(ΔH – ΔU) for the formation of carbon monoxide (CO) from its elements at 298 K is (R = 8.314 JK^{–1} mol^{–1})

- 1238.78 J/mol
- 2477.57 J/mol
- –2477.57 J/mol
- –1238.78 J/mol

Two masses m_{1} = 5 kg and m_{2} = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure.

The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m_{2} to stop the motion is

- 23.3 kg
- 43.3 kg
- 10.3 kg
- 18.3 kg

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities +σ, -σ and +σ respectively. The potential of shell B is

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii r_{e}, r_{p}, r_{α} respectively in a uniform magnetic field B. The relation between r_{e}, r_{p}, r_{α} is :

- r
_{e}< r_{p}= r_{α} - r
_{e}< r_{p}< r_{α} - r
_{e}< r_{α}< r_{p} - r
_{e}> r_{p}= r_{α}

**The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:**

- 3.5%
- 4.5%
- 6%
- 2.5%

**The reading of the ammeter for a silicon diode in the given circuit is:**

- 15 mA
- 11.5 mA
- 13.5 mA
- 0

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λ_{n}, λ_{g} be the de Broglie wavelength of the electron in the n^{th} state and the ground state respectively. Let Λ_{n} be the wavelength of the emitted photon in the transition from the n^{th} state to the ground state. For large n, (A, B are constants)

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1 µm. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance ? (i.e. distance between the centres of each slit.)

- 50 µm
- 75 µm
- 100 µm
- 25 µm

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output voltages will be:

- 180°
- 45°
- 90°
- 135°

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is:

- 12/5
- 6
- 4
- 6/25

If two different numbers are taken from the set {0, 1, 2, 3, ..., 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is

- 6/55
- 12/55
- 14/45
- 7/55

The eccentricity of an ellipse whose centre is at the origin is ½. If one of its directrices is x = -4, then the equation of the normal to it at (1, 3/2) is

- 2y - x = 2
- 4x - 2y = 1
- 4x + 2y = 7
- x + 2y = 4

For any three positive real numbers a, b and c, 9(25a^{2} + b^{2}) + 25(c^{2} – 3ac) = 15b(3a + c). Then

- b, c and a are in G.P.
- b, c and a are in A.P.
- a, b and c are in A.P.
- a, b and c are in G.P.

Let a vertical tower AB have its end A on the level ground. Let C be the midpoint of AB and P be a point on the ground such that AP = 2AB. If ∠BPC = β, then tan β is equal to:

- 6/7
- 1/4
- 2/9
- 4/9

If (2 + sin x) dy/dx + (y + 1)cos x = 0 and y(0) = 1, then y(π/2) is equal to

- 1/3
- -2/3
- -1/3
- 4/3

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, x/1 = y/4 = z/5 is Q, then PQ is equal to:

- 3√5
- 2√42
- √42
- 6√5

The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x^{2} ≤ 4y and y ≤ 1 + √x } is

- 59/12
- 3/2
- 7/3
- 5/2

Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point

- 2, -1/2
- 1, 3/4
- 1, -3/4
- 2, 1/2

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = 1/4 and P(All the three events occur simultaneously) = 1/16. Then the probability that at least one of the events occurs, is

- 7/32
- 7/16
- 7/64
- 3/16

If 5(tan^{2} x – cos^{2}x) = 2 cos 2x + 9, then the value of cos 4x is

- -3/5
- 1/3
- 2/9
- -7/9

The following statement (p → q) → [(~p→q)→q] is:

- a tautology
- equivalent to ~p → q
- equivalent to p → ~q
- a fallacy

If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1

x + ay + z = 1

ax + by + z = 0

has no solution, then S is:

- an empty set
- an infinite set
- a finite set containing two or more elements
- a singleton

Bakelite is obtained from phenol by reaction with

- CH
_{3}CHO - HCHO
- CH
_{3}COCH_{3} - (CH2OH)
_{2}

Which of the following is fully fluorinated polymer?

- PVC
- Teflon
- Neoprene
- Thiokol

The decreasing order of nucleophilicity among the nucleophiles is

- 3, 2, 1, 4
- 4, 3, 2, 1
- 2, 3, 1, 4
- 1, 2, 3, 4

Due to the presence of an unpaired electron, free radicals are

- anions
- chemically inactive
- chemically reactive
- cations

Which of the following is the correct order of decreasing S_{N}^{2} reactivity? (X is a halogen)

- RCH
_{2}X > R_{2}CHX > R_{3}CX - R
_{3}CX > R_{2}CHX > RCH_{2}X - R
_{2}CHX > R_{3}CX > RCH_{2}X - RCHX > R
_{3}CX > R_{2}CHX

For which of the following parameters the structural isomers C_{2}H_{5}OH and CH_{3}OCH_{3} would be expected to have the same values? (Assume ideal behavior)

- Boiling points
- Vapor pressure at the same temperature
- Gaseous densities at the same temperature and pressure
- Heat of vaporization

The coordination number and the oxidation state of the element E in the complex [E(en)_{2}(C_{2}O_{4})]NO_{2} (where (en) is ethylene diamine) are, respectively

- 6 and 3
- 4 and 2
- 4 and 3
- 6 and 2

Which of the following facts about the complex [Cr(NH_{3})_{6}]Cl_{3} is wrong?

