Question Bank - Geometry


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Number of Questions : 15
    Topic : Geometry
    Answer key available ? : Yes (last post)
    Source :


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q1) Hexagon ABCDEF is inscribed in a circle. The sides AB, CD, and EF are each x units in length whereas the sides BC, DE, and FA are each y units in length. Then, the radius of the circle is

    (a) rt[(x² + y² + xy)/3]
    (b) rt[(x² + y² + xy)/2]
    (c) rt[(x² + y² – xy)/3]
    (d) rt[(x² + y² – xy)/2]


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q2) ABC is an isosceles triangle with AB= AC = 4. O is a point inside the triangle ABC.
    Find the area of triangle OBC.
    I. ∠BAC = 45˚.
    II. ∠BOC = 90˚.

    (a) question can be answered by using one statement alone but not by other statement alone.
    (b) question can be answered by using either statement alone.
    (c) question can be answered by using both statements together but not by either alone.
    (d) question cannot be answered even by using both statements together.


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q3) In figure, CD = BC, ∠BAD = 66˚, AB is the diameter and O the center of the semicircle.
    Measure the angle ∠DEC
    0_1487226566008_g1.jpg
    (a) 48˚
    (b) 54˚
    (c) 57˚
    (d) 63˚


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q4) ABCDHFEG is a cuboid and EFHGJ is a right pyramid with base EFHG and J lying on plane ABCD. If volume inside cuboid but outside pyramid is 480cm³, find h.

    0_1487226671108_g2.jpg

    (a) 8
    (b) 10
    (c) 12
    (d) 16


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q5) ABCD is a square with side length 2 cm. It is divided into five rectangles of equal areas, as shown in the figure. The perimeter of the rectangle BEFG is

    0_1487226723810_g3.jpg

    (a) 51/16
    (b) 36/11
    (c) 58/15
    (d) 47/13


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q6) Three circles are in a row touching each other such that all three of them have two common tangents. The radii of the largest and the smallest circle are 9 and 4 respectively. Line segment AB passes through the centres of the circles and lies on the two outer circles. What is the length of AB?

    0_1487226775025_g4.jpg

    (a) 38
    (b) 26 + 3rt(32)
    (c) 26 + 2rt(38)
    (d) 19


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q7) A regular hexagon with a perimeter of 12rt(2) units lies in the Cartesian plane in such a way that its center is on the origin, two of the vertices lie on the x-axis, and the midpoints of two of its sides lie on the y-axis. If the portion of the hexagon that lies in Quadrant I is completely revolved around the x-axis, a solid whose volume is X cubic units results. If the same portion is completely revolved around the y-axis, a solid with a volume of Y cubic units results. Evaluate (X/Y)² .

    (a) 48/49
    (b) 1
    (c) 4/3
    (d) 16/9


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q8) One angle of a regular polygon measures 179˚. How many sides does it have?

    (a) 179
    (b) 180
    (c) 280
    (d) 360


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q9) In two equilateral triangles ABC and BMN, ∠ABM = 120˚. AN & CM intersects at O. Find ∠MON.

    (a) 120˚
    (b) 90˚
    (c) 60˚
    (d) 30˚


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q10) In a parallelogram ABCD, let M be the midpoint of the side AB and N the midpoint of BC. Let P be the intersection point of the lines MC and ND. Find the ratio of area of ▲s APB : BPC : CPD : DPA.

    (a) 3:1:2:4
    (b) 3:2:1:4
    (c) 2:1:3:4
    (d) 1:2:3:4


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 11) In a quadrilateral ABCD, sides AD and BC are parallel but not equal and sides AB = DC = x. The area of the quadrilateral is 676 cm². A circle with centre O and radius 13 cm is inscribed in the quadrilateral such that it is tangent to each of the four sides of the quadrilateral. Determine the length of x.

    (a) 13
    (b) 24
    (c) 26
    (d) 12


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 12) C and D are two points on a semicircle with AB as diameter such that AC – BC = 7 and AD – BD = 13. AD and BC intersect at P. Find the difference in area of triangles ACP and BDP.

    (a) 24
    (b) 26
    (c) 28
    (d) 30


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 13) Points A, D and C lie on the circumference of a circle. The tangents to the circle at points A and C meet at the point B. If ∠DAC = 83˚ and ∠DCA = 54˚. Find ∠ABC.

    (a) 88˚
    (b) 94˚
    (c) 100˚
    (d) 104˚


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 14) The sum of all interior angles of eight polygons is 3240˚. What is the total number of sides of polygons?

    (a) 16
    (b) 18
    (c) 32
    (d) 34


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Q 15) Circles with centers P and Q have radii 20 and 15 cm respectively and intersect at two points A, B such that ∠PAQ = 90°. What is the difference in the area of two shaded regions?

    0_1487227157333_g5.jpg

    (a) 175 Pi
    (b) 150 Pi
    (c) 125 Pi
    (d) 90 Pi


  • Faculty and Content Developer at Tathagat | Delhi College of Engineering


    Answer Key:

    #1. (a)
    #2. (d)
    #3. (c)
    #4. (b)
    #5. (c)
    #6. (a)
    #7. (a)
    #8. (d)
    #9. (c)
    #10. (a)
    #11. (c)
    #12. (d)
    #13. (b)
    #14. (d)
    #15. (a)


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