Geometry Aptitude Questions & Formulas with answer


Ques 31 GATE 2016 SET-2


A wire of length 340 mm is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of 1:2. What is the length of the side of the square (in mm) such that the combined area of the square and the rectangle is a MINIMUM?

A

30

B

40

C

120

D

180

(a) is the correct answer.

Ques 32 GATE 2015


A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible

A

1:4

B

1:3

C

1:2

D

2:3

(c) is the correct answer.

Ques 33 GATE 2015


In the given figure angle Q is a right angle, PS:QS=3:1, RT:QT=5:2 and PU:UR=1:1. If area of triangle QTS is 20 cm², then the area of triangle PQR in cm² is __________.

(280) is the correct answer.

Ques 34 GATE 2015


Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and line PR is parallel to the x-axis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: -4 ≤ x ≤ 5 and 6 ≤ y ≤ 16. How many different triangles could be constructed with these properties?

A

110

B

1,100

C

9,900

D

10,000

(c) is the correct answer.

Ques 35 GATE 2014


The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

(180) is the correct answer.