JEE Main 2023 6 April Shift 2 Question Paper with Solution PDF- Download Here

If the coefficient of x⁷ in (\(ax^2 +\frac{ 1}{2bx}^{11}\)) and x^-7 in (\(ax - \frac{1}{3bx^2}^{11}\)), are euual then

• (1) 32ab=729
• (2) 64ab=243
• (3) 243ab=64
• (4) 729ab=32

The area enclosed by \(y = |x-1| + |x-2|\) and \(y = 3\)

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is:

• (1) 580
• (2) 578
• (3) 576
• (4) 582

If \(a ≠ ±b\) and are purely real, z ϵ complex number, \(Re(az^{2}+bz)=a\) and \(Re(bz^{2}+az)=b\) then number of value of z possible is

• (1) 0
• (2) 1
• (3) 2
• (4) 3

Let \(P\) be a square matrix such that \(P^2 = I - P\). For \(\alpha, \beta, \gamma, \delta \in \mathbb{N}\), if \(P^\alpha + P^\beta = \gamma I - 29P\) and \(P^\alpha - P^\beta = \delta I - 13P\), then \(\alpha + \beta + \gamma - \delta\) is equal to:

• (1) 40
• (2) 24
• (3) 22
• (4) 18

Among the statements:

• (1) only (S₁) is correct
   
• (2) both (S₁) and (S₂) are correct
• (3) only (S₂) is correct
• (4) both (S₁) and (S₂) are incorrect

If the solution curve f(x, y) = 0 of the differential equation (1+log_e x) \(\frac{dx}{dy} \)- x log_e x = e^y , x > 0, passes through the points (1,0) and (α, 2) then α^a is equal to

• (1) \(e^{e^{2}}\)
• (2) \(e^{\sqrt2e^{2}}\)
• (3) \(e^{2e^{\sqrt2}}\)
• (4) \(e^{2e^{2}}\)

If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?

• (1) π²
• (2) \(\frac{\pi_2}{4}\)
• (3) 2π²
• (4) \(\frac{\pi_2}{8}\)

\(lim _{n→∞}{(2^½-2^½)(2^½-2^½)….(2^½-^2{\frac{1}{2n+1}})}\) is equal to

• (1) 1
• (2) 0
• (3) \(\frac{1}{\sqrt2}\)
• (4) \(\sqrt2\)

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is a and the number of persons who speak only Hindi is b, then the eccentricity of the ellipse 25(β2 x² + α² y2) = α² β² is

• (1) \(\frac{117}{12}\)
• (2) \(\frac{119}{12}\)
• (3) \(\frac{129}{12}\)
• (4) \(3\frac{15}{12}\)

Three dice are rolled. If the probability of getting different numbers on the three dice is \(\frac{p}{q}\), where \(p\) and \(q\) are co-prime, then \(q - p\) is equal to:

• (1) 1
• (2) 2
• (3) 4
• (4) 3

For the system of equations
\(x+y+z=6\)
\(x+2y+\alpha z=10\)
\(x+3y+5z=\beta\),
which one of the following is NOT true?

• (1) System has a unique solution for \(\alpha=3,\ \beta\neq 14\).
• (2) System has infinitely many solutions for \(\alpha=3,\ \beta=14\).
• (3) System has no solution for \(\alpha=3,\ \beta=24\).
• (4) System has a unique solution for \(\alpha=-3,\ \beta=14\).

