CAT4MBA

Q4. In the above figure triangle ABC is inscribed in a circle with center at E AE when produced meets BC at point D.  If angle ABE is 30 degree and AEC is 140 degree, find BEC.

a. 120
b. 110
c. 100
d. 90

here angle ABE=30 so BAE also 30 ,
now AEC=140 so EAC & ECA=20

so BEC=360-120-140=100

Q7. In the figure above, A and B are the centers of two circles of radii 9 cm and 2 cm respectively. Such that AB = 13 cm and ang(ACB) = 90, where C is the center of another circle which touches the above two circles. The area of the circle with center C is : (figure not drawn to scale)
a. 3pi
b. 9pi
c. 9pi^2
d. 9sqrt(pi)

here angle ACB=90

now if the radius of the cirlcle C is x, then

(9+x)^2+(x+2)^2=13^2

so x=3 satisfy (13,12,5 right-angle triangle possible)

so area of the circle with centre C=9pi^2

Q6. A rectangular box has edges with integer valued lengths, minimum surfaces area and a volume of 2002 cm. Find the sum of the lengths of the edge
a. 114 cm
b. 152 cm
c. 38 cm
d. 35 cm

here volume=2002=14x13x11 (in this case surface area is minimum)

so  sum of the lenghts of the edges=4*(14+11+13)=152

Q1. The perimeter of a right angled triangle is four times the shortest side. The ratio of the other two sides is
a. 5 : 6
b. 3 : 4
c. 4 : 5
d. 2 : 3

if we assume side of triangle are x,y,z then (x+y+z)=4y  (assume y is the shortest side)

so x+z=3y--------(1)

now x^2+y^2=z^2  so z^2-x^2=y^2----(2)

put value of y from eq(1) to eq(2)

we get 8z=10x

so ration of other two side =4:5 or 5:4

Little Star

Q5.  In a right angled triangle ABC, angle B is right angle, side AB is half of the hypotenuse. AE is parallel to median BD and CE is parallel to BA. What is the ratio of length BC to that of EC?
a. sqrt(2) : 1
b. sqrt(3) : 2
c. sqrt(5) : sqrt(3)
d. Can’t be determined

here  triangle ADB and CAE are similar

so (AD/AB)=(CA/cE)

(x/x)=(2x/CE)

so CE=2x

so ratio=sqrt3:2

Little Star