Question Bank  Geometry  Hemant Malhotra

hemant_malhotra last edited by zabeer
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Number of Questions: 100
Topic: Geometry
Answer key available?: No
Source: Elite's Grid forum

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q1) Centroid of triangle is at (1,1) while its orthocenter is at (5,3) then circumcentre of triangle could be
(1) (1,3)
(2) (8/3 , 0)
(3) (0,8/3)
(4) (7/3,1/3)

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q2) The legs of a right triangle are 8 and 15. Find the altitude to the hypotenuse

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q3) When the base of a triangle is increased 10% and the altitude to this base is decreased 10%, the change in area is

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q4) Let us take a point P inside an equilateral triangle. The sum of lengths of the perpendiculars dropped to the 3 sides of the triangle is equal to 1000. Then the length of the altitude of the triangle is:

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q5) In a ∆ABC,AD & BE are medians and G is the centroid, ∠AGE = 30°, AD=12cm & BE= 18cm. Find the area of the triangle?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q6) In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q7) Given 10 distinct points, A_1 through A_5 on line R, and B_1 through B_5 on line S, draw the 25 possible line segments A_i B_j. Excluding the 10 given points themselves, what is the minimum number of distinct points at which these 25 segments can intersect?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q8) PQ and RS are perpendicular chords of a circle intersecting at T. RT= 2.5, TS=11, PT= 3. Find the radius of the circle (approximately).
a) 4.5
b) 12.1
c) 7.4
d) 15.6

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q9) For a trapezium, S1 denotes the sum of the squares of the sides and S2 denotes the sum of the squares of the diagonals. S1 – S2 = 576. If the longer parallel side is 50 cm, the shorter parallel side is _______.
a) 26 cm
b) 22 cm
c) 18 cm
d) 30 cm

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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

hemant_malhotra last edited by zabeer
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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 ?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q14) A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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?

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
Q16) If ΔPAB is formed by three tangents to a circle having centre O and ∠APB = 40º, find ∠AOB.

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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

hemant_malhotra last edited by
Director at ElitesGrid  CAT 2017  QA 100 Percentile / CAT 2016  QA : 99.94, LRDI  99.70% / XAT 2017  QA : 99.975
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?