GATE Physic Sample Test Paper with Solutions

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Question

Consider an anti-symmetric tensor $P_{ij}$ with the indices i and j running 1 to 5. The number of independent components of the tensor is

Possible Answers

Selected	Possible Answer
	3
	10
	9
	6

Question

The value of the integral $\overset{\int}{c}$ $\cfrac{e^z\ sin(z)}{z^2}$ dz, where the contour C is the unit circle:
|z – 2| = 1, is

Possible Answers

Selected	Possible Answer
	$2 \pi i$
	$4 \pi i$
	$\pi i$

Question

The eigenvalues of the matrix $\bigg($ $\overset{2}{\underset{0}{3}}$ $\overset{3}{\underset{0}{2}}$ $\overset{0}{\underset{1}{0}}$ $\bigg)$ are

Possible Answers

Selected	Possible Answer
	5, 2, – 2
	- 5, -1, -1
	5, 1, -1
	- 5, 1, 1

Question

If f(x) = $\Big \{ \overset{0}{x - 3}$ $\overset{for\ x\ < 3,}{for\ x\ \ge 3,}$ then the laplace transform of f(x) is

Possible Answers

Selected	Possible Answer
	$s^{-2}\ e^{3x}$
	$s^2 \ e^{-3x}$
	$s^{-2}$
	$s^{-2}\ e^{-3x}$

Question

The valence electrons do not directly determine the following property of a metal.

Possible Answers

Selected	Possible Answer
	Electrical conductivity
	Thermal conductivity
	Shear modulus
	Metallic lustre

Question

Consider X-ray diffraction from a crystal with a face-centered-cubic (fcc) lattic. The lattice plane for which there is NO diffraction peak is

Possible Answers

Selected	Possible Answer
	(2, 1, 2)
	(1, 1, 1)
	(2, 0, 0)
	(3, 1, 1)

Question

The hall coefficient, RH, of sodium depends on

Possible Answers

Selected	Possible Answer
	The effective charge carrier mass and carrier density
	The charge carrier density and relaxation time
	The charge carrier density only
	The effective charge carrier mass

Question

The Bloch theorem states that within a crystal, the wavefunction, $\Psi ( \vec r )$ , of an electron has the form

Possible Answers

Selected	Possible Answer
	$\Psi ( \vec r ) =$ $u ( \overline{r} )\ e^{i \vec k \vec r}$ where u $( \vec r )$ is an arbitrary function and $\vec k$ is an arbitrary vector
	$\Psi ( \vec r ) =$ $u ( \overline{r} )\ e^{i \vec G \vec r}$ where u $( \vec r )$ is an arbitrary function and $\vec G$ is a reciprocal lattice vector
	$\Psi ( \vec r ) =$ $u ( \overline{r} )\ e^{i \vec G \vec r}$ where u $( \vec r )$ $= u( \vec r + \overline{\Lambda} )$ , $\overline{\Lambda}$ is a lattice vector and $\vec G$ is
	$\Psi ( \vec r ) =$ $u ( \overline{r} )\ e^{i \vec k \vec r}$ where u $( \vec r )$ $= u( \vec r + \overline{\Lambda} )$ , $\overline{\Lambda}$ is a lattice vector and $\vec k$ is

Question

In an experiment involving ferromagnetic medium, the following observations were made. Which one of the plots does NOT correctly represent the property of the medium?
(T_C) is the Curie temperature)

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Selected	Possible Answer

Question

The thermal conductivity of a given material reduces when it undergoes a transition from its normal state to the superconducting state. The reason is:

Possible Answers

Selected	Possible Answer
	The cooper pairs cannot transfer energy to the lattice
	Upon the formation of Copper pairs, the lattice becomes less efficient in heat transfer
	The electrons in the normal state lose their ability to transfer heat because of their coupling to the cooper pairs
	The heat capacity increases on transition to the superconducting state leading to a reduction in thermal conductivity

Question

The basic process underlying the neutron $\beta$ – decay is

Possible Answers

Selected	Possible Answer
	$d \rightarrow u+e^-+ \overline{V_e}$
	$d \rightarrow u+e^-$
	$s \rightarrow u+e^-+$ $\overline{V_e}\ (D)$
	$u \rightarrow d+e^- \overline{V_e}$

Question

In the nuclear shell model the spin parity of $\ {}^{15} N$ is given by

Possible Answers

Selected	Possible Answer
	$\cfrac{1 {}^-}{2}$
	$\cfrac{1 {}^+}{2}$
	$\cfrac{3 {}^-}{2}$
	$\cfrac{3 {}^+}{2}$

Question

Match the reactions on the left with the associated interactions on the right.

