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Ques 21 Gate 2022
A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise).
The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm.
What is the shortest distance between PQ and SR (in cm)?
(b) is the correct answer.
Ques 22 GATE 2021
On a planar field, you traveled 3 units East from a point O. Next you traveled 4 units South to arrive at point P. Then you traveled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you traveled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.
The distance of point Q to point O, in the same units, should be _______.
(c) is the correct answer.
Ques 23 GATE 2021
In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer.
The minimum area of the triangle PQR possible, in cm2 is _______.
(d) is the correct answer.
Ques 24 GATE 2021
A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.
Which one of the following is NOT a convex polygon?
(a) is the correct answer.
Ques 25 GATE 2021
For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:
(d) is the correct answer.
Ques 26 GATE 2021
A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon. Which one of the following is NOT a convex polygon?
(a) is the correct answer.
Ques 27 GATE 2020
Given a semicircle with O as the centre, as shown in the figure, the ratio AC + CB / AB where AC, CB, and AB are chords.
(a) is the correct answer.
Ques 28 GATE 2020
Given a semicircle with O as the center, as shown in the figure, what is the ratio (A̅C̅ + C̅B̅) / A̅B̅?
where A̅C̅, C̅B̅, and A̅B̅ are chords.
(a) is the correct answer.
Ques 29 Gate 2018
The area of a square is ‘d’. What is the area of the circle which has the diagonal of the square as its diameter?
(Geometry) is the correct answer.
Ques 30 GATE 2017
A right-angled cone (with base radius 5 cm and height 12 cm), as shown in the figure below, is rolled on the ground keeping the point P fixed until the point Q (at the base of the cone, as shown) touches the ground again. By what angle (in radians) about P does the cone travel?
(d) is the correct 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) 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
(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.