JEE Main 2022 June 25 Shift 1 Question Paper with Solution PDF- Download Here

The value of \(\int\limits_0^π \frac {e^{cos⁡\ x} sin⁡x}{(1+cos^2⁡x)(e^{cos⁡\ x}+e^{−cos⁡\ x})}dx\) is equal to :

• (1) \(\frac {\pi^2}{4}\)
• (2) \(\frac {\pi^2}{2}\)
• (3) \(\frac {\pi}{4}\)
• (4) \(\frac {\pi}{2}\)

Let \(ƒ : N→R\) be a function such that \(ƒ(x + y) = 2ƒ(x) ƒ(y)\) for natural numbers x and y. If \(ƒ(1) = 2\), then the value of α for which \(\displaystyle\sum_{k=1}^{10} f(α+k)=\frac {512}{3} (2^{20}−1)\) holds, is:

• (1) 2
• (2) 3
• (3) 4
• (4) 6

Let A be a \(3×3\) real matrix such that \(A\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 0  \end{pmatrix}\); \(A\begin{pmatrix}   1 \\0  \\ 1  \end{pmatrix}\)=\(A\begin{pmatrix}   -1 \\0  \\ 1  \end{pmatrix}\) and \(A\begin{pmatrix}   0 \\0  \\ 1  \end{pmatrix}\)=\(\begin{pmatrix}   1 \\1  \\ 2  \end{pmatrix}\)
If \(X = [x_1, x_2, x_3]^T \)and \(I\) is an identity matrix of order \(3\), then the system \([A−2I]X \)= \(\begin{pmatrix}   4 \\1  \\ 1 \end{pmatrix}\) has:

• (1) No solution
• (2) Infinitely many solutions
• (3) Unique solution
• (4) Exactly two solutions

Let \(ƒ : R→R\) be defined as \(ƒ(x) = x^3 + x – 5\) . If g(x) is a function such that \(ƒ(g(x)) = x\), ∀‘x‘∈R. Then \(g^′(63)\) is equal to_____.

• (1) \(\frac {1}{49}\)
• (2) \(\frac {3}{49}\)
• (3) \(\frac {43}{49}\)
• (4) \(\frac {91}{49}\)

If \(\frac {1}{2⋅3^{10}}+\frac {1}{2^2⋅3^9}+⋯+\frac {1}{2^{10}⋅3} = \frac {K}{2^{10}⋅3^{10}}.\) Then the remainder when \(K\) is divided by \(6\) is:

• (1) 1
• (2) 2
• (3) 3
• (4) 5

Let \(ƒ(x)\) be a polynomial function such that \(ƒ(x) + ƒ^′(x) + ƒ^{′′}(x) = x^5 + 64\). Then, the value of \(\lim\limits_{x \to 1}\frac {f(x)}{x−1}\) is equal to :

• (1) -15
• (2) -60
• (3) 60
• (4) 15

Let \(E_1\) and \(E_2\) be two events such that the conditional probabilities \(P(E_1|E_2)=\frac 12\), \(P(E_2|E_1)=\frac 34\) and \(P(E_1∩E_2)=\frac 18\)⋅ Then:

• (1) \(P(E_1∩E_2)=P(E_1)⋅P(E_2)\)
• (2) \(P(E'_1∩E'_2)=P(E'_1)⋅P(E'_2)\)
• (3) \(P(E_1∩E'_2)=P(E_1)⋅P(E_2)\)
• (4) \(P(E'_1∩E_2)=P(E_1)⋅P(E_2)\)

Let \(A = \begin{bmatrix} 0 & -2 \\[0.3em] 2 & 0 \end{bmatrix}\). If \(M\) and \(N\) are two matrices given by \(M = \displaystyle\sum_{k=1}^{10} A^{2k}\) and \(N = \displaystyle\sum_{k=1}^{10} A^{2k-1}\)
then \(MN^2 \) is :