Let the sets A and B denote the domain and range respectively of the function \(f(x)=\frac{1}{\sqrt[x]-x}\) where [x] denotes the smallest integer greater than or equal to x . Then among the statements 
(S1) : A ∩ B = (1, ∞) – N and  
(S2) : A ∪ B = (1, ∞) 

• (1) (1) only (S1) is true
• (2) both (S1) and (S2) are true 
• (3) neither (S1) nor (S2) is true
• (4) only (S2) is true

A plane P contains the line of intersection of the plane  \(\overrightarrow{r} .( \^i+\^j+\^k )=6\) and \(\overrightarrow{r }.( 2\^i+3\^j+4\^k) = − 5\).  If P passes through the point (0, 2, –2), then the square of distance of the point (12, 12, 18) from the plane P is 

• (1) 155
• (2) 310
• (3) 620
• (4) 1240

If gcd \( (m, n) = 1 \) and \[ 1^2 - 2^2 + 3^2 - 4^2 + \cdots + (2022)^2 - (2023)^2 = 1012 \, m^2 n \] then \( m^2 - n^2 \) is equal to:

• (1) 240
• (2) 180
• (3) 220
• (4) 200

Let the vectors \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) represent three coterminous edges of a parallelepiped of volume \(V\). Then the volume of the parallelepiped, whose coterminous edges are represented by \(\mathbf{a} + \mathbf{b} + \mathbf{c}\) and \(\mathbf{a} + 2\mathbf{b} + 3\mathbf{c}\), is equal to:

• (1) V
• (2) 2 V
• (3) 3 V
• (4) 6 V

If the tangents at the points P and Q on the circle x² + y² – 2x + y = 5 meet at the point R  \(( \frac{9}{4},2 ) \)then the area of the triangle PQR is 

• (1) \(\frac{13}{8}\)
• (2) \(\frac{13}{4}\)
• (3) \(\frac{5}{8}\)
• (4) \(\frac{5}{4}\)

Among the statements
(S1) : \((p\Rightarrow q)\vee((\sim p)\wedge q)\) is a tautology
(S2) : \((q\Rightarrow p)\Rightarrow((\sim p)\wedge q)\) is a contradiction

• (1) neither (S1) and (S2) is True
• (2) only (S2) is True
• (3) both (S1) and (S2) are True
• (4) only (S1) is True

Let the line L pass through the point (0, 1, 2), intersect the line  \(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) and be parallel to the plane 2x + y – 3z = 4. Then the distance of the point P(l, –9, 2) from the line L is 

• (1) \(\sqrt54\)
• (2) \(\sqrt69\)
• (3) \(\sqrt74\)
• (4) 9

• (1) -2
• (2) 2
• (3) 6
• (4) 4

Let the eccentricity of an ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), is reciprocal to that of the hyperbola 2x²-2y²=1. if the ellipse intersects the hyperbola at right angles, then square of length of the latus-rectum of the ellipse is___.

Find all the four letter words with two vowels and 2 consonants from the word UNIVERSE?

The value of tan 9°-tan27°-tan63°+tan81° is____.

For α, β, z ∈ C and λ > 1, if \(\sqrt{λ - 1}\) is the radius of the circle |z - α|² + |z - β|² = 2λ, then |α - β| is equal to _____.

If the lines \(\frac{x−1}{2}=\frac{2−y }{−3} =\frac{ z−3 }{α}\)  and \( \frac{x−4 }{5} =\frac{y−1}{ 2}= \frac{z}{ β}\) intersect, then the magnitude of the minimum value of 8αβ is ___.

The number of points, where the curve y = x⁵ – 20x³ + 50x + 2 crosses the x-axis, is _____.

Let a curve y = f(x), x ∈ (0, ∞) pass through the points  \(p ( 1\frac{3 }{2} )\) and  Q \( ( a,\frac{1 }{2} )\). If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S (0, c) such that bc = 3, then (PQ)² is equal to ______.

Let \(f(x) = \frac{x}{(1 + x^n)^{1/n}},\ x \in \mathbb{R} - \{-1\},\ n \in \mathbb{N},\ n > 2\).
If \(f^n(x) = (f \circ f \circ f \circ \ldots\) upto \(n\) times\()(x)\), then \(\lim_{n \to \infty} \int_0^1 x^{n-2}\left(f^n(x)\right)dx\) is equal to ___________.