(1)	$\pi^+ \rightarrow \mu^+ + v_\mu$	(i)	Strong
(2)	$\pi^0 \rightarrow \gamma + \gamma$	(ii)	Electromagnetic
(3)	$\pi^0 + n \rightarrow \pi^- +p$	(iii)	Weak

Possible Answers

Selected	Possible Answer
	(1, iii), (2, ii), (3, i)
	(1, i), (2, ii), (3, iii)
	(1, ii), (2, i), (3, iii)
	(1, iii), (2, i), (3, isi)

Question

To detect trace amounts of a gaseous species in a mixture of gases, the preferred probing tool is

Possible Answers

Selected	Possible Answer
	Ionization spectroscopy with X-rays
	NMR spectroscopy
	ESR spectroscopy
	Laser spectroscopy

Question

The collection of N atoms is exposed to a strong resonant electromagnetic radiation with N_g atoms in the ground state and Ne atoms in the excited state, such that N_g + N_e = N . This collection of two-level atoms will have the following population distribution:

Possible Answers

Selected	Possible Answer
	$N_g\ < < \ N_e$
	$N_g\ > > \ N_e$
	$N_g\ \approx \ N_e = \cfrac{N}{2}$
	$N_g - N_e \approx\cfrac{N}{2}$

Question

Two states of an atom have definite parties. An electric dipole transition between these states is

Possible Answers

Selected	Possible Answer
	Allowed if both the states have even parity
	Allowed if both the states have odd parity
	Allowed if the two states have opposite parities
	Not allowed unless a static electric field is applied

Question

The spectrum of radiation emitted by a black body at a temperature 1000 K peaks in the

Possible Answers

Selected	Possible Answer
	Visible range of frequencies
	Infrared range of frequencies
	Ultraviolet range of frequencies
	microwave range of frequencies

Question

order term for the electric field at a distance d, far away p $(\overline{r}) = p_0 (a^2-r^2)$ $cos\ \theta, r < a$ . The leading order term for the electric field at a distance d, far away

Possible Answers

Selected	Possible Answer
	$d^{-1}$
	$d^{-2}$
	$d^{-3}$
	$d^{-4}$

Question

The voltage resolution of a 12 – bit digital to analog converter (DAC), whose output varies from – 10 V to + 10 V is ,approximately

Possible Answers

Selected	Possible Answer
	1 mV
	5 mV
	20 mV
	100 mV

Question

In one of the following circuits, negative feedback does not operate for a negative input. Which one is it? The opamps are running from $\pm$ 15 V supplies.

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Selected	Possible Answer

Question

A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is

Possible Answers

Selected	Possible Answer
	$\cfrac{3}{2} \ NK_BT(B)$
	$\cfrac{1}{2} \ NK_BT$

	$\cfrac{5}{2} \ NK_BT$

Question

Which of the following atoms cannot exhibit Bose-Einstein condensation. even in principle?

Possible Answers

Selected	Possible Answer
	${}^tH_1$
	${}^4He_z$
	${}^{21}Na_{11}$
	${}^{40}K_{19}$

Question

For the set of all Lorentz transformations with velocities along the x-axis, consider the two statements given below:
P: If L is a Lorentz transformation then, $L^{-1}$ is also a Lorentz transformation.
If $L_1\ and\ L_2$ are Lorentz transformations then, L_1L_2 is necessarily a Lorentz transformation.
Choose the correct option.

Possible Answers

Selected	Possible Answer
	P is true and Q is false.
	Both P and Q are true
	Both P and Q are false.
	P is false and Q is true

Question

Which of the following is an allowed wavefunction for a particle in a bound state? N is a constant and $\alpha , \beta > 0$

Possible Answers

Selected	Possible Answer
	$\Psi = N \cfrac{e^{- \alpha r}}{r^3}$
	$\Psi = N (1-e^{- \alpha r})$
	$\Psi = Ne^{-ax}\ e^{- B(x^2+y^2+z^2)$
	$\Psi = \Big \{$ $\overset{non-zerocons\ tan\ t}{0}$ $\overset{ifr < R}{ifr. > R}$

Question

A particle is confined within a spherical region of radius one femtometer $(10^{-15}m)$ . Its momentum can be expected to be about

Possible Answers

Selected	Possible Answer
	$20 \cfrac{KeV}{c}$
	$200 \cfrac{KeV}{c}$
	$200 \cfrac{MeV}{c}$
	$2 \cfrac{GeV}{c}$

Question

For the complex function, , which of the following statements is correct?

