JEE Questions

The negation of the statement If I become a teacher, then I will open a school is

• Mathematical Reasoning

The negation of the statement "If I become a teacher, then I will open a school" is

1. I will not become a teacher or I will open a school
2. Either I will not become a teacher or I will not open a school
3. Neither I will become a teacher nor I will open a school
4. I will become a teacher and I will not open a school

(ΔH – ΔU) for the formation of carbon monoxide (CO)

• Chemical Thermodynamics

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

1. 1238.78 J/mol
2. 2477.57 J/mol
3. –2477.57 J/mol
4. –1238.78 J/mol

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible string

• Laws of Motion

Two masses m₁ = 5 kg and m₂ = 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 m₂ to stop the motion is

1. 23.3 kg
2. 43.3 kg
3. 10.3 kg
4. 18.3 kg

Three concentric metal shells A, B and C of respective radii a, b and c

• Electrostatics

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

• Magnetism

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 :

1. r_e < r_p = r_α
2. r_e < r_p < r_α
3. r_e < r_α < r_p
4. r_e > r_p = r_α

The density of a material in the shape of a cube is determined

• Measurement

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:

1. 3.5%
2. 4.5%
3. 6%
4. 2.5%

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

• Electronic Devices

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

1. 15 mA
2. 11.5 mA
3. 13.5 mA
4. 0

An electron from various excited states of hydrogen atom emit radiation

• Matter & Atoms

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°

• Optics

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.)

1. 50 µm
2. 75 µm
3. 100 µm
4. 25 µm

In a common emitter amplifier circuit using an n-p-n transistor

• Electronic Devices

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

1. 180°
2. 45°
3. 90°
4. 135°

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn

• Statistics
• Probability

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:

1. 12/5
2. 6
3. 4
4. 6/25

If two different numbers are taken from the set

• Probability

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

1. 6/55
2. 12/55
3. 14/45
4. 7/55

The eccentricity of an ellipse whose centre is at the origin is ½

• Coordinate Geometry

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

1. 2y - x = 2
2. 4x - 2y = 1
3. 4x + 2y = 7
4. x + 2y = 4

For any three positive real numbers a, b and c

• Sequences Series

For any three positive real numbers a, b and c, 9(25a² + b²) + 25(c² – 3ac) = 15b(3a + c). Then

1. b, c and a are in G.P.
2. b, c and a are in A.P.
3. a, b and c are in A.P.
4. a, b and c are in G.P.

If A, then adj (3A^2 + 12A) is equal to

• Matrices Determinants

If  then adj (3A² + 12A) is equal to

Let a vertical tower AB have its end A on the level ground

• Trigonometry

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

1. 6/7
2. 1/4
3. 2/9
4. 4/9

If (2 + sin x) dy/dx + (y + 1)cos x = 0 and y(0) = 1

• Differential Equation

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

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

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0

• 3D Geometry

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:

1. 3√5
2. 2√42
3. √42
4. 6√5

The area (in sq. units) of the region

• Integration

The area (in sq. units) of the region {(x, y) : x ≥ 0, x + y ≤ 3, x² ≤ 4y and y ≤ 1 + √x } is

1. 59/12
2. 3/2
3. 7/3
4. 5/2

Let k be an integer such that the triangle with vertices (k, –3k), (5, k) and (–k, 2)

• Matrices Determinants
• Coordinate Geometry

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

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

For three events A, B and C, P(Exactly one of A or B occurs)

• Probability

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

1. 7/32
2. 7/16
3. 7/64
4. 3/16

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

• Trigonometry

If 5(tan² x – cos²x) = 2 cos 2x + 9, then the value of cos 4x is

1. -3/5
2. 1/3
3. 2/9
4. -7/9

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

• Mathematical Reasoning

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

1. a tautology
2. equivalent to ~p → q
3. equivalent to p → ~q
4. a fallacy

If S is the set of distinct values of 'b' for which

• Matrices Determinants
• Sets

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:

1. an empty set
2. an infinite set
3. a finite set containing two or more elements
4. a singleton

Bakelite is obtained from phenol by reaction with

• Polymers
• Organic Oxygen

Bakelite is obtained from phenol by reaction with

1. CH₃CHO
2. HCHO
3. CH₃COCH₃
4. (CH2OH)₂

Which of the following is fully fluorinated polymer

• Polymers

Which of the following is fully fluorinated polymer?

1. PVC
2. Teflon
3. Neoprene
4. Thiokol

The decreasing order of nucleophilicity among the nucleophiles is

• Basic Organic

The decreasing order of nucleophilicity among the nucleophiles is

1. 3, 2, 1, 4
2. 4, 3, 2, 1
3. 2, 3, 1, 4
4. 1, 2, 3, 4

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

• Basic Organic

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

1. anions
2. chemically inactive
3. chemically reactive
4. cations

Which is the correct order of decreasing SN2 reactivity

• Organic Halogens
• Basic Organic

Which of the following is the correct order of decreasing S_N² reactivity? (X is a halogen)

