113 Official GATE PH Questions with Verified Solutions & Answer Keys
Two matrices A and B are said to be similar if B = P-'AP for some invertible matrix P. Which of the following statements is NOT TRUE? (A) Det A = Det B (B) Trace of A = Trace of B ...
If a force F is derivable from a potential function V(r), where r is the distance from the origin of the coordinate system, it follows that (A) ЙxF=0 (В) V.F=0 (C) VV=0 (D) V'V=0...
The quantum mechanical operator for the momentum of a particle moving in one dimension is given by (A) ih- d (B) -ih- d (C) ih (D) n d' dx dx дt 2m dx?...
A Carnot cycle operates on a working substance between two reservoirs at temperatures T, and 7,, with T, > T,. During each cycle, an amount of heat &, is extracted from the reservo...
In a first order phase transition, at the transition temperature, specific heat of the system (A) diverges and its entropy remains the same (B) diverges and its entropy has finite ...
The semi-empirical mass formula for the binding energy of nucleus contains a surface correction term. This term depends on the mass number A of the nucleus as (A) A-13 (B) A''3 (C)...
The population inversion in a two level laser material CANNOT be achieved by optical pumping because (A) the rate of upward transitions is equal to the rate of downward transitions...
The order of magnitude of the energy gap of a typical superconductor is (A) 1 MeV (B) 1 KeV (C) 1 eV (D) 1 meV...
The order of magnitude of the energy gap of a typical superconductor is (A) 1 MeV (B) 1 KeV (C) 1eV (D) 1 meV...
Which of the following statements is CORRECT for a common emitter amplifier circuit? (A) The output is taken from the emitter (B) There is 180° phase shift between input and output...
Identify the CORRECT statement for the following vectors ˆ ˆ 3 2 a i j and ˆ ˆ 2 b i j ...
The space-time dependence of the electric field of a linearly polarized light in free space is given by 0 cos( ) xE t kz - where E0, and k are the amplitude, the angular frequen...
If the peak output voltage of a full wave rectifier is 10 V, its d.c. voltage is...
A particle of mass m is confined in a two dimensional square well potential of dimension a. This potential V(x,y) is given by ( , ) 0 V x y for a x a - and a y a - elsewh...
The isothermal compressibility, of an ideal gas at temperature T0 and volume V0, is given by...
The ground state of sodium atom (11Na) is a 2S1/2 state. The difference in energy levels arising in the presence of a weak external magnetic field B, given in terms of Bohr magneto...
For an ideal Fermi gas in three dimensions, the electron velocity vF at the Fermi surface is related to electron concentration n as,...
Which one of the following sets corresponds to fundamental particles?...
In case of a Geiger-Muller (GM) counter, which one of the following statements is CORRECT?...
f (x) is a symmetric periodic function of x i.e. f (x) = f (-x). Then, in general, the Fourier series of the function f(x) will be of the form...
In the most general case, which one of the following quantities is NOT a second order tensor? (A) Stress (B) Strain (C) Moment of inertia (D) Pressure...
An electron is moving with a velocity of 0.85c in the same direction as that of a moving photon. The relative velocity of the electron with respect to photon is (A) c (B) -c (C) 0....
If Planck's constant were zero, then the total energy contained in a box filled with radiation of all frequencies at temperature T would be ( k is the Boltzmann constant and T is n...
Across a first order phase transition, the free energy is...
Two gases separated by an impermeable but movable partition are allowed to freely exchange energy. At equilibrium, the two sides will have the same...
The entropy function of a system is given by ) where aand _0 are positive constants. The temperature of the system is...
Consider a linear collection of N independent spin 1/2 particles, each at a fixed location. The entropy of this system is (k is the Boltzmann constant) (A) Zero (B) kܰC) 1 2kܰD) (2...
The decay process \nu̅ violates (A) baryon number (B) lepton numb er (C) isospin (D) strangeness 2013 PHYSICS - PH PH 5/13...
The isospin (I) and baryon number (B) of the up quark is (A) I=1, B=1 (B) I=1, B=1/3 (C) I=1/2, B=1 (D) I=1/2, B=1/3...
A student is required to demonstrate a high level of comprehension of the subject, especially in the social sciences. The word closest in meaning to comprehension is (A) understand...
Choose the most appropriate word from the options given below to complete the following sentence. One of his biggest ______ was his ability to forgive. (A) vice (B) virtues (C) cho...