Possible Answers

Selected	Possible Answer
	z = 0 is a branch point
	z = 0 is a pole of order one
	z = 0 is a removable singularity
	z = 0 is a essential singularity

Question

The solution of the differential equation for y(t) : $\cfrac{d^2 y}{dt^2}$ – y = 2 cosh(t), subject to the initial conditions y(0) = 0 and $\cfrac{dy}{dt} \bigg|_{t=0}$ = 0, is

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{2}$ cosh(t) + tsinh (t)
	- sinh(t) + t cosh(t)
	t cosh)t)
	t sinh (t)

Question

Given the recurrence relation for the Legendre polynomials
(2n + 1) x P_n (x) = (n+1) $P_{n+1}$ (x) + n $P_{n-1}$ (x)
which of the following integrals has a non-zero value?

Possible Answers

Selected	Possible Answer
	$\overset{+1}{\underset{-1}{\int}}$ $X {}^2P_n (X) P_{N+1}\ (X)dx$
	$\overset{+1}{\underset{-1}{\int}}$ $X {}^2P_n (X) P_{N+2}\ (X)dx$
	$\overset{+1}{\underset{-1}{\int}}$
	$\overset{+1}{\underset{-1}{\int}}$ $X {}^2P_n (X) P_{N-2}\ (X)dx$

Question

For a two-dimensional free electron gas, the electronic density n, and the Fermi energy E_F , are related by

Possible Answers

Selected	Possible Answer
	$n = \cfrac{(2mE_F)^{3/2}}{3 \pi^2 \hbar^2}$
	$n = \cfrac{mE_F}{\pi \hbar^2}$
	$n = \cfrac{mE_F}{2 \pi \hbar^2}$
	$n = \cfrac{2^{3/2}(mE_F)^{1/2}}{ \pi \hbar}$

Question

Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is

Possible Answers

Selected	Possible Answer
	Always independent of frequency
	Monotonically decreasing with frequency
	Monotonically increasing with frequency
	A non-monotonic function of frequency

Question

The ground state wavefunction of deuteron is in a superposition of s and d states. Which of the following is NOT true as consequence?

Possible Answers

Selected	Possible Answer
	It has a non-zero quadruple moment
	The neutron-proton potential is non-central
	The orbital wavefunction is not spherically symmetric
	The hamiltonian does not conserve the total angular momentum

Question

The first three energy levels of ${}^{228}Th_{90}$ are shown below
4^+

—-—-——- 187 keV
2^+

—-—-—-- 57.5 keV
0^+

—-—-—-——0 keV
The expected spin-parity and energy of the next level are given by

Possible Answers

Selected	Possible Answer
	(6* ; 400 keV)
	(6* ; 300 keV)
	(2* ; 400 keV)
	(4* ; 300 keV)

Question

The quark content of $\sum^+ , K^- , \pi^-$ and p is indicated:

$| \sum^+ \rangle = |\ uus \rangle ;$ $|\ K^- \rangle = | s \overline{u}$ $\rangle ;\ | \pi^- \rangle = |$ $\underlin{u} \ d \rangle ; | p \rangle$ $= | uud \rangle$ .
In the pricess, $\pi^-+p \rightarrow K^- + \sum^+$ , considering strong interactions only, which of the following statements is true?

Possible Answers

Selected	Possible Answer
	The process is allowed because $\Delta S = 0$
	The process is allowed because $\Delta I_3 = 0$
	The process is not allowed because $\Delta S \ne 0$ and $\Delta I_2 \ne 0$
	The process is not allowed because the baryon number is violated

Question

The three principal moments of inertia of a methanol $(CH_3\ OH)$ molecule have the property $I_x = I_y = I\ and\ I_z \ne I$ . The rotational energy eigenvalues are

Possible Answers

Selected	Possible Answer
	$\cfrac{\hbar^2}{2I}\ I(l+I) +$ $\cfrac{\hbar^2 m_1^2}{2} \bigg($ $\cfrac{I}{I_z} - \cfrac{I}{l} \bigg)$
	$\cfrac{\hbar^2}{2I}\ I(l+I)$
	$\cfrac{\hbar^2 m_1^2}{2} \bigg($ $\cfrac{I}{I_z} - \cfrac{I}{l} \bigg)$
	$\cfrac{\hbar^2}{2I}\ I(l-I) +$ $\cfrac{\hbar^2 m_1^2}{2} \bigg($ $\cfrac{I}{I_z} + \cfrac{I}{l} \bigg)$

