such points exist?
a) 1
b) 3
c) 4
d) 2

Q11) A triangle, whose sides are 20 cm, 48 cm and 52 cm, is to be cut into two pieces of equal area by a single straight cut, which passes through one of the vertices of the triangle. What is the approximate maximum value of the sum of the perimeters of the two pieces

Q12) A goat is tied at the corner of a rectangular shed of dimensions 14 m x 7 m, with a rope 21 m long. If the goat can graze on the ground around and outside the shed as far as it is permitted by the rope, find the area (in sq.m.) on which it can graze.
a) 1232
b) 1560.5
c) 1260
d) 1543.5

Q13) The 2 adjacent sides of a quadrilateral are 6cm and 8cm. What is the maximum area of the quadrilateral (in sq cm) if it is inscribed in a circle of radius 5cm ?

Q14) A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

Q15) Four cubes of volume 1, 8, 27, and 125 are glued together at their faces. What is the smallest possible surface area of the resulting solid figure?

Q16) If ΔPAB is formed by three tangents to a circle having centre O and ∠APB = 40º, find ∠AOB.

Q17) A green colour cube is cut into smaller and identical cubes with 6 cuts. The cube is cut with a knife which applies red colour to the surfaces of the cubes while cutting. The smaller cubes are further cut with 6 cuts into smaller and identical cubes, with a knife which does not apply any colour to the surface. The questions are based on the cubes obtained after these cuts. How many smaller cubes have three faces coloured red?
a) 48
b) 52
c) 56
d) 64

@hemant_malhotra right angled triangle is of form 81517
area of triangle = (1/2)xhx17 = 1/2x8x15
h = 7

Q18) A, B, C, ..... till K are 11 points, spaced on the circumference of a circle in that order. What is the sum of all the corner angles of the ‘star’ formed by joining the points AEIBFJCGKDHA  in that order?

Q19) In a cyclic quadrilateral ABCD, if AB = 2, BC = 3, CD = 4 and DA = 5, what is the ratio of the lengths of the diagonals?
(1) 7 : 11
(2) 11 : 13
(3) 10 : 11
(4) 13 : 15

@hemant_malhotra
simple ..centroid will be 1,3

@hemant_malhotra decrease by 1 percent

Q20) What is the least possible number of cuts required to cut a cube into 34 identical pieces ?

let number of cuts along length , width and height is a,b,c and total number of cuts=a+b+c
number of cubes =(a+1)(b+1)(c+1)
If product is cnstant sum will be minimum if they are very close to each other
here (a+1)(b+1)(c+1)=1 * 2 * 17
so a+1+b+1+c+1=1+2+17 so a+b+c=17

Q21) A right circular cylindrical vessel having height 20 cm and inner diameter 10 cm is filled with water upto 15 cm of it's height as measured from the base. Find the angle by which the cylinder must be tilted so that the water in the cylinder is just about to fall out?

Q22) The sides of a triangle of area 6 are in AP. If the sides have integer lengths, what is the length of the longest side?

Q23) If in a triangle ABC, AB = BC = 6m and CD = 10cm then what is the difference between the incentre and centroid of the triangle ?

Q24) In an art class the teacher tells the students to draw the largest circle possible on a piece of paper in the shape of a square and then draw a rectangle lying between the circumference of the circle and the edge of the square such that a corner of the rectangle lies on the circumference of the circle and two sides of the rectangle coincide with those of the square. If the rectangle measures 10 cm × 20 cm then what is the area of the sheet of paper?

Q25) A circle circumscribes a regular hexagon H1 and is inscribed inside a regular hexagon H2. What is the ratio of the areas of H1 and H2?