A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s\(^2\). The time taken by the particle to reach the velocity of 60.0 m/s is

• (1) 25 S
• (2) 20 S
• (3) 30 S
• (4) 15 S

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R  
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.  
Reason R: The wavelengths of waves are different in different media.  
In the light of the above statements, choose the most appropriate answer from the options given below 

• (1) Both A and R are correct and R is the correct explanation of A
• (2) Both A and R are correct but R is NOT the correct explanation of A
• (3) A is correct but R is not correct
• (4) A is not correct but R is correct

The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200K is v0. Then, r.m.s. speed of the gas at 800 K will be

• (1) \(\frac{v_o}{4}\)
• (2) \(2v_0\)
• (3) \(v_0\)
• (4) \(4v_0\)

The energy associated with electric field is E and with magnetic field is B for an electromagnetic wave in free space is given by( \(∈_0\)-permittivity of free space \(μ_0\)-permeability of free space) 

• (1) \(U_E=\frac{E^2}{2∈_0},U_B=\frac{μ_0B^2}{2}\)
• (2) \(U_E=\frac{∈E^2}{2},U_B=\frac{μ_0B^2}{2}\)
• (3) \(U_E=\frac{E^2}{2∈_0},U_B=\frac{B^2}{2μ_0}\)
• (4) \(U_E=\frac{∈_0E^2}{2},U_B=\frac{B^2}{2μ_0}\)

A 2 meter long scale with least count of 0.2 cm is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at 80 cm mark and lm mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at 180 cm mark. The % error in the estimation of focal length is

• (1) 0.51
• (2) 0.85
• (3) 1.02
• (4) 1.70

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R  
Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. 
Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.
In the light of the above statements, choose the most appropriate answer from the options given below:

• (1) Both A and R are correct and R is the correct explanation of A
• (2) Both A and R are correct but R is NOT the correct explanation of A
• (3) A is not correct but R is correct
• (4) A is correct but R is not correct

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.  
Assertion A: Diffusion current in a p-n junction is greater than the drift current in magnitude if the junction is forward biased.  
Reason R: Diffusion current in a p-n junction is from the n-side to the p-side if the junction is forward biased.  
In the light of the above statements, choose the most appropriate answer from the options given below

• (1) Both A and R are correct and R is the correct explanation of A
• (2) Both A and R are correct but R is NOT the correct explanation of A
• (3) A is correct but R is not correct
• (4) A is not correct but R is correct

A capacitor of capacitance 150.0 µF is connected to an alternating source of emf given by E = 36 sin(120πt) V. The maximum value of current in the circuit is approximately equal to

• (1) \(\sqrt{2A}\)
• (2) \(2\sqrt{2A}\)
• (3) \(\frac{1}{\sqrt{2}}A\)
• (4) 2A

Figure shows a part of an electric circuit. The potentials at the points a, b and c are 30V, 12V and 2V respectively. the currents through the 20 resistors will be.

• (1) 0.2 A
• (2) 0.6 A
• (3) 0.4 A
• (4) 1.0 A

As shown in the figure, a particle is moving with constant speed π m/s. Considering its motion from A to B, the magnitude of the average velocity is

• (1) π m/s
• (2) \(\sqrt3\,m/s\)
• (3) \(1.5\sqrt3\,m/s\)
• (4) \(2\sqrt3\,m/s\)

The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

• (1) 1.24
• (2) 1
• (3) 1.5
• (4) 2

The temperature of the body drops from 60°C to 40°C in 7 min. The surrounding temperature is 10°C. The temperature of the body drops from 40°C to T°C in 7 min. Find the value of T

• (1) 16
• (2) 20
• (3) 28
• (4) 30

A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass ‘m’ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ‘l’. If the dipole is placed in a uniform electric field ‘\(\overrightarrow{E}\); such a way that dipole axis makes a very small angle with the electric field, ‘\(\overrightarrow{E}\)'. The angular frequency of the oscillations of the dipole when released is given by.

