Quant Boosters - Geometry - Raman Sharma - Set 2


  • Faculty and Content Developer at TathaGat


    Number of Questions : 30
    Topic : Geometry
    Answer Key Available ? Yes
    Source : Selected Questions from CAT Prep Forums.


  • Faculty and Content Developer at TathaGat


    Q1) In the given figure, medians QX and RY of ΔPQR are perpendicular, QX = 8 and RY = 12. The area of ΔPQR is

    0_1507021288569_0b7e63a7-70ae-4147-b35d-4e7997a52266-13528697_976062732511358_9127419505535707549_n.jpg

    [OA: 64]


  • Faculty and Content Developer at TathaGat


    0_1507021332539_9e6f5349-e2a0-43a4-ac66-dacc613a16fe-13512221_976378735813091_8996168066372223641_n.jpg


  • Faculty and Content Developer at TathaGat


    Q2) PQRS is a rectangle. PQ=40cm QR=30cm. Both the circles touch each other externally and also touches the two sides QS and PQ of triangle PQS. If diagonal QS is a common tangent. Find the radius of the smaller circle?

    0_1507021569566_58747c4e-76b8-4259-a977-f3a1319e3fda-13438997_976061759178122_3729413014815975460_n.jpg

    [OA: 20/3]


  • Faculty and Content Developer at TathaGat


    0_1507021610987_d9ae7c32-bc67-4524-866d-a6e2b703e779-13501639_976070752510556_2621033750875626009_n.jpg


  • Faculty and Content Developer at TathaGat


    Q3) In triangle ABC, angle bisectors AD and BE intersected at P. If the sides of triangle are 3, 5, 7 opposite to A, B, C respectively and BP = x and PE = y , compute for the ratio x:y where x and y are relatively prime integers.

    [OA: 2 : 1]


  • Faculty and Content Developer at TathaGat


    Credits : Sahabudeen Salaeh

    0_1507021739592_c3402bb4-05db-4d70-a48b-a1d4e6093f56-image.png


  • Faculty and Content Developer at TathaGat


    Q4) A semicircle is inscribed in an equilateral triangle as shown. What fraction of the triangle lies inside the semicircle?

    0_1507021773450_34e768d2-4ab9-4fa8-94ce-2c2721ce2e3c-12592349_885557224895243_5455117907032341670_n.jpg

    [OA: √3π/8 ]


  • Faculty and Content Developer at TathaGat


    Q5) In ∆ABC , AD ia the altitude from A onto the side BC. If b > c , angle C =23° and AD = abc/(b² - c²) , then angle B is equal to
    a. 83°
    b. 113°
    c. 123°
    d. 75°
    e. NoT

    [OA: 113]


  • Faculty and Content Developer at TathaGat


    Q6) On a circle 26 equidistant points are marked. These points are joined to form triangles. Of the triangles formed, how many of them will have their circumcenter on one of their sides?

    [OA : 312]


  • Faculty and Content Developer at TathaGat


    Q7) ABCD is a square with side length r units .
    AB is trisected by two points R and S ,
    CD is trisected by two points P and Q ,
    AP and DR intersect at E
    AP and DS intersect at N
    AQ and DR intersect at M
    AQ and DS intersect at F
    What is the area of the quadrilateral EMFN ?

    [OA: (r/6)^2]


  • Faculty and Content Developer at TathaGat


    Credits : Turan Bey

    0_1507022011636_f9becc24-5041-48cc-bf77-95122345e53a-image.png


  • Faculty and Content Developer at TathaGat


    Q8) In the square ABCD , a line through B intersects the extension of CD at E , the side AD at F and the diagonal AC at G if BG = 9 and GF = 3 , then what is the length of EF ?

    0_1507022062356_f3f516fd-814e-49a2-8ad6-189e9d957eec-image.png

    [OA: 24]


  • Faculty and Content Developer at TathaGat


    Q9) Two of the sides of a triangle are in the ratio 3:4. The medians to these sides are perpendicular to each other. If the third side of the triangle is 12root(5), find the smaller of the first two sides of the triangle.

    [OA: 36]


  • Faculty and Content Developer at TathaGat


    0_1507022284504_72d32eeb-7099-46f7-83c7-4c62c0d73eb9-image.png


  • Faculty and Content Developer at TathaGat


    Q10) The shortest median of a right-angled triangle is 25 units. If the area of the triangle is 336 sq.units, what is the length (in units) of the longest median of the triangle?

    [OA: 48.5]


  • Faculty and Content Developer at TathaGat


    0_1507022589502_1cf95aac-4514-4d5e-a276-0cf210e023dc-13781761_992876177496680_2726106952529985480_n.jpg


  • Faculty and Content Developer at TathaGat


    Q11) In triangle ABC, two lines DE and FG are drawn parallel to BC such that they divide AC in the ratio 2:3:5. Find the ratio of area of triangle ABC to area of the trapezium DEGF.

    [OA: 100 : 21]


  • Faculty and Content Developer at TathaGat


    Q12) The parallel sides of Trapezium is 6 and 8 units respectively. Find the length of the line segment parallel to these sides and which divides the area of trapezium in equal halves.
    A. 4 √3
    B. 5 √ 2
    C. 7
    D. 7/√2

    [OA: Option b]


  • Faculty and Content Developer at TathaGat


    0_1507022873128_5d5ae6e7-88a6-403f-aa7d-ceb52fd2f8b9-12107268_835647809886185_7228629521719374536_n.jpg


  • Faculty and Content Developer at TathaGat


    credits : @swetabh_kumar

    let length be x..so 1/2 * (6x) * h1= 1/2 * (1/2 * 14 * h2)..h1 is the height of the smaller trapezium...h2 is overall heght.
    so (6+x)h1=7h2
    now the line of legth x is divided into length 6 and 2 equal corner segments of legth (x-6)/2 each.
    by similar triangles, h1/h2= (x-6)/2.
    plug in the 1st eqn7/(6+x)=(x-6)/2
    x^2 - 36 = 14
    x = 5 root 2


 

Looks like your connection to MBAtious was lost, please wait while we try to reconnect.