• (1) a non-identity symmetric matrix
• (2) a skew-symmetric matrix
• (3) neither symmetric nor skew-symmetric matrix
• (4) an identity matrix

Let \(g : (0, ∞) →R\) be a differentiable function such that \(∫(\frac {x(cos⁡x−sin⁡x)}{e^x+1} + \frac {g(x)(e^x+1−xe^x)}{(e^x+1)2})dx = \frac {xg(x)}{e^x+1}+c,\) for all \(x>0\), where c is an arbitrary constant. Then:

• (1) g is decreasing in \((0, \frac \pi4)\)
• (2) g′ is increasing in \((0, \frac \pi4)\)
• (3) g+g′ is increasing in \((0, \frac \pi2)\)
• (4) g-g' is increasing in \((0, \frac \pi2)\)

Let \(f :R→R\) and \(g : R→R\) be two functions defined by \(f(x) = log_e(x^2 + 1) – e^{–x} + 1\) and \(g(x)=\frac {1−2e^{2x}}{e^x}\). Then, for which of the following range of α, the inequality \(f(g((\frac {α−1)^2}{3}))>f(g(α−\frac 53))\) holds?

• (1) (2, 3)
• (2) (–2, –1)
• (3) (1, 2)
• (4) (–1, 1)

Let \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\), \(a_i>0,\ i=1, 2, 3\) be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of \(\vec a\) on the vector \(3\hat i+4\hat j\) be 7. Let \(\vec b\) be a vector obtained by rotating \(\vec a\) with 90°. If \(\vec a,\vec b\) and x-axis are co-planar, then projection of a vector \(\vec b\) on \(3\hat i+4\hat j\) is equal to :

• (1) \(\sqrt 7\)
• (2) \(\sqrt 2\)
• (3) \(2\)
• (4) \(7\)

Let \(y = y(x)\) be the solution of the differential equation \((x + 1)y' – y = e^{3x}(x + 1)^2\), with \(y(0)=\frac 13\). Then, the point \(x=−\frac 43\) for the curve \(y = y(x)\) is :

• (1) not a critical point
• (2) a point of local minima
• (3) a point of local maxima
• (4) a point of inflection

If the solution curve \(y = y(x)\) of the differential equation\( y^2dx + (x^2 – xy + y^2)dy = 0\), which passes through the point \((1,1)\) and intersects the line \(y=\sqrt 3x\) at the point \((α,\sqrt 3α)\), then value of \(log_e(\sqrt 3α)\) is equal to :

• (1) \(\frac {\pi}{3}\)
• (2) \(\frac {\pi}{2}\)
• (3) \(\frac {\pi}{12}\)
• (4) \(\frac {\pi}{6}\)

Let \(x=2t,\ y=\frac {t^2}{3}\) be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then \(\lim\limits_{t \to 1} k\) is equal to

• (1) \(\frac {17}{18}\)
• (2) \(\frac {19}{18}\)
• (3) \(\frac {11}{18}\)
• (4) \(\frac {13}{18}\)

Let a circle C in complex plane pass through the points \(z_1 = 3 + 4i\), \(z_2 = 4 + 3i\) and \(z_3 = 5i\). If \(z(≠z_1)\) is a point on C such that the line through \(z\) and \(z_1\) is perpendicular to the line through \(z_2\) and \(z_3\), then \(arg\ (z)\) is equal to:

• (1) \(tan^{-1}(\frac {2}{\sqrt5})-\pi\)
• (2) \(tan^{-1}(\frac {24}{7})-\pi\)
• (3) \(tan^{-1}(3)-\pi\)
• (4) \(tan^{-1}(\frac 34)-\pi\)

Let a circle C touch the lines L₁ : 4x – 3y +K₁ = 0 and L₂ : 4x – 3y + K₂ = 0, K₁, K₂∈R. If a line passing through the centre of the circle C intersects L₁ at (–1, 2) and L₂ at (3, –6), then the equation of the circle C is :