1. RCH₂X > R₂CHX > R₃CX
2. R₃CX > R₂CHX > RCH₂X
3. R₂CHX > R₃CX > RCH₂X
4. RCHX > R₃CX > R₂CHX

For which parameters the structural isomers C2H5OH and CH3OCH3

• Basic Organic
• Organic Oxygen

For which of the following parameters the structural isomers C₂H₅OH and CH₃OCH₃ would be expected to have the same values? (Assume ideal behavior)

1. Boiling points
2. Vapor pressure at the same temperature
3. Gaseous densities at the same temperature and pressure
4. Heat of vaporization

The coordination number and the oxidation state of the element E

• Coordination Compounds

The coordination number and the oxidation state of the element E in the complex [E(en)₂(C₂O₄)]NO₂ (where (en) is ethylene diamine) are, respectively

1. 6 and 3
2. 4 and 2
3. 4 and 3
4. 6 and 2

Which facts about the complex [Cr(NH3)6]Cl3 is wrong

• Coordination Compounds

Which of the following facts about the complex [Cr(NH₃)₆]Cl₃ is wrong?

1. The complex is paramagnetic.
2. The complex gives white precipitate with silver nitrate solution.
3. The complex is an outer orbital complex.
4. The complex involves d²sp³ hybridisation and is octahedral in shape.

The coordination number of a central metal atom in a complex

• Coordination Compounds

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

1. the number of only anionic ligands bonded to the metal ion
2. the number of ligands around a metal ion bonded by sigma and pi ­bonds both
3. the number of ligands around a metal ion bonded by pi­ bonds
4. the number of ligands around a metal ion bonded by sigma bonds

The value of the ‘spin only’ magnetic moment is 2.84 BM

• Coordination Compounds

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

1. d⁵ (in strong ligand field)
2. d³ (in weak as well as in strong fields)
3. d⁴ (in weak ligand field)
4. d⁴ (in strong ligand field)

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

• Coordination Compounds

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

1. Optical
2. Ionisation
3. Linkage
4. Polymerisation

In the coordination compound, K4[Ni(CN)4], the oxidation state of nickel is

• Coordination Compounds

In the coordination compound, K₄[Ni(CN)₄], the oxidation state of nickel is

1. 0
2. –1
3. +1
4. +2

Which has largest number of isomers

• Coordination Compounds

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

1. [Co(en)₂Cl₂]⁺
2. [Co(NH₃)₅Cl]²⁺
3. [Ir(PR₃)₂H(CO)]²⁺
4. [Ru(NH₃)₄Cl₂]⁺

Larger number of oxidation states are exhibited by the actinoids

• df-Block

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

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

The lanthanide contraction is responsible for the fact that

• df-Block

The lanthanide contraction is responsible for the fact that

1. Zr and Hf have about the same radius
2. Zr and Y have about the same radius
3. Zr and Zn have the same oxidation state
4. Zr and Nb have similar oxidation state

A reduction in atomic size with increase in atomic number

• df-Block

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

1. radioactive series
2. d ­block
3. high atomic masses
4. f ­block

The number of d ­electrons retained in Fe2+ ions is

• df-Block

The number of d ­electrons retained in Fe²⁺ (At. no. Fe = 26) ions is

1. 3
2. 4
3. 5
4. 6

A metal M readily forms its sulphate MSO4 which is water-soluble

• s-Block

A metal M readily forms its sulphate MSO₄ 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

1. Mg
2. Be
3. Ba
4. Ca

One mole of magnesium nitride on the reaction

• s-Block

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

1. one mole of ammonia
2. two moles of nitric acid
3. one mole of nitric acid
4. two moles of ammonia

During the process of electrolytic refining of copper

• Isolation Metals

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

1. Ag and Au
2. Sn and Ag
3. Fe and Ni
4. Pb and Zn

Which presents the correct sequence of the increasing basic nature

• Periodic Properties

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

1. MgO < K₂O < Al₂O₃ < Na₂O
2. K₂O < Na₂O < Al₂O₃ < MgO
3. Na₂O < K₂O < MgO < Al₂O₃
4. Al₂O₃ < MgO < Na₂O < K₂O

According to the periodic law of elements, the variation in properties

• Periodic Properties

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

1. atomic masses
2. atomic numbers
3. nuclear masses
4. nuclear neutron­-proton number ratios

The set representing the correct order of ionic radius is

• Periodic Properties

The set representing the correct order of ionic radius is

1. Li⁺ > Na⁺ > Mg²⁺ > Be²⁺
2. Na⁺ > Li⁺ > Mg²⁺ > Be²⁺
3. Li⁺ > Be²⁺ > Na⁺ > Mg²⁺
4. Mg²⁺ > Be²⁺ > Li⁺ > Na⁺

Which characteristics is not correct for physical adsorption

• Surface Chemistry

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

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

3 g of activated charcoal was added to 50 mL of acetic acid solution

• Surface Chemistry

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:

1. 54 mg
2. 42 mg
3. 36 mg
4. 18 mg

Which statement is incorrect regarding physissorptions

• Surface Chemistry

Which of the following statement is incorrect regarding physissorptions?

1. It occurs because of van der Waal's forces.
2. More easily liquiefiable gases are adsorbed readily.
3. Enthalpy of adsorption (ΔH_adsorption) is low and positive.
4. Under high pressure it results into multi molecular layer on adsorbent surface.