Rajan was not happy that Sajan decided to do the project on his ow n. On observing his unhappiness, Sajan explained to Rajan that he preferred to work independently. Which one of t...
If y = 5x2 + 3, then the tangent at x = 0, y = 3 (A) passes through x = 0, y = 0 (B) has a slope of +1 (C) is parallel to the x-axis (D) has a slope of −1...
A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs 800Q, where Q is the daily production in tonnes. What is the cost of production in Rs p...
Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK (A) ALRVX (B) EPVZB (C) ITZDF (D) OYEIK...
Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six -storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on ...
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...
One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country...
The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? (k percentile is the value such that k percent o...
Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Apparent lifelessness (A) harbours (B) leads to dormant life. (C) suppo...
Choose the statement where underlined word is used correctly. (A) When the teacher eludes to different authors, he is being elusive. (B) When the thief keeps eluding the police, he...
Tanya is older than Eric. Cliff is older than Tanya. Enic is older than Chff. If the first two statements are true, then the third statement is: (A) True (B) False (C) Uncertain (D...
Question Type : MCO Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to be ...
Select the appropriate option in place of underlined part of the sentence. Increased productivity necessary reflects greater efforts made by the employees. (A) Increase in producti...
Question Type : MCO Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: I. No manager ...
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 cm', then the area of triangle PQR in cm' is. R P Q...
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 in...
A coin is tossed thrice. Let X be the event that head occurs in each of the first two tosses. Let Y be the event that a tail occurs on the third toss. Let Z be the event that two t...
The volume of a sphere of diameter 1 unit is _ (A) least (B) less General Aptitude - GA Set-2 (C) lesser than the volume of a cube of side 1 unit. (D) low 0.2...
Which of the following magnetic vector potentials gives rise to a uniform magnetic field k Bˆ 0 ? (A) k z Bˆ 0 (B) j x Bˆ0- (C) j x i yB ˆ ˆ 2 0 - (D) j x i yB ˆ ˆ 2 0 ...
The unruly crowd demanded that the accused be (A) hanged (B) hanging (C) hankering without trial. (D) hung Choose the statement(s) where the underlined word is used correctly: (i) ...
Fact: If it rains, then the field is wet. Read the following statements: It rains (ii) (iii) (iv) The field is not wet The field is wet It did not rain Which one of the options giv...
A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimet...
Students taking an exam are divided into two groups, P and Q such that each group has the same number of students. The performance of each of the students in a test was evaluated o...
(C) Most students of group Q scored marks in a narrower range than students in group P. (D) The median of the marks of group P is 100. A smart city integrates all modes of transpor...
The total power emitted by a spherical black body of radius R at a temperature T is P1. Let P2 be the total power emitted by another spherical black body of radius R/2 kept at temp...
Find the missing sequence in the letter series. B, FH, LNP, _ (A) SUWY (B) TUVW (C) TVXZ (D) TWXZ The binary operation o is defined as a O b = abt(a+b), where a and b are any two r...
Which of the following curves represents the function [| (||)|]|) for \pi ? Here, xrepresents the abscissa and yrepresents the ordinate. (A) (B) (C) (D) END OF THE QUESTION PAPER 1...
The ninth and the tenth of this month are Monday and Tuesday _ (A) figuratively (B) retrospectively (C) respectively (D) rightfully...
It is (A) easier, than Correct: 1 Wrong : -0.33 the last year's. to read this year's textbook (B) most easy, than (C) easier, from (D) easiest. from...
A rule states that in order to drink beer, one must be over 18 years old. In a bar, there are 4 people. P is 16 years old. Q is 25 years old. R is drinking milkshake and S is drink...
Fatima starts from point P. goes North for 3 km. and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6...
500 students are taking one or more courses out of Chemistry. Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329). Physics (186). M...
"If you are looking for a history of India, or for an account of the rise and fall of the British Raj. or for the reason of the cleaving of the subcontinent into two mutually antag...
Each of P. Q. R. S. W. X. Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Further. Z and W ar...
1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?...
The number of 3-digit numbers such that the digit 1 is never to the immediate right of 2 is (A) 781 (B) 791 (C) 881 (D) 891...
A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25 m intervals ...
"When she fell down the , she received many _ The words that best fill the blanks in the above sentence are General Aptitude (GA) Set-4 but little help." (A) stairs, stares (C) sta...
"In spite of being warned repeatedly, he failed to correct his The word that best fills the blank in the above sentence is behaviour." (A) rational (B) reasonable (C) errant (D) go...