• (1) (x – 1)² + (y – 2)² = 4
• (2) (x + 1)² + (y – 2)² = 4
• (3) (x – 1)² + (y + 2)² = 16
• (4) (x – 1)² + (y – 2)² = 16

Let a, b and c be the length of sides of a triangle ABC such that:
\(\frac {a+b}{7}=\frac {b+c}{8}=\frac {c+a}{9}\)
If \(r\) and \(R\) are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of \(\frac Rr\) is equal to :

• (1) \(\frac 52\)
• (2) \(2\)
• (3) \(\frac 32\)
• (4) \(1\)

Consider the following two propositions:
\(P_1 : ~ (p → ~ q)\)
\(P_2: (p ∧ ~q) ∧ ((-~p) ∨ q)\)
If the proposition \(p → ((~p) ∨ q)\) is evaluated as FALSE, then:

• (1) P₁ is TRUE and P₂ is FALSE
• (2) P₁ is FALSE and P₂ is TRUE
• (3) Both P₁ and P₂ are FALSE
• (4) Both P₁ and P₂ are TRUE

If \(y = m_1x + c_1 \)and \(y = m_2x + c_2\), \(m_1≠m_2\) are two common tangents of circle \(x_2 + y_2 = 2\) and parabola \(y^2 = x\), then the value of \(8|m_1m_2|\) is equal to :

• (1) \(3+4\sqrt 2\)
• (2) \(-5+6\sqrt 2\)
• (3) \(-4+3\sqrt 2\)
• (4) \(7+6\sqrt 2\)

Let \(Q\) be the mirror image of the point \(P(1, 0, 1)\) with respect to the plane \(S\): \(x + y + z = 5\). If a line L passing through \((1, –1, –1)\), parallel to the line \(PQ\) meets the plane \(S\) at \(R\), then \(QR_2\) is equal to :

• (1) 2
• (2) 5
• (3) 7
• (4) 11

The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.

Let \(θ\) be the angle between the vectors \(\vec a\) and \(\vec b\), where \(|\vec a|=4\), \(|\vec b|=3\) and \(θ(\frac \pi 4,\ \frac \pi3)\) . Then \(|(\vec a−\vec b)×(\vec a+\vec b)|^2+4(\vec a.\vec b)^2\) is equal to ______.

Let the abscissae of the two points \(P\) and \(Q\) be the roots of \(2x^2 – rx + p = 0\) and the ordinates of \(P\) and \(Q\) be the roots of \(x^2 – sx – q = 0\). If the equation of the circle described on \(PQ\) as diameter is \(2(x^2 + y^2) – 11x – 14y – 22 = 0\), then \(2r + s – 2q + p\) is equal to _________.

Let \(f :R→R\) be a function defined by \(f(x)=(2(1−\frac {x^{25}}{2})(2+x^{25}))^{\frac {1}{50}}\). If the function \(g(x) = f (f (f (x))) + f (f (x))\), then the greatest integer less than or equal to \(g(1)\) is _________.

Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ______.

Let \(C_r\) denote the binomial coefficient of \(x^r \)in the expansion of \((1 + x)^{10}\). If for \(α, β∈R\), \(C_1 + 3⋅2 C_2 + 5⋅3 C_3 + …\) upto 10 terms =\(\frac {α×211}{2^β−1}(C_0+\frac {C_1}{2}+\frac {C_2}{3}…..\)upto 10 terms) then the value of \(α + β\) is equal to _______.

The number of values of x in the interval \((\frac \pi 4, \frac {7\pi }{4})\) for which \(14cosec^2x – 2sin^2x = 21 – 4cos^2x\) holds, is ______.

For a natural number \(n\), let \(α_n = 19n – 12n\). Then, the value of \(\frac {31α_9−α_{10}}{57α_8}\) is _____.

Let the lines
\(L_1:\vec r=λ(\hat i+2\hat j+3 \hat k), \ λ∈R\)
\(L_2:\vec r=(\hat i+3\hat j+\hat  k)+μ(\hat i+\hat j+\hat 5k), \ μ∈R\)
intersect at the point \(S\). If a plane \(ax + by – z + d = 0\) passes through \(S\) and is parallel to both the lines \(L_1\) and \(L_2\) then the value of \(a + b + d\) is equal to _______.

