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Ques 11 GATE 2025
A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?
(a) is the correct answer.
Ques 12 GATE 2025
A circle with center at (x,y)=(0.5,0) and radius =0.5 intersects with another circle with center at (x,y)=(1,1) and radius =1 at two points. One of the points of intersection (x,y) is:
(a) is the correct answer.
Ques 13 GATE 2025
An object is said to have an n-fold rotational symmetry if the object, rotated by an angle of 2π/n, is identical to the original.
Which one of the following objects exhibits 4-fold rotational symmetry about an axis perpendicular to the plane of the screen?
Note: The figures shown are representative.
(a) is the correct answer.
Ques 14 GATE 2025
A stick of length one meter is broken at two locations at distances of b1 and b2 from the origin (0), as shown in the figure. Note that 0
Note: All lengths are in meter. The figure shown is representative.
(d) is the correct answer.
Ques 15 GATE 2025
Spheres of unit diameter are centered at (l,m,n) where l, m, and n take every possible integer values.
The distance between two spheres is computed from the center of one sphere to the center of the other sphere. For a given sphere, x is the distance to its nearest sphere and y is the distance to its next nearest sphere. The value of y/x is:
(c) is the correct answer.
Ques 16 GATE 2025
In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2. ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as shown in the figure.
Which one of the following statements is true about the shaded area PQS?
Note: The figure shown is representative.
(a) is the correct answer.
Ques 17 GATE 2025
Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?
(b) is the correct answer.
Ques 18 GATE 2025
In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in cm2) of the rectangle PLMN?
Note: The figure shown is representative.
(c) is the correct answer.
Ques 19 GATE 2025
Three villages P, Q, and R are located in such a way that the distance PQ=13 km, QR=14 km, and RP=15 km as shown in the figure. A straight road joins Q and R. It is proposed to connect P to this road QR by constructing another road. What is the minimum possible length (in km) of this connecting road?
Note: The figure shown is representative.
(c) is the correct answer.
Ques 20 GATE 2025
In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in cm2) of the rectangle PLMN?
Note: The figure shown is representative.
(c) is the correct answer.
Ques 21 GATE 2024 SET-2
A cube is to be cut into 8 pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.
The minimum number of such cuts required is
(a) is the correct answer.
To find the minimum number of cuts required to divide a cube into 8 pieces of equal size and shape, let us analyze the dimensions of the cube:
• A cube is a three-dimensional object with three distinct axes: length, width, and height.
• To ensure that all resulting pieces have the exact same size and shape, our cuts must be symmetrical along these axes.
• If we make 1 straight cut passing completely through the middle along the length, the cube is divided into 2 equal parts.
• Making a 2nd straight cut through the middle along the width divides those parts further, resulting in 4 equal pieces.
• Making a 3rd straight cut through the middle along the height cuts all existing pieces in half, resulting in exactly 8 equal pieces (each piece being a smaller, identical cube).
Since each cut must go completely from one side to the other, making 1 cut along each of the 3 coordinate planes gives us exactly 2 × 2 × 2 = 8 identical pieces. Thus, the minimum number of cuts required is 3, matching option (a).
Ques 22 GATE 2023 SET-2
Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?
(a) is the correct answer.
Ques 23 GATE 2023
In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)
(b) is the correct answer.