• (1) \(\sqrt{\frac{4qE}{3ml}}\)
• (2) \(\sqrt{\frac{8qE}{3ml}}\)
• (3) \(\sqrt{\frac{4qE}{ml}}\)
• (4) \(\sqrt{\frac{8qE}{ml}}\)

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

• (1) 4 : 1
• (2) 1 : 2
• (3) 1 : 1
• (4) 1 : 4

A student is provided with a variable voltage source V, a test resistor R_r = 10Ω, two identical galvanometers G₁ and G₂ and two additional resistors, R₁ = 10MΩ and R₂ = 0.001Ω. For conducting an experiment to verify ohms law, the most suitable circuit is

• (1)
• (2)
• (3)
• (4)

• (1) n²
• (2) \(\frac{1}{\sqrt{n}}\)
• (3) \(\sqrt{n}\)
• (4) \(n^\frac{2}{3}\)

A child of mass 5 kg is going round a merry-goround that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

• (1) 40 N
• (2) 50 N
• (3) 80 N
• (4) 100 N

The weight of a body on the surface of the earth is 100 N. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

• (1) 25 N
• (2) 64 N
• (3) 100 N
• (4) 50 N

Choose the incorrect statement from the given statements.

• (1) Planets revolve around the Sun with constant linear speed.
• (2) Energy of the planet in elliptical orbit is constant.
• (3) Satellites in circular motion have constant energy.
• (4) Body falling towards the Earth results in negligible displacement of the Earth.

For an amplitude modulated wave the minimum amplitude is 3V, while the modulation index is 60%. The maximum amplitude of the modulated wave is

• (1) 5 V
• (2) 10 V
• (3) 12 V
• (4) 15 V

Experimentally it is found that 12.8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is\(\frac{ 9}{x} x 10^{-10}\)m. The value of the x is _____.
(1eV = 1.6 x 10^-19J, \(\frac{1}{4π∈_0}\) = 9 x 10⁹ NM² / C² and electronic charge = 1.6 x 10^-19JC)

Two concentric circular coils with radii 1 cm and 1000 cm, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____× 10^-8 H.
(Take, π² = 10)

As shown in the figure, two parallel plate capacitors having equal plate area of 200 cm2 are joined in such a way that a ≠ b. The equivalent capacitance of the combination is x ∈0 F. The value of x is_____.

A body is dropped on ground from a height ‘h₁’ and after hitting the ground, it rebounds to a height ‘h₂’ If the ratio of velocities of the body just before and after hitting ground is \(4\). then percentage loss in kinetic energy of the body is\(\frac{x}{4}\). The value of x is_____.

As shown in the figure, the voltmeter reads 2V across 5Ω resistor. The resistance of the voltmeter is_____Ω.

A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic field of magnitude \(\dfrac{\pi}{2} \times 10^{-3} \text{T}\). The angle between the direction of magnetic field and velocity of proton is 60°. The pitch of the helical path taken by the proton is \_\_\_\ cm.

• (1) 65 cm
• (2) 40 cm
• (3) 50 cm
• (4) 80 cm

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10cm. The maximum tension in the string is found to be \(\frac{x}{40}\) N. The value of x is___.

A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7× 10⁵ Nm^-2 . The value of mass m is ___ kg. (Take, g = 9.8 ms-2 and π =\(\frac{ 22}{7}\))

A solid sphere and a ring have equal masses and equal radius of gyration. If the sphere is rotating about its diameter and ring about an axis passing through and perpendicular to its plane, then the ratio of radius is \(\sqrt{\frac{x}{2} }\) then find the value of x.

A beam of light consisting of two wavelengths 7000 Å and 5500 Å is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is 2.5 mm and the distance between the plane of slits and the screen is 150 cm. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is n × 10^-5 m. The value of n is_____.