For 0 ≤ x ≤ 2nt, sin x and cos x are both decreasing functions in the interval (A) (0,7) (в) (f,т) (C) (T, 3) (D) (7,27)...
The area of an equilateral triangle is V3. What is the perimeter of the triangle? (A) 2 (B) 4 (C) 6 (D) 8...
Arrange the following three-dimensional objects in the descending order of their volumes: (i) (ii) A cuboid with dimensions 10 cm, 8 cm and 6 cm (iii) A cube of side 8 cm A cylinde...
An automobile travels from city A to city B and returns to city A by the same route. The speed of the vehicle during the onward and return journeys were constant at 60 km/h and 90 ...
A set of 4 parallel lines intersect with another set of 5 parallel lines. How many parallelograms are formed? (A) 20 (B) 48 (C) 60 (D) 72...
To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of 6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30...
I522 +x-1= 0 what is the value of ** + 2? (A) 1 (B) 5 (C) 7 (D) 9...
In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another...
The fishermen, _______ the flood victims owed their lives, were rewarded by the government....
Some students were not involved in the strike. If the above statement is true, which of the following conclusions is/are logically necessary? 1. Some who were involved in the strik...
The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is _______....
Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following the directions given below: 1. No two odd or even numbers are next to each other. 2. Th...
Until Iran came along, India had never been _______ in kabaddi....
Since the last one year, after a 125 basis point reduction in repo rate by the Reserve Bank of India, banking institutions have been making a demand to reduce interest rates on sma...
In a country of 1400 million population 70% own mobile phones. Among the mobile phone owners, only 294 million access the Internet. Among these Internet users, only half buy goods ...
The nomenclature of Hindustani music has changed over the centuries. Since the medieval period dhrupad styles were identified as baanis. Terms like gayaki and baaj were used to ref...
Two trains started at 7 AM from the same point. The first train travelled north at a speed of 80 / km h and the second train travelled south at a speed of 100 / km h . The time at ...
“I read somewhere that in ancient times the prestige of a kingdom depended upon the number of taxes that it was able to levy on its people. It was very much like the prestige of a ...
Define [x] as the greatest integer less than or equal to x, for each x ∈ (-∞, ∞). If y = [x], then area under y for x ∈ [1, 4] is (A) 1 (B) 3 (C) 4 (D) 6...
P, Q, R and S are to be uniquely coded using α and β. If P is coded as αα and Q as αβ, then R and S, respectively, can be coded as (A) βα and αβ (B) ββ and αα (C) αβ and ββ (D) βα ...
Select the graph that schematically represents BOTH y = x^m and y = x^(1/m) properly in the interval 0 ≤ x ≤ 1, for integer values of m, where m > 1....
The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four sc...
Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is: (A) (B) (C) 1 36 1 12 1...
(A) (B) (C) (D) \cdot and © are two operators on numbers p and q such that pOq = p-q, and p©q= pxq Then, (9 O (6 @ 7)) 0(7 0(60 5))= 40 -26 -33 -40...
On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that...
P R In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S...
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 ...
Two straight lines pass through the origin (x_0, y_0) = (0,0). One of them passes through the point (x1, y1) = (1,3) and the other passes through the point (x2, y2) = (1,2). What i...
If p ∶ q = 1 ∶ 2 q ∶ r = 4 ∶ 3 r ∶ s = 4 ∶ 5 and u is 50% more than s, what is the ratio p ∶ u?...
P invested ₹ 5000 per month for 6 months of a year and Q invested ₹ x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total ...
The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam. From the data presented above, which one of the following is CORRECT?...
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position. 3 9 11 7 14 2 4 0 2 4 6 8 10 12 14 16 3 4 5 6 7 8 9 Frequency Marks The o...
To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2. If the total cost of sand and cement to construct t...
Take two long dice (rectangular parallelepiped), each having four rectangular faces labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces and has 1/4...
How many combinations of non-null sets A, B, C are possible from the subsets of {2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?...
The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following option...
The sum of the following infinite series is: 1 1! + 1 2! + 1 3! + 1 4! + 1 5! + ⋯...
The figures I, II and III are parts of a sequence. Which one of the following options comes next in the sequence at IV? (A) (B) (C) (D) I II III IV ?...
"Why do they pull down and do away with crooked streets, I wonder, which are my delight, and hurt no man living? Every day the wealthier nations are pulling down one or another in ...
Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about a...
A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays...
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 intersec...
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 -f...