- The complex is paramagnetic.
- The complex gives white precipitate with silver nitrate solution.
- The complex is an outer orbital complex.
- The complex involves d
^{2}sp^{3}hybridisation and is octahedral in shape.

The coordination number of a central metal atom in a complex is determined by

- the number of only anionic ligands bonded to the metal ion
- the number of ligands around a metal ion bonded by sigma and pi bonds both
- the number of ligands around a metal ion bonded by pi bonds
- the number of ligands around a metal ion bonded by sigma bonds

The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is

- d
^{5}(in strong ligand field) - d
^{3}(in weak as well as in strong fields) - d
^{4}(in weak ligand field) - d
^{4}(in strong ligand field)

The type of isomerism present in nitropentamine chromium (III) chloride is

- Optical
- Ionisation
- Linkage
- Polymerisation

In the coordination compound, K_{4}[Ni(CN)_{4}], the oxidation state of nickel is

- 0
- –1
- +1
- +2

Which one of the following has largest number of isomers? (R = alkyl group, en = ethylenediamine)

- [Co(en)
_{2}Cl_{2}]^{+} - [Co(NH
_{3})_{5}Cl]^{2+} - [Ir(PR
_{3})_{2}H(CO)]^{2+} - [Ru(NH
_{3})_{4}Cl_{2}]^{+}

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

- Lesser energy difference between 5f and 6d than between 4f and 5d orbitals
- More energy difference between 5f and 6d than between 4f and 5d orbitals
- More reactive nature of the actinoids than the lanthanoids
- 4f orbitals more diffused than the 5f orbitals

The lanthanide contraction is responsible for the fact that

- Zr and Hf have about the same radius
- Zr and Y have about the same radius
- Zr and Zn have the same oxidation state
- Zr and Nb have similar oxidation state

A reduction in atomic size with increase in atomic number is a characteristic of elements of

- radioactive series
- d block
- high atomic masses
- f block

The number of d electrons retained in Fe^{2+} (At. no. Fe = 26) ions is

- 3
- 4
- 5
- 6

A metal M readily forms its sulphate MSO_{4} which is water-soluble. It forms its oxide MO which becomes inert on heating. It forms an insoluble hydroxide M(OH)_{2} which is soluble in NaOH solution. Then M is

- Mg
- Be
- Ba
- Ca

One mole of magnesium nitride on the reaction with an excess of water gives

- one mole of ammonia
- two moles of nitric acid
- one mole of nitric acid
- two moles of ammonia

During the process of electrolytic refining of copper, some metals present as impurity settle as 'anode mud'. These are

- Ag and Au
- Sn and Ag
- Fe and Ni
- Pb and Zn

Which one of the following orders presents the correct sequence of the increasing basic nature of the given oxides?

- MgO < K
_{2}O < Al_{2}O_{3}< Na_{2}O - K
_{2}O < Na_{2}O < Al_{2}O_{3}< MgO - Na
_{2}O < K_{2}O < MgO < Al_{2}O_{3} - Al
_{2}O_{3}< MgO < Na_{2}O < K_{2}O

According to the periodic law of elements, the variation in properties of elements is related to their

- atomic masses
- atomic numbers
- nuclear masses
- nuclear neutron-proton number ratios

The set representing the correct order of ionic radius is

- Li
^{+}> Na^{+}> Mg^{2+}> Be^{2+} - Na
^{+}> Li^{+}> Mg^{2+}> Be^{2+} - Li
^{+}> Be^{2+}> Na^{+}> Mg^{2+} - Mg
^{2+}> Be^{2+}> Li^{+}> Na^{+}

Which one of the following characteristics is not correct for physical adsorption?

- Both enthalpy and entropy of adsorption are negative.
- Adsorption is spontaneous.
- Adsorption increases with increase in temperature.
- Adsorption on solids is reversible.

3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06 N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is:

- 54 mg
- 42 mg
- 36 mg
- 18 mg

Which of the following statement is incorrect regarding physissorptions?

- It occurs because of van der Waal's forces.
- More easily liquiefiable gases are adsorbed readily.
- Enthalpy of adsorption (ΔH
_{adsorption}) is low and positive. - Under high pressure it results into multi molecular layer on adsorbent surface.

In Langmuir’s mode of adsorption of a gas on a solid surface

- the adsorption at a single site on the surface may involve multiple molecules at the same time.
- the mass of gas striking a given area of surface is independent of the pressure of the gas.
- the mass of gas striking a given area of surface is proportional to the pressure of the gas.
- the rate of dissociation of adsorbed molecules from the surface does not depend on the surface covered.

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