The greatest integer less than or equal to the sum of first \(100\) terms of the sequence \(\frac 13, \frac 59, \frac {19}{27}, \frac {65}{81},…...\) is equal to ______.

If \(Z=\frac {A^2B^3}{C^4},\) then the relative error in Z will be

• (1) \(\frac {△A}{A}+\frac {△B}{B}+\frac {△C}{C}\)
• (2) \(\frac {2△A}{A}+\frac {3△B}{B}-\frac {4△C}{C}\)
• (3) \(\frac {2△A}{A}+\frac {3△B}{B}+\frac {4△C}{C}\)
• (4) \(\frac {△A}{A}+\frac {△B}{B}-\frac {△C}{C}\)

\(\vec A\) is a vector quantity such that
\(|\vec A|\) = non-zero constant.
Which of the following expression is true for \(\vec A\)?

• (1) \(\vec A.\vec A=0\)
• (2) \(\vec A \times \vec A<0\)
• (3) \(\vec A \times\vec A=0\)
• (4) \(\vec A \times\vec A>0\)

Which of the following relations is true for two unit vector \(\hat A\) and \(\hat B\) making an angle θ to each other?

• (1) \(|\hat A+\hat B| = |\hat A-\hat B|\ tan\frac {θ}{2}\)
• (2) \(|\hat A-\hat B| = |\hat A+\hat B|\ tan\frac {θ}{2}\)
• (3) \(|\hat A+\hat B| = |\hat A-\hat B|\ cos\frac {θ}{2}\)
• (4) \(|\hat A-\hat B| = |\hat A+\hat B|\ cos\frac {θ}{2}\)

If force \(\vec F=3\hat i+4\hat j−2\hat k\) acts on a particle having position vector \(2\hat i+\hat j+2\hat k\) then, the torque about the origin will be

• (1) \(3\hat i+4\hat j−2\hat k\)
• (2) \(-10\hat i+10\hat j+5\hat k\)
• (3) \(10\hat i+5\hat j-10\hat k\)
• (4) \(10\hat i+\hat j-5\hat k\)

The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be (Given g = acceleration due to gravity at the surface of earth).

• (1) \(\frac g2\)
• (2) \(\frac g4\)
• (3) \(\frac g3\)
• (4) \(\frac g9\)

The terminal velocity \((v_t)\) of the spherical rain drop depends on the radius (r) of the spherical rain drop as

• (1) \(r^{\frac 12}\)
• (2) \(r\)
• (3) \(r^2\)
• (4) \(r^3\)

The relation between root mean square speed \((v_{rms})\) and most probable speed (\(v_p\)) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

• (1) \(v_{rms} = \sqrt {\frac 23}v_p\)
• (2) \(v_{rms} = \sqrt {\frac 32}v_p\)
• (3) \(v_{rms} = v_p\)
• (4) \(v_{rms} = \sqrt {\frac 13}v_p\)

In the figure, a very large plane sheet of positive charge is shown. \(P_1\) and \(P_2\) are two points at distance \(l \) and \(2l\) from the charge distribution. If \(σ \) is the surface charge density, then the magnitude of electric fields \(E_1\) and \(E_2\) and \(P_1\) and \(P_2\) respectively are

• (1) \(E_1 = \frac {σ}{ε_0}, E_2 = \frac {σ}{2ε_0}\)
• (2) \(E_1 = \frac {2σ}{ε_0}, E_2 = \frac {σ}{ε_0}\)
• (3) \(E_1 = E_2 = \frac {σ}{2ε_0}\)
• (4) \(E_1 = E_2 = \frac {σ}{ε_0}\)