Question

where $\Psi_0\ and\ \Psi_1$ are the eigenfunctions of the ground state and the first excited state respectively.
The expectation value of the energy is

Possible Answers

Selected	Possible Answer
	$\cfrac{31}{10} \ \hbar \omega$
	$\cfrac{25}{10} \ \hbar \omega$
	$\cfrac{13}{10} \ \hbar \omega$
	$\cfrac{11}{10} \ \hbar \omega$

Question

Match the typical spectra of stable molecules with the corresponding wave-number range

(1)	Electronic spectra	i	$10^6 \cm^{-1}$ and above
(2)	Rotational spectra	ii	$10^5 - 10^6\ cm^{-1}$
(3)	Molecular dissociation	iii	$10^0 - 10^2\ cm^{-1}$

Possible Answers

Selected	Possible Answer
	1 – ii, 2 – i, 3 – iii
	1 – ii, 2 – iii, 3 – i
	1 – iii, 2 – ii, 3 – i
	1 – i, 2 -ii, 3 – iii

Question

Consider the operations P : $\vec r \vec \rightarrow - \vec r$ (parity) and T : t $\rightarrow$ – t (time-reversal). For the electric and magnetic fields $\vec Eand \vec B$ , which of the following set of transformations is correct?

Possible Answers

Selected	Possible Answer
	$P : \vec E \rightarrow - \bar{E}, \vec B$ $\rightarrow \overset{\leftarrow}{B}$ $T ; \vec E \rightarrow$ $\overset{\leftarrow}{E}, \bar B$ $\rightarrow - \bar B$
	$P : \vec E \rightarrow - \bar{E}, \bar B$ $\rightarrow \overset{\leftarrow}{B}$ $T ; \vec E \rightarrow$ $\overset{\leftarrow}{E}, \bar B$ $\rightarrow \bar B$
	$P : \vec E \rightarrow - \bar{E}, \bar B$ $\rightarrow \bar B$ $T ; \vec E \rightarrow$ $\overset{\leftarrow}{E}, \bar B$ $\rightarrow - \bar B$
	$P : \bar E \rightarrow \vec E, \vec B$ $\rightarrow - \overset{\leftarrow}{B}$ $T ; \vec E \rightarrow$ $\overset{\leftarrow}{E}, \bar B$ $\rightarrow \bar B$

Question

Two magnetic dipoles of magnitude m each are placed in a plane as shoen.

The energy of interaction given by

Possible Answers

Selected	Possible Answer
	Zero
	$\cfrac{\mu_0}{4 \pi} \cfrac{m^2}{d^3}$
	$\cfrac{3 \mu_0}{2 \pi} \cfrac{m^2}{d^3}$
	$\cfrac{3 \mu_0}{8 \pi} \cfrac{m^2}{d^3}$

Question

Consider a conducting loop of radius a and loop resistance R placed in a region with a magnetic field B thereby enclosing a flux $\Phi_0$ . The loop is connected to an electronic circuit as shown, the capacitor being initially uncharged.

If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage $V_{out}$ is independent of

Possible Answers

Selected	Possible Answer
	$\Phi_0$
	U
	R
	C

Question

The figure shows a constant current source charging a capacitor that is initially uncharged.

If the switch is closed at t = 0, which of the following plots depicts correctly the output voltage of the circuit as a function of time?

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Selected	Possible Answer

Question

For any set of inputs, A and B, the following circuits give the same output, Q, except one. Which one is it?