Formation of which complex, among the following, is not a confirmatory test of Pb²⁺ ions

• (1) lead sulphate
• (2) lead nitrate
• (3) lead chromate
• (4) lead iodide

Element not present in Nessler’s reagent is

• (1) K
• (2) Hg
• (3) N
• (4) I

Consider the following reaction that goes from A to B in three steps as shown

below Choose the correct option:

• (1)

  Number of intermediates	Number of Activated complexes	Rate determining step
  2	3	II

• (2)

  Number of intermediates	Number of Activated complexes	Rate determining step
  2	3	III

• (3)

  Number of intermediates	Number of Activated complexes	Rate determining step
  3	2	II

• (4)

  Number of intermediates	Number of Activated complexes	Rate determining step
  2	3	I

Find out the major product from the following reaction.

• (1)
• (2)
• (3)
• (4)

• (1) 3\(\pi\)a₀
• (2) 6\(\pi\)a₀
• (3) 9\(\pi\)a₀
• (4) 12\(\pi\)a₀

Which one of the following elements will remain as liquid inside pure boiling water?

• (1) Li
• (2) Ga
• (3) Cs
• (4) Br

Given below are two statements: One is labelled as "Assertion A" and the other is labelled as "Reason R".
Assertion A: In the complex Ni(CO), and Fe(CO)s, the metals have zero oxidation state.
Reason R: Low oxidation states are found when a complex has ligands capable of π-donor character in addition to the o-bonding.
In the light of the above statements, choose the most appropriate answer from the option given below.

• (1) Both A and R are correct and R is the correct explanation of A.
• (2) Both A and R are correct but R is NOT the correct explanation of A
• (3) A is correct but R is not correct
• (4) A is not correct but R is correct

Group-13 elements react with O₂ in amorphous form to form oxides of type M₂O₃ (M = element). Which among the following is the most basic oxide?

• (1) Al₂O₃
• (2) Tl₂O₃
• (3) Ga₂O₃
• (4) B₂O₃

During the reaction of permanganate with thiosulphate, the change in oxidation of manganese occurs by value of 3. Identify which of the below medium will favour the reaction

• (1) aqueous neutral
• (2) aqueous acidic
• (3) both aqueous acidic and neutral
• (4) both aqueous acidic and faintly alkaline

In the following reaction 'B' is

• (1)
• (2)
• (3)
• (4)

IUPAC name of the compound \(K_{3}[Co(C_{2}O_{4})_{3}]\) is

• (1) Potassium trioxalatocobaltate (III)
• (2) Potassium trioxalatocobaltate (III)
• (3) Potassium cobalt tris oxalate (II)
• (4) Potassium oxalato cobaltate (III)

The strongest acid from the following is

• (1)
• (2)
• (3) <
• (4)

• (1) 1-Q; 2-S; 3-P; 4-R
• (2) 1-Q; 2-S; 3-R; 4-P
• (3) 1-S; 2-P; 3-R; 4-Q
• (4) 1-S; 2-P; 3-P; 4-R

From the figure of column chromatography given below, identify incorrect statements

A. Compound 'c' is more polar than 'a' and 'b' 
B. Compound 'a' is least polar
C. Compound 'b' comes out of the column before 'c' and after 'a' 
D. Compound 'a' spends more time in the column 
Choose the correct answer from the options given below

• (1) B, C and D only
• (2) A, B and C only
• (3) B and D only
• (4) A, B and D only

The volume of 0.02 M aqueous HBr required to neutralize 10.0 mL of 0.01 M aqueous Ba(OH)₂ is ____ . (Assume complete neutralization)

• (1) 2.5 mL
• (2) 5.0 mL
• (3) 7.5 mL
• (4) 10.0 mL

The product , which is not obtained during the electrolysis of brine solution is ____ .

