Question Bank - Geometry


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Number of Questions: 14
    Topic: Geometry
    Answer key available?: No
    Source: Elite's Grid forum


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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)


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q2) The legs of a right triangle are 8 and 15. Find the altitude to the hypotenuse


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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:


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 99.70% / XAT 2017 - QA : 99.975


    Q12) If the volume of all the figures are constant, then which of the following has the maximum surface area?
    a) sphere
    b) square
    c) pentagon
    d) hexagon
    e) none


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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 ?


  • Director at ElitesGrid | CAT 2016 - QA : 99.94, LR-DI - 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.


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