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Selected	Possible Answer

Question

molecule has the first few energy levels uniformly separated by approximately 2.5 me V. At a temperature of 300 K, the ratio of the number of molecules in the $4^{th}$ excited to the number in the $2^{nd}$ excited state is about

Possible Answers

Selected	Possible Answer
	0.5
	0.6
	0.8
	0.9

Question

Which among the following sets of Maxwell relations is correct? (U – internal energy, H – enthalpy, A – Helmholtz free energy and G – Gibbs free energy and G – Gibbs free energy)

Possible Answers

Selected	Possible Answer
	$T = \bigg ($ $\cfrac\partial U}{\partial V}$ $\bigg )_s$ and P = $\bigg ($ $\cfrac{\partial U}{\partial V}$ $\bigg )_v$
	$V = \bigg ($ $\cfrac{\partial H}{\partial P}$ $\bigg )_s$ and T = $\bigg ($ $\cfrac{\partial H}{\partial S}$ $\bigg )_p$
	$P = \bigg ($ $\cfrac{\partial G}{\partial V}$ $\bigg )_T$ and V = $\bigg ($ $\cfrac{\partialG}{\partial P}$ $\bigg )_s$
	$P = \bigg ($ $\cfrac{\partial A}{\partial S}$ $\bigg )_T$ and P = $\bigg ($ $\cfrac{\partial A}{\partial S}$ $\bigg )_v$

Question

For a spin-s particle, in the eigen basis of $\bar S^2 ,\ S_z$ the expectation value $\langle s\ m\ |s_x^2 |s\ m \rangle$ is

Possible Answers

Selected	Possible Answer
	$\cfrac{\hbar^2 \{s(s+1)- m^2 \}}{2}$
	$\hbar^2 \left \{s (s+1) - 2m^2 \right \}$
	$\hbar^2 \left \{s (s+1) - m^2 \right \}$
	$\hbar^2 \ m^2$

Question

A particle is placed in a region with the potential V (x) = $\cfrac{1}{2}\ k\ x^2$ $-\cfrac{\lambda}{3}\ x^3$ . where k, $\lambda > 0$ . then.

Possible Answers

Selected	Possible Answer
	x = 0 and x = $\cfrac{k}{\lambda}$ are points of stable equilibrium
	x = 0 is a points of stable equilibrium and x = $\cfrac{k}{\lambda}$ is a point of unstable equilibrium
	x = 0 and x = $\cfrac{k}{\lambda}$ are points of unstable equilibrium
	There are no points of stable or unstable equilibrium

Question

A $\pi^0$ meson at rest decays into two photons, which move along the x-axis. They are both detected simultaneously after a time, t = 10 s. In an inertial frame moving with a velocity V = 0.6 c in the direction of one of the photons, the time interval between the two detections is

Possible Answers

Selected	Possible Answer
	15 s
	0 s
	10 s
	20 s

Question

A particle of mass m is confined in an infinite potential well:

$V(X) = \ge \bigg \{ \overset{0}{\infty}$ $\overset{ifo<x<L}{otherwise.}$

It is subjected to a perturbing potential V_p(x) = V_0

sin $\bigg (\cfrac{2 \pi x}{L} \bigg )$ within the well. Let $E^{(1)}\ and\ E^{(2)}$ be the corrections to the ground state energy in the first and second order in V_0 , respectively. Which of the following are true?

Possible Answers

Selected	Possible Answer
	$E^{(1)} = 0;$ $E^{(2)} < 0$
	$E^{(1)} > 0;$ $E^{(2)} = 0$
	$E^{(1)} = 0;$ $E^{(2)}$ depends on the sign of
	$E^{(1)} < 0;$ $E^{(2)} < 0$

Question

The number of distinct spectral lines that are observed in the resultant Zeeman spectrum is

Possible Answers

Selected	Possible Answer
	2
	3
	4
	6

Question

The spectral line corresponding to the transition

${}^2P_{y2} \bigg (m_1 = + \cfrac{1}{2}$ $\bigg ) \rightarrow^1\ S_{y2}\ \bigg($ $m_1 = - \cfrac{1}{2} \bigg )$

Is observed along the direction of the applied magnetic field. The emitted electromagnetic field is

Possible Answers

Selected	Possible Answer
	Circularly polarized
	Linearly polarized
	Unpolarized
	Not emitted along the magnetic field directin

Question

Directions for next two questions: The partition function for a gas of photons is given by

$In Z = \cfrac{\pi^2}{45}$ $\cfrac{(k_B\ T)^3}{\hbar^3 C^3}$

The specific heat of the photon gas varies with temperature as
(A) (B) (C) (D)

Possible Answers

Selected	Possible Answer

Question

The pressure of the photon gas is

Possible Answers

Selected	Possible Answer
	$\cfrac{\pi^2}{15}$ $\cfrac{(k_B\ T)^3}{\hbar^3 C^3}$
	$\cfrac{\pi^2}{8}$ $\cfrac{(k_B\ T)^4}{\hbar^3 C^3}$
	$\cfrac{\pi^2}{45}$ $\cfrac{(k_B\ T)^4}{\hbar^3 C^3}$
	$\cfrac{\pi}{45}$ $\cfrac{(k_B\ T)^{3/2}}{\hbar^3 C^3}$