• (1) (A) – (II), (B) – (I), (C) – (IV), (D) – (III)
• (2) (A) – (II), (B) – (I), (C) – (III), (D) – (IV)
• (3) (A) – (III), (B) – (IV), (C) – (II), (D) – (I)
• (4) (A) – (III), (B) – (I), (C) – (II), (D) – (IV)

A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre

• (1) \(B∝r^2\)
• (2) \(B∝r\)
• (3) \(B∝\frac {1}{r^2}\)
• (4) \(B∝\frac {1}{r}\)

If wattless current flows in the AC circuit, then the circuit is:

• (1) Purely Resistive circuit
• (2) Purely Inductive circuit
• (3) LCR series circuit
• (4) RC series circuit only

The electric field in an electromagnetic wave is given by \(E = 56.5\ sin ω(t – \frac xc)\ NC^{–1}\). Find the intensity of the wave if it is propagating along x-axis in the free space. (Given \(∈_0 = 8.85 × 10^{–12} C^2N^{–1}m^{–2}\))

• (1) \(5.65\ Wm^{–2}\)
• (2) \(4.24\ Wm^{–2}\)
• (3) \(1.9 × 10–7\ Wm^{–2}\)
• (4) \(56.5\ Wm^{–2}\)

The two light beams having intensities \(I\) and \(9I\) interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\frac {\pi}{2}\) at point P and \(\pi\) at point Q. Then the difference between the resultant intensities at P and Q will be:

• (1) \(2I\)
• (2) \(6I\)
• (3) \(5I\)
• (4) \(7I\)

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:
(Given : relative permeability of medium μ_r = 1)

• (1) 10°
• (2) 20°
• (3) 30°
• (4) 60°

The ratio for the speed of the electron in the 3^rd orbit of He⁺ to the speed of the electron in the 3^rd orbit of hydrogen atom will be :

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

The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because:

• (1) fractional change in majority carriers produce higher forward bias current.
• (2) fractional change in majority carriers produce higher reverse bias current.
• (3) fractional change in minority carriers produce higher forward bias current.
• (4) fractional change in minority carriers produce higher reverse bias current.

The difference of speed of light in the two media A and B(υ_A – υ_B) is 2.6 × 10⁷ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: speed of light in vacuum C = 3 × 10⁸ ms^–1)

• (1) 1.303
• (2) 1.318
• (3) 1.13
• (4) 0.12

A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for \(\frac 13\) deflection in the galvanometer. Which of the below is true for measuring value of G?

• (1) \(\frac 13\) deflection method cannot be used for determining the resistance of the galvanometer.
• (2) \(\frac 13\) deflection method can be used and in this case the G equals to twice the value of shunt resistance(s).
• (3) \(\frac 13\) deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s).
• (4) \(\frac 13\) deflection method can be used and in this case the G value equals to the shunt resistance(s).

Given below are two statements :
Statement I: Davisson-Germer experiment establishes the wave nature of electrons.
Statement II: If electrons have wave nature, they can interfere and show diffraction.
In the light of the above statements choose the correct answer from the option 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.

A signal of 100 THz frequency can be transmitted with maximum efficiency by :

• (1) Coaxial cable
• (2) Optical fibre
• (3) Twisted pair of copper wires
• (4) Water

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is ____m.

A \(0.5\ kg\) block moving at a speed of \(12\ ms^{–1}\) compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _____ \(Nm^{–1}\).

The velocity of upper layer of water in a river is \(36\ kmh^{–1}\). Shearing stress between horizontal layers of water is \(10^{–3} Nm^{–2}\). Depth of the river is ______ m. (Co-efficient of viscosity of water is \(10^{–2} Pa.s\))

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

The equivalent capacitance between points A and B in below shown figure will be ______ μF.

A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ______ J.

The total current supplied to the circuit as shown in figure by the 5 V battery is _______ A.

The current in a coil of self inductance \(2.0\ H\) is increasing according to \(I = 2\ sin(t^2)\ A\). The amount of energy spent during the period when current changes from 0 to \(2\ A\) is _______ \(J\).

