28 Official GATE PH Questions with Verified Solutions & Answer Keys
Two uniform thin rods of equal length, L, and masses M1 and M2 are joined together along the length. The moment of inertia of the combined rod of length 2L about an axis passing th...
The sum of the first n terms in the sequence 8, 88, 888, 8888, ... is (A) 80/81 (10^n - 1) + 8/9 n (B) 80/81 (10^n - 1) - n (C) 80/81 (10^n - 1) + 8n (D) 80/81 (10^n - 1) - 8/9 n...
PHYLAXIS (A) The mirror image of the above text about the X-axis is РНАГУХІ2 (B) ВНАГУХІ (C) (D) bHATVXIS...
Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possib...
1. Some football players play cricket. 2. . All cricket players play hockey. Among the options given below, the statement that logically follows from the two statements 1 and 2 abo...
Given the statements: P is the sister of Q. Q is the husband of R. R is the mother of S. T is the husband of P. Based on the above information, T is ______ of S....
In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQ...
"You are delaying the completion of the task. Send _______ contributions at the earliest."...
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.)...
In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International M...
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure cons...
Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statemen...
The coefficient of x4 in the polynomial (x - 1)3(x - 2)3 is equal to _______....
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in bet...
Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}...
In the following series, identify the number that needs to be changed to form the Fibonacci series. 1, 1, 2, 3, 6, 8, 13, 21,…...
The real variables x, y, z, and the real constants p, q, r satisfy x pq - r2 = y qr - p2 = z rp - q2 Given that the denominators are non-zero, the value of px + qy + rz is...
A planar rectangular paper has two V-shaped pieces attached as shown below. This piece of paper is folded to make the following closed three-dimensional object. The number of folds...
Four equilateral triangles are used to form a regular closed three-dimensional object by joining along the edges. The angle between any two faces is...
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 requir...
In the sequence of tiles shown below, the missing tile indicated by the question mark should be (A) (B) (C) (D)...
A school has 100 students distributed among 1st to 10th standards. Based on this, which one of the following statements is always correct?...
How many 3-digit numbers can be formed using three distinct single digit prime numbers?...
In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. T...
A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cub...
Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are...
Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill. ii. Neither H2 nor H3 is the wes...
As shown in the figure, circle C1 with center O1 and radius r1 touches the square VWXY at points P and Q while circle C2 with center O2 and radius r2 touches the square VWXY at poi...