Question

Directions for next two questions: Statement for Linked Answer Questions

For a plane wave of angular frequency $\omega$ and propagation vector $\bar k$ propagating in the medium Maxwell’s equations reduce to

Possible Answers

Selected	Possible Answer

Question

If $\epsilon\ and\ \mu$ assume negative values in a certain frequency range, then the directions of the propagation vector $\overset{\rightharpoonup}{k}$ and the poynting vector $\overset{\rightharpoonup}{S}$ in that frequency range are related as

Possible Answers

Selected	Possible Answer
	$\overset{\rightharpoonup}{k}$ and $\overset{\rightharpoonup}{S}$ are parallel
	$\overset{\rightharpoonup}{k}$ and $\overset{\rightharpoonup}{S}$ are anti – parallel
	$\overset{\rightharpoonup}{k}$ and $\overset{\rightharpoonup}{S}$ are perpendicular to each other
	$\overset{\rightharpoonup}{k}$ and $\overset{\rightharpoonup}{S}$ are make an angler that depends on the magnitude f $\| \epsilon \| \ and\ \| \mu \|$

Question

Directions for next two questions: Statement for Linked Answer Questions

The Lagrangian for a simple pendulum is given by

Possible Answers

Selected	Possible Answer
	$P_\theta = - mgl\ sin\ \theta ;$ $\theta = \cfrac{P_\theta}{ml^2}$
	$P_\theta = mgl\ sin\ \theta ;$ $\theta = \cfrac{P_\theta}{ml^2}$
	$P_\theta = - m \theta ;$ $\theta = \cfrac{P_\theta}{m}$
	$P_\theta = - \cfrac{\delta}{l}\ \theta ;$ $\theta = \cfrac{P_\theta}{ml}$

Question

The poisson bracket between $\theta\ and\ \theta$ is

Possible Answers

Selected	Possible Answer
	$\{ \theta ,\ \theta \} = 1$
	$\{ \theta ,\ \theta \} = \cfrac{1}{ml^2}$
	$\{ \theta ,\ \theta \} = \cfrac{1}{m}$
	$\{ \theta ,\ \theta \} = \cfrac{\delta}{l}$

Question

Choose the most appropriate word from the options given below to complete the following sentence His rather casual remarks on politics —-—-—-—-—-—-—-- his lack of seriousness about the subject.

Possible Answers

Selected	Possible Answer
	masked
	belied
	betrayed
	suppressed

Question

Which of the following options is the closest in meaning to the word below:

Circuitous

Possible Answers

Selected	Possible Answer
	cyclic
	indirect
	confusing
	crooked

Question

Choose the most appropriate word from the options given below to complete the following sentence:
If we manage to —-—-- our natural resources, we would leave a better planet for our children.

Possible Answers

Selected	Possible Answer
	uphold
	restrain
	conserve
	conserve

Question

25 persons are in a room. 15 of them play hockey,17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is:

Possible Answers

Selected	Possible Answer
	2
	17
	13
	3

Question

The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair.

Unemployed : Worker

Possible Answers

Selected	Possible Answer
	fallow : land
	unaware : sleeper
	wit : jester
	renovated : house

Question

If 137 + 276 = 435 how much is 731 + 672?

Possible Answers

Selected	Possible Answer
	534
	1403
	1623
	1513

Question

Hari (H); Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ January. The age difference between any two successive siblings (that is born one after another is less than 3 years. Given the following facts:

i. Hari’s age + Gita’s age + Irfan’s age + Saira’s age.
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are no twins.

In what order were they born (oldest first)?

Possible Answers

Selected	Possible Answer
	HSIG
	SGHI
	IGSH
	IHSG

Question

Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.

Which of the following statements best sums up the meaning of the above passage:

Possible Answers

Selected	Possible Answer
	Modern warfare has resulted in civil strife.
	Chemical agents are useful in modern warfare.
	Use of chemical agents in warfare would be undesirable.
	People in military establishments like to use chemical agents in war.

Question

5skilled workers can build a wall kin 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

Possible Answers

Selected	Possible Answer
	20 days
	18 days
	15 days
	15 days

Question

Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?

Possible Answers

Selected	Possible Answer
	50
	51
	52
	54

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