A force on an object of mass \(100\ g\) is \((10\hat i+5\hat j)\ N\). The position of that object at \(t = 2s\) is \((a\hat i+b\hat j)\ m\) after starting from rest. The value of \(\frac ab\) will be _______ .

A steam engine intakes \(50\ g\) of steam at \(100°C\) per minute and cools it down to \(20°C\). If latent heat of vaporization of steam is \(540\ cal\ g^{–1}\), then the heat rejected by the steam engine per minute is ______ \(× 10^3\) \(cal.\)
(Given : specific heat capacity of water : \(1\ cal \ g^{–1} °C^{–1}\))

Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron?
(A) NO
(B) N₂
(C) O₂
(D) C₂
(E) B₂
Choose the most appropriate answer from the options given below :

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

The pair, in which ions are isoelectronic with \(Al^{3+}\) is:

• (1)

  Br^– and Be²⁺

• (2) Cl^– and Li⁺
• (3) S^2– and K⁺
• (4) O^2– and Mg²⁺

Number of electron deficient molecules among the following
\(PH_3, B_2H_6, CCl_4, NH_3, LiH \) and \(BCl_3\) is

• (1) 0
• (2) 1
• (3) 2
• (4) 3

White precipitate of \(AgCl\) dissolves in aqueous ammonia solution due to formation of:

• (1) \([Ag(NH_3)_4]CI_2\)
• (2) \([Ag(Cl)_2(NH_3)_2]\)
• (3) \([Ag(NH_3)_2]Cl\)
• (4) \([Ag(NH_3)Cl]Cl\)

Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

• (1) It will not prefer to undergo redox reactions.
• (2) It will prefer to gain electron and act as an oxidizing agent
• (3) It will prefer to give away an electron and behave as reducing agent
• (4) It acts as both, oxidizing and reducing agent.

Among the following which is the strongest oxidizing agent?

• (1) \(Mn^{3+}\)
• (2) \(Fe^{3+}\)
• (3) \(Ti^{3+}\)
• (4) \(Cr^{3+}\)

Phenol on reaction with dilute nitric acid, gives two products. Which method will be most efficient for large scale separation?

• (1) Chromatographic separation
• (2) Fractional crystallisation
• (3) Steam distillation
• (4) Sublimation

In the following structures, which one is having staggered conformation with maximum dihedral angle?

• (1)
• (2)
• (3)
• (4)

The product formed in the following reaction.

• (1)
• (2)
• (3)
• (4)

The IUPAC name of ethylidene chloride is:

• (1) 1-Chloroethene
• (2) 1-Chloroethyne
• (3) 1, 2-Dichloroethane
• (4) 1, 1-Dichloroethane

The major product in the reaction is:

• (1) t-Butyl ethyl ether
• (2) 2, 2-Dimethyl butane
• (3) 2-Methyl pent-1-ene
• (4) 2-Methyl prop-1-ene

The intermediate X, in the reaction is:

• (1)
• (2)
• (3)
• (4)

In the following reaction:The compound A and B respectively are:

• (1)
• (2)
• (3)
• (4)

The reaction of
 
with bromine and \(KOH\) gives \(RNH_2\) as the end product. Which one of the following is the intermediate product formed in this reaction?

• (1)
• (2) \(R-NH-Br\)
• (3) \(R-N=C=O\)
• (4)

Incorrect statement for Tyndall effect is:

• (1) The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.
• (2) The diameter of the dispersed particles is much smaller than the wavelength of the light used.
• (3) During projection of movies in the cinemas hall, Tyndall effect is noticed.
• (4) It is used to distinguish a true solution from a colloidal solution.

Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :

• (1) \([Au(CN)_4]^–\) and \([Zn(CN)_2 (OH)_2]^{2-}\)
• (2) \([Au(CN)_2]^–\) and \([Zn (OH)_4]^{2-}\)
• (3) \([Au(CN)_2]^–\) and \([Zn (CN)_4]^{2-}\)
• (4) \([Au(CN)_4]^{2-}\) and \([Zn (CN)_6]^{4-}\)

Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution?

• (1) \(Be^{2+}\)
• (2) \(Mg^{2+}\)
• (3) \(Ca^{2+}\)
• (4) \(Sr^{2+}\)

The eutrophication of water body results in:

• (1) loss of Biodiversity.
• (2) breakdown of organic matter.
• (3) increase in biodiversity.
• (4) decrease in BOD.

Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes, because:

• (1) soap particles remain floating in water as ions.
• (2) the hydrophobic part of soap is not able to take away grease.
• (3) the micelles are not formed due to concentration of soap, below its CMC value.
• (4) colloidal structure of soap in water is completely distributed.

Which one of the following is an example of artificial sweetner?

• (1) Bithional
• (2) Alitame
• (3) Salvarsan
• (4) Lactose

The number of N atoms in \(681\ g\) of \(C_7H_5N_3O_6\) is \(x × 10^{21}\). The value of \(x\) is ______ . (\(N_A\) = \(6.02 × 10^{23}\ mol^{–1}\)) (Nearest Integer)

The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is \(x × 10^{–8}\ m\). The value of \(x\) is ______. (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom is \(2.2 \times 10^{–18} J\);
\(h = 6.63 × 10^{–34}Js\) and \(c = 3 × 10^8 ms^{–1}\))

The standard entropy change for the reaction \(4Fe(s) + 3O_2(g) → 2Fe_2O_3(s)\) is \(–550\ J K^{–1}\) at \(298\ K\). The temperature in K at which the reaction attains equilibrium is ______. (Nearest Integer)
[Given: The standard enthalpy change for the reaction is \(–165\ kJmol^{–1}\)].

1L aqueous solution of \(H_2SO_4\) contains 0.02 m mol \(H_2SO_4\). 50% of this solution is diluted with deionized water to give 1L solution (A). In solution (A), 0.01 m mol of \(H_2SO_4\) are added. Total m mols of \(H_2SO_4\) in the final solution is ______ \(× 10^3\) m mols.

The standard free energy change \((ΔG°)\) for \(50%\) dissociation of \(N_2O_4\) into \(NO_2\) at \(27°C\) and 1 atm pressure is \(x\ J mol^{–1}\). The value of \(x\) is _____. (Nearest Integer)
[Given : \(R = 8.31\ JK^{–1} mol^{–1}\), \(log\ 1.33 = 0.1239\), \(ln\ 10 = 2.3\)]

In a cell, the following reactions take place
\(Fe^{2+} → Fe^{3+} + e^-\)
\(E°_{Fe^{3+}/Fe^{2+}} = 0.77\ V\)
\(2I^- → I_2 + 2e^-\)
\(E_{I_2/I^-} = 0.54\ V\)
The standard electrode potential for the spontaneous reaction in the cell is \(x×10^{–2} V\) at \(208\ K\). The value of \(x\) is _______. (Nearest Integer)

For a given chemical reaction
\(γ_1A + γ_2B → γ_3C + γ_4D\)
Concentration of C changes from 10 mmol dm^–3 to 20 mmol dm^–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm^–3 s^–1. Therefore, the rate of reaction is _____ mmol dm^–3 s^–1. (Nearest Integer)

If \([Cu(H_2O)_4]^{2+}\) absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [\(Cu(H_2O)_6]^{2+}\) will be _______ \(×10^{–21} J\). [Nearest integer]
(Given : h = \(6.63 × 10^{–34} Js\) and \(c = 3.08×10^8 ms^{–1}\))

Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is ______ × 10^–2 g. (Atomic mass of Br = 80 g/mol) [Nearest integer]

The distance between \(Na^+\) and \(Cl^–\) ions in solid \(NaCl\) of density \(43.1\ g\ cm^{–3}\) is ____ \(× 10^{–10}\ m\). (Nearest Integer)
(Given : \(N_A = 6.02 × 10^{23} mol^{–1}\))