• (1) \(cl_2\)
• (2) H₂
• (3) HCl
• (4) N_aOH

Ion having highest hydration enthalpy among the given alkaline earth metal ions is:

• (1) Be⁺²
• (2) Mg⁺²
• (3) Ca⁺² 
• (4) Ba⁺²

In which form does \(BeCl_{2}\) exist in the solid state, vapor state and high temperature?
(1) Polymeric, Dimeric, Monomeric
(2) Dimeric, Polymeric, Monomeric
(3) Monomeric, Dimeric, Polymeric
(4) Polymeric, Monomeric, Dimeric

The group of chemicals used as pesticide is

• (1) Dieldrin, Sodium arsinite, Tetrachloroethene
• (2) Sodium chlorate, DDT, PAN
• (3) DDT, Aldrin
• (4) Aldrin, Sodium chlorate, Sodium arsinite

Given below are two statements :
Statement-I: Morphine is a narcotic analgesis. It helps in relieving pain without producing sleep. 
Statement-II: Morphine and its derivatives are obtained from opium poppy. 
In the light of the above statements, choose the correct answer from the options given below.

• (1) Both Statement I and Statement II are true
• (2) Both Statement I and Statement II are false
• (3) Statement I is true but Statement II is false
• (4) Statement I is false but Statement II is true

The number of species having a square planar shape from the following is __
\(XeF_4, SF_4, SiF_4, BF^-_4 BrF^-_4,[Cu(NH_3)_4]^{2+}, [FeCl_4]^{2-}, [PtCl_4]^{2-}\)

The standard reduction potential at 298 K for the following half cells are given below  
NO − 3 3 − + 4H+ + 3e- → NO(g) +2H2O E0 = 0.97V 
\(V^{2+} (aq) + 2e^-→V\)           E⁰ = -1.19V 
\(Fe^{3+}(aq) + 3e^- → Fe\)        E⁰ = -0.04V 
\(Ag^+ (aq) + e^- → Ag(s)\)      E⁰ = 0.80V 
\(Au^{3+}(aq)+3e^-→Au(s)\) E⁰ = 1.40V 
The number of metal(s) which will be oxidized by  \(N0^-_3\) Oin aqueous solution is______.

Consider the following date
Heat of combustion of H₂(g)           = -241.8 kJ mol^-1 
Heat of combustion of C(s)              = -393.5 kJ mol^-1 
Heat of combustion of C₂H₅OH(1)  = -1234.7 kJ mol^-1
The heat of formation of C₂H₅OH(1) is (-) ____ kJ mol^-1 (Nearest integer)

Number of isomeric aromatic amines with synthesized by Gabriel Phthalimide synthesis molecular formula C₈H₁₁N, which can be is ______. jee main 2023

The equilibrium composition for the reaction PCl₃ + Cl₂ ⇌ PCI5, at 298 K is given below. 
[PCl₃]_eq = 0.2 mol L^-
[Cl₂]eq = 0.1 mol L^-1,
[PCl₅]_eq = 0.40 mol L^-1 
If 0.2 mol of Cl₂ is added at the same temperature, the equilibrium concentrations of PCl5 is ___ × 10^-2 mol L^-1
Given: K_c for the reaction at 298 K is 20

In an ice crystal, each water molecule is hydrogen bonded to ___ neighbouring molecules

Among the following, the number of compounds which will give positive iodoform reaction is ____ .
(a) 1-Phenylbutan-2-one 
(b) 2-Methylbutan-2-ol 
(c) 3-Methylbutan-2-ol 
(d) 1-Phenylethanol 
(e) 3,3-dimethylbutan-2-one 
(f) 1-Phenylpropan-2-ol

Consider the following pairs of solution which will be isotonic at the same temperature. The number of pairs of solutions is/are...... 
A. 1 M aq. NaCl and 2 M aq. Urea 
B. 1 M aq. CaCl₂ and 1.5 M aq. KCl 
C. 1.5 M aq. AlCl₃ and 2 M aq. Na₂SO₄ 
D. 2.5 M aq. KCl and 1 M aq. Al₂(SO₄)₃

The number of colloidal systems from the following, which will have 'liquid' as the dispersion medium, is____.
Gem stones, paints, smoke, cheese, milk, hair cream, insecticide sprays, froth, soap lather.

Number of crystal systems from the following where body centred unit cell can be found, is......
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic.