JEE Main 2020 January 7 Shift 1 Question Paper with Solutions PDF

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :

• (A) \( \sqrt 3 \)
• (B) \( 3\sqrt 2 \)
• (C) \( {3 \over {\sqrt 2 }} \)
• (D) \( 2\sqrt 3 \)

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is :

• (A) \( {5 \over 2}\left( {6!} \right) \)
• (B) \( {6!} \)
• (C) 5⁶
• (D) \( {1 \over 2}\left( {6!} \right) \)

If \( y\left( \alpha \right) = \sqrt {2\left( {{{\tan \alpha + \cot \alpha } \over {1 + {{\tan }^2}\alpha }}} \right) + {1 \over {{{\sin }^2}\alpha }}} ,\alpha \in \left( {{{3\pi } \over 4},\pi } \right) \)

\( {{dy} \over {d\alpha }}\,\,at\,\alpha = {{5\pi } \over 6}is \) :

• (A) 4
• (B) -4
• (C) \( {4 \over 3} \)
• (D) -\( {1 \over 4} \)

Let \( \alpha \) be a root of the equation x² + x + 1 = 0 and the
matrix A = \( {1 \over {\sqrt 3 }}\left[ {\matrix{ 1 & 1 & 1 \cr 1 & \alpha & {{\alpha ^2}} \cr 1 & {{\alpha ^2}} & {{\alpha ^4}} \cr } } \right] \)

then the matrix A³¹ is equal to

• (A) A²
• (B) A
• (C) I₃
• (D) A³

If y = y(x) is the solution of the differential equation, \( {e^y}\left( {{{dy} \over {dx}} - 1} \right) = {e^x} \) such that y(0) = 0, then y(1) is equal to:

• (A) 2 + log_e2
• (B) log_e2
• (C) 1 + log_e2
• (D) 2e

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value −1. Then the expected value of X, is :

• (A) \( \frac{1}{8} \)
• (B) \( \frac{3}{16} \)
• (C) \( -\frac{1}{8} \)
• (D) \( -\frac{3}{16} \)

Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is -\( {1 \over 2} \) , then the greatest number amongst them is:

• (A) \( {{21} \over 2} \)
• (B) 27
• (C) 7
• (D) 16

The greatest positive integer k, for which 49^k + 1 is a factor of the sum
49¹²⁵ + 49¹²⁴ + ..... + 49² + 49 + 1, is:

• (A) 32
• (B) 60
• (C) 63
• (D) 65

If \( {\mathop{\rm Re}\nolimits} \left( {{{z - 1} \over {2z + i}}} \right) = 1 \), where z = x + iy, then the point (x, y) lies on a :

• (A) straight line whose slope is \( {3 \over 2} \)
• (B) straight line whose slope is \( -{2 \over 3} \)
• (C) circle whose diameter is \( {{\sqrt 5 } \over 2} \)
• (D) circle whose centre is at \( \left( { - {1 \over 2}, - {3 \over 2}} \right) \)

Let x^k + y^k = a^k, (a, k > 0 ) and \( {{dy} \over {dx}} + {\left( {{y \over x}} \right)^{{1 \over 3}}} = 0 \), then k is:

• (A) \( {1 \over 3} \)
• (B) \( {2 \over 3} \)
• (C) \( {4 \over 3} \)
• (D) \( {3 \over 2} \)

If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then

\( {1 \over {a + b}}\int_a^b {x\left( {f(x) + f(x + 1)} \right)} dx \) is equal to:

• (A) \( \int_{a - 1}^{b - 1} {f(x+1)dx} \)
• (B) \( \int_{a + 1}^{b + 1} {f(x + 1)dx} \)
• (C) \( \int_{a - 1}^{b - 1} {f(x)dx} \)
• (D) \( \int_{a + 1}^{b + 1} {f(x)dx} \)

The area of the region, enclosed by the circle x² + y² = 2 which is not common to the region bounded by the parabola y² = x and the straight line y = x, is:

• (A) \( {1 \over 6}\left( {24\pi - 1} \right) \)
• (B) \( {1 \over 3}\left( {12\pi - 1} \right) \)
• (C) \( {1 \over 3}\left( {6\pi - 1} \right) \)
• (D) \( {1 \over 6}\left( {12\pi - 1} \right) \)

If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c \( \in \) R are non-zero distinct; has a non-zero solution, then:

• (A) \( {1 \over a},{1 \over b},{1 \over c} \) are in A.P.
• (B) a + b + c = 0
• (C) a, b, c are in G.P.
• (D) a,b,c are in A.P.

Let \( \alpha \) and \( \beta \) be two real roots of the equation
(k + 1)tan²x - \( \sqrt 2 \) . \( \lambda \)tanx = (1 - k), where k(\( \ne \) - 1) and \( \lambda \) are real numbers. if tan² (\( \alpha \) + \( \beta \)) = 50, then a value of \( \lambda \) is:

• (A) 5\( \sqrt 2 \)
• (B) 10
• (C) 5
• (D) 10\( \sqrt 2 \)

A vector \( \overrightarrow a = \alpha \widehat i + 2\widehat j + \beta \widehat k\left( {\alpha ,\beta \in R} \right) \) lies in the plane of the vectors, \( \overrightarrow b = \widehat i + \widehat j \) and \( \overrightarrow c = \widehat i - \widehat j + 4\widehat k \). If \( \overrightarrow a \) bisects the angle between \( \overrightarrow b \) and \( \overrightarrow c \), then:

• (A) \( \overrightarrow a .\widehat i + 3 = 0 \)
• (B) \( \overrightarrow a .\widehat k - 4 = 0 \)
• (C) \( \overrightarrow a .\widehat i + 1 = 0 \)
• (D) \( \overrightarrow a .\widehat k + 2 = 0 \)

If g(x) = x² + x - 1 and
(goƒ) (x) = 4x² - 10x + 5, then ƒ\( \left( {{5 \over 4}} \right) \) is equal to:

• (A) \( {1 \over 2} \)
• (B) \( {3 \over 2} \)
• (C) -\( {1 \over 2} \)
• (D) -\( {3 \over 2} \)

The logical statement (p \( \Rightarrow \) q) \( \Lambda \) ( q \( \Rightarrow \) ~p) is equivalent to :

• (A) q
• (B) \( \sim \)p
• (C) p
• (D) \( \sim \)q

Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R in the plane P is :

• (A) (4, 3, 2)
• (B) (6, 5, - 2)
• (C) (3, 4, -2)
• (D) (6, 5, 2)

If y = mx + 4 is a tangent to both the parabolas, y² = 4x and x² = 2by, then b is equal to :

• (A) -128
• (B) 128
• (C) -64
• (D) -32

Let the function, ƒ:[-7, 0]\( \to \)R be continuous on [-7,0] and differentiable on (-7, 0). If ƒ(-7) = - 3 and ƒ'(x) \( \le \) 2, for all x \( \in \) (-7,0), then for all such functions ƒ, ƒ(-1) + ƒ(0) lies in the interval:

• (A) \( \left[ { - 6,20} \right] \)
• (B) \( \left( { - \infty ,\left. {20} \right]} \right. \)
• (C) \( \left[ { - 3,11} \right] \)
• (D) \( \left( { - \infty ,\left. {11} \right]} \right. \)

Let A(1, 0), B(6, 2) and C \( \left( {{3 \over 2},6} \right) \) be the vertices of a triangle ABC. If P is a Point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point \( \left( { - {7 \over 6}, - {1 \over 3}} \right) \), is ________.

\( \mathop {\lim }\limits_{x \to 2} {{{3^x} + {3^{3 - x}} - 12} \over {{3^{ - x/2}} - {3^{1 - x}}}} \) is equal to_______.

If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to_____.

Let S be the set of points where the function, ƒ(x) = |2-|x-3||, x \( \in \) R is not differentiable. Then \( \sum\limits_{x \in S} {f(f(x))} \) is equal to_____.

If the sum of the coefficients of all even powers of x in the product
(1 + x + x² + ....+ x²ⁿ)(1 - x + x² - x³ + ...... + x²ⁿ) is 61, then n is equal to _______.

Two infinite planes each with uniform surface charge density to are kept in such a way that the angle between them is 30^o. The electric field in the region shown between them is given by :

• (A) \( {\sigma \over {{ \in _0}}}\left[ {\left( {1 + {{\sqrt 3 } \over 2}} \right)\widehat y + {{\widehat x} \over 2}} \right] \)
• (B) \( {\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y + {{\widehat x} \over 2}} \right] \)
• (C) \( {\sigma \over {2{ \in _0}}}\left[ {\left( {1 + \sqrt 3 } \right)\widehat y - {{\widehat x} \over 2}} \right] \)
• (D) \( {\sigma \over {2{ \in _0}}}\left[ {\left( {1 - {{\sqrt 3 } \over 2}} \right)\widehat y - {{\widehat x} \over 2}} \right] \)

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If \( \gamma \) = 1.40, the work done by air is : (3^1.4 = 4.6555) [Take air to be an ideal gas]

• (A) 60.7 J
• (B) 100.8 J
• (C) 90.5 J
• (D) 48 J

The time period of revolution of electron inits ground state orbit in a hydrogen atom is \( 1 .6 \times 10^{- 16} \) s. The frequency of revolution of the electron in its first excited state (in \( s ^{- 1} \)) is :

• (A) \( 56 \times 10^{12} \)
• (B) \( 1.6 \times 10^{14} \)
• (C) \( 7.8 \times 10^{14} \)
• (D) \( 6.2 \times 10^{15} \)

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

• (A) L \( \leftrightarrow \) k, C \( \leftrightarrow \) b, R \( \leftrightarrow \) m
• (B) L \( \leftrightarrow \) m, C \( \leftrightarrow \) k, R \( \leftrightarrow \) b
• (C) L \( \leftrightarrow \) m, C \( \leftrightarrow \) \( {1 \over k} \), R \( \leftrightarrow \) b
• (D) L \( \leftrightarrow \) \( {1 \over b} \), C \( \leftrightarrow \) \( {1 \over m} \), R \( \leftrightarrow \) \( {1 \over k} \)

If the magnetic field in a plane electromagnetic wave is given by
\( \overrightarrow B \) = 3 \( \times \) 10^-8 sin(1.6 \( \times \) 10³x + 48 \( \times \) 10¹⁰t)\( \widehat j \) T, then what will be expression for electric field ?

• (A) \( \overrightarrow E \) = (9sin(1.6 \( \times \) 10³x + 48 \( \times \) 10¹⁰t)\( \widehat k \) V/m)
• (B) \( \overrightarrow E \) = (60sin(1.6 \( \times \) 10³x + 48 \( \times \) 10¹⁰t)\( \widehat k \) V/m)
• (C) \( \overrightarrow E \) = (3 \( \times \) 10^-8 sin(1.6 \( \times \) 10³x + 48 \( \times \) 10¹⁰t)\( \widehat i \) V/m)
• (D) \( \overrightarrow E \) = (3 \( \times \) 10^-8 sin(1.6 \( \times \) 10³x + 48 \( \times \) 10¹⁰t)\( \widehat j \) V/m)

The current I₁ (in A) flowing through 1 \( \Omega \) resistor in the following circuit is :

• (A) 0.4
• (B) 0.25
• (C) 0.2
• (D) 0.5

• (A) \( {{A{ \in _0}K} \over d}\left( {1 + {{\left( {{{\alpha d} \over 2}} \right)}^2}} \right) \)
• (B) \( {{A{ \in _0}K} \over d}\left( {1 + {{\alpha d} \over 2}} \right) \)
• (C) \( {{A{ \in _0}K} \over d}\left( {1 + {{{\alpha ^2}{d^2}} \over 2}} \right) \)
• (D) \( {{A{ \in _0}K} \over d}\left( {1 + \alpha d} \right) \)

Which of the following gives a reversible operation?

• (A)
• (B)
• (C)
• (D)

• (A) \( r\sqrt {{3 \over {2gh}}} \)
• (B) \( r\sqrt {{3 \over {4gh}}} \)
• (C) \( {1 \over r}\sqrt {{{4gh} \over 3}} \)
• (D) \( {1 \over r}\sqrt {{{2gh} \over 3}} \)

A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass \( {m \over {10}} \) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :

• (A) \( {{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2} \)
• (B) \( {m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right) \)
• (C) \( 5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right) \)
• (D) \( {m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2} \)

If we need a magnification of \( 375 \) from a compound microscope of tube length \( 150 \,mm \) and an objective of focal length \( 5\, mm \), the focal length of the eye-piece, should be close to :

• (A) \( 22\, mm \)
• (B) \( 12 \,mm \)
• (C) \( 33\, mm \)
• (D) \( 2 \,mm \)

Two moles of an ideal gas with \( {{{C_P}} \over {{C_V}}} = {5 \over 3} \) are mixed with 3 moles of another ideal gas with \( {{{C_P}} \over {{C_V}}} = {4 \over 3} \). The value of \( {{{C_P}} \over {{C_V}}} \) for the mixture is :

• (A) 1.50
• (B) 1.45
• (C) 1.47
• (D) 1.42

Consider a circular coil of wire carrying constant current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by \( \phi \)_i. The magnetic flux through the area of the circular coil area is given by \( \phi \)₀. Which of the following option is correct?

• (A) \( \phi \)_i = \( \phi \)₀
• (B) \( \phi \)_i < \( \phi \)₀
• (C) \( \phi \)_i \( > \) \( \phi \)₀
• (D) \( \phi \)_i = - \( \phi \)₀

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just 10% of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is :

• (A) 71.6^o
• (B) 90^o
• (C) 18.4^o
• (D) 45^o

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (\( 1 \,HP = 746 \,W, \,g = 10\, ms^{-2} \) )

• (A) \( 1.5 \,ms^{- 1} \)
• (B) \( 1.7 \,ms^{- 1} \)
• (C) \( 2.0 \,ms^{- 1} \)
• (D) \( 1.9 \,ms^{- 1} \)

A long solenoid of radius R carries a time (t) - dependent current
I(t)=I₀t(1 - t). A ring of radius 2R is placed coaxially near its middle. During the time interval 0 \( \le \) t \( \le \) 1, the induced current (I_R) and the induced EMF(V_R) in the ring change as :

• (A) Direction of I_R remains unchanged and V_R is zero at t = 0.25
• (B) Direction of I_R remains unchanged and V_R is maximum at t = 0.5
• (C) At t = 0.25 direction of I_R reverses and V_R is maximum
• (D) At t = 0.5 direction of I_R reverses and V_R is zero

Visible light of wavelength 6000 \( \times \) 10^-8 cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at 60^o from the central maximum. If the first minimum is produced at \( \theta \)₁, then \( \theta \)₁, is close to :

• (A) 45^o
• (B) 30^o
• (C) 25^o
• (D) 20^o

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm²) is 90 ms^-1. If the Young's modulus of wire is 16 \( \times \) 10¹¹ Nm^-2, the extension of wire over its natural length is :

• (A) 0.03 mm
• (B) 0.04 mm
• (C) 0.02 mm
• (D) 0.01 mm

The radius of gyration of a uniform rod of length \( l \), about an axis passing through a point \( {l \over 4} \) away from the centre of the rod, and perpendicular to it, is :

• (A) \( {1 \over 8}l \)
• (B) \( {1 \over 4}l \)
• (C) \( \sqrt {{7 \over {48}}} l \)
• (D) \( \sqrt {{3 \over 8}} l \)

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at a point:

• (A) 2.0 cm right and 0.9 cm above 1 kg mass
• (B) 0.9 cm right and 2.0 cm above 1 kg mass
• (C) 0.6 cm right and 2.0 cm above 1 kg mass
• (D) 1.5 cm right and 1.2 cm above 1 kg mass

A loop ABCDEFA of straight edges has six corner points A(0, 0, 0), B(5, 0, 0), C(5, 5, 0), D (0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is \( \overrightarrow B = \left( {3\widehat i + 4\widehat k} \right)T \) . The quantity of flux through the loop ABCDEFA (in Wb) is _______.

A beam of electromagnetic radiation of intensity 6.4 × 10^–5 W/cm² is comprised of wavelength, \( \lambda \) = 310 nm. It falls normally on a metal (work function \( \phi \) = 2eV) of surface area of 1 cm². If one in 10³ photons ejects an elctron, total number of electrons ejected in 1 s is 10^x. (hc = 1240 eVnm, 1eV = 1.6 × 10^–19 J), then x is _____.

A non-isotropic solid metal cube has coefficients of linear expansion as :
5 \( \times \) 10^-5/^oC along the x-axis and 5 \( \times \) 10^-6/^oC along the y and the z-axis. If the coefficient of volume expansion of the solid is C \( \times \) 10^-6/^oC then the value of C is

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is :
(Figure drawn is schematic and not to scale; take g = 10 ms^-2)

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is _______.

What is the product of following reaction ?

• (A)
• (B)
• (C)
• (D)

At 35\( ^{\circ} \)C, the vapour pressure of \( CS_2 \) is 512 mm Hg and that of acetone is 344 mm Hg. A solution of \( CS_2 \), in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is :

• (A) heat must be absorbed in order to produce the solution at 35\( ^{\circ} \)C
• (B) a mixture of 100 mL \( CS_2 \), and 100 mL acetone has a volume < 200 mL
• (C) \( CS_2 \), and acetone are less attracted to each other than to themselves
• (D) Raoult's law is not obeyed by this system

The number of orbitals associated with quantum number n = 5, m_s = +\( {1 \over 2} \) is :

• (A) 11
• (B) 25
• (C) 15
• (D) 50

Given that the standard potentials (E^o) of Cu²⁺/Cu and Cu⁺/Cu are 0.34 V and 0.522 V respectively, the E^o of Cu²⁺/Cu⁺ :

• (A) - 0.182 V
• (B) - 0.158 V
• (C) 0.182 V
• (D) +0.158 V

Match the following :
(i) Riboflavin    (a) Beriberi
(ii) Thiamine    (b) Scurvy
(iii) Pyridoxine   (c) Cheliosis
(iv) Ascorbic acid    (d) Convulsions

• (A) (i)-(c), (ii)-(d), (iii)-(a), (iv)-(b)
• (B) (i)-(d), (ii)-(b), (iii)-(a), (iv)-(c)
• (C) (i)-c, (ii)-(a), (iii)-(d), (iv)-(b)
• (D) (i)-(a), (ii)-(d), (iii)-(c), (iv)-(b)

The relative strength of interionic/intermolecular forces in decreasing order is :

• (A) dipole-dipole \( > \) ion-dipole \( > \) ion-ion
• (B) ion-dipole \( > \) dipole-dipole \( > \) ion-ion
• (C) ion-dipole \( > \) ion-ion \( > \) dipole-dipole
• (D) ion-ion \( > \) ion-dipole \( > \) dipole-dipole

The increasing order to P_kb for the following compounds will be :

• (A) (A) < (B) < (C)
• (B) (C) < (A) < (B)
• (C) (B) < (A) < (C)
• (D) (B) < (C) < (A)

Consider the following reaction :


The product 'X' is used :

• (A) as food grade colourant
• (B) in acid base titration as an indicatior.
• (C) in laboratory test for phenols
• (D) in protein estimation as an alternative to ninhydrin.

The dipole of CCl₄, CHCl₃ and CH₄ are in the order :

• (A) CCl₄ < CH₄ < CHCl₃
• (B) CH₄ = CCl₄ < CHCl₃
• (C) CH₄ < CCl₄ < CHCl₃
• (D) CHCl₃ < CH₄= CCl₄

The theory that can completely/properly explain the nature of bonding in [Ni(Co)₄] is :

• (A) Wemer's theory
• (B) Valence bond theory
• (C) Crystal field theory
• (D) Molecular orbital theory

1- methyl ethylene oxide when treated with an excess of HBr produces :

• (A)
• (B)
• (C)
• (D)

The electron gain enthalpy (in KJ/mol) of fluorine, chlorine, bromine and iodine, respectively are:

• (A) -296, -325, -333 and -349
• (B) 349, -333, -325 and -296
• (C) -333, -349, -325 and -296
• (D) -333, -325, -349 and -296

Amongst the following statements, that which was not proposed by Dalton was :

• (A) Matter consists of indivisible atoms all the atoms of a given element have.
• (B) Chemical reactions involve reorganization of atoms. These are neither created not destroyed in a chemical reaction.
• (C) When gases combine or reproduced in a chemical reactionn they do so in a simple ratio by volume provided all gases are the same T & P.
• (D) Identical properties including identical mass. Atoms of differemt element differ in mass.

Consider the following reaction :

\( {\left( {C{H_3}} \right)_3}CCH\left( {OH} \right)C{H_3}\buildrel {conc.\,\,\,{H_2}S{O_4}} \over \longrightarrow \)

\( {\left( {C{H_3}} \right)_2}CHCH\left( {Br} \right)C{H_3}\buildrel {alc.\,\,KOH} \over \longrightarrow \)

\( {\left( {C{H_3}} \right)_2}{\rm{ }}CHCH\left( {Br} \right)C{H_3}\buildrel {{{(C{H_3})}_3}{O^\Theta }{K^ \oplus }} \over \longrightarrow \)

\( {\left( {C{H_3}} \right)_2}\mathop C\limits_{\mathop |\limits_{OH} } - C{H_2} - CHO\buildrel \Delta \over \longrightarrow \)

Which of these reaction(s) will not produce Saytzeff product ?

• (A) (d) only
• (B) (b) and (d)
• (C) (a), (c) and (d)
• (D) (c) only

Oxidation number of potassium in K₂O. K₂O₂ and KO₂ respectively is :

• (A) +1, +2 and + 4
• (B) +1, +1 and + 1
• (C) +2, +1 and \( + {1 \over 2} \)
• (D) +1, +4, and +2

The atomic radius of Ag is closed to :

• (A) Au
• (B) Cu
• (C) Hg
• (D) Ni

A solution of m-chloronailimne, m-chlorophenol and m-chlorobenzoic acid in ethyal acetate was extracted initially with a saturated solution of NaHCO₃ to give fraction A. The left over organic phase was extracted with dilute NaoH solution tio give fraction B. The final organiic layer was labelled as fraction C. Fractions A,B and C, contain respectively :

• (A) m-chlorobenzoic acid, m-chloroaniline and m-chlorophenol.
• (B) m-chlorobenzoic acid, m-chlorophenol and m-chloroaniline.
• (C) m-chlorophenol, m-chlorobenzoic acid and m-chloronailine.
• (D) m-chloroaniline m-chlorobenzoic acid and m-chlorophenol.

The IUPAC name of the complex \( [Pt(NH_3)_2Cl(NH_2CH_3)]Cl \) is :

• (A) Diammine(methanamine)chlorido platinum(II)chloride
• (B) Diamminechlorido(methanamine) platinum(II)chloride
• (C) Diamminechlorido(aminomethane) platinum(II)chloride
• (D) Bisammine(methanamine)chlorido platinum(II)chlorid e

In comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is :

• (A) less efficient as the resins cannot be regenerated
• (B) less efficient as it exchanges only anions
• (C) more efficient as it can exchange only cations
• (D) more efficient as it can exchange both cations as well as anions

The purest from of commercial iron is :

• (A) pig iron
• (B) wrought iron
• (C) cast iron
• (D) scrap iron and pig iron

For the reaction :

A(\( l \)) \( \to \) 2B(g)

\( \Delta U = 2.1\,kcal,\,\Delta S = 20\,cal\,{K^{ - 1}} \) at 300 K

Hence \( \Delta \)G in kcal is :

During the nuclear explosion, one of the products is ⁹⁰Sr with half life of 6.93 years. If 1 \( \mu \) g of ⁹⁰Sr was absorbed in the bones of newly born baby in placed of Ca, how much time, in years, is required to reduce much time, in year, is required to reduce it by 90% if it not lost metabolically.

Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between CI and O atoms in (Y) is.

Two solutions, A and B, each of 100L was made by dissolving 4g of NaOH and 9.8 g of H₂SO₄ in water, respectively. The pH of the resultant solution obtained from mixing 40L of solution A and 10L of solution B is :

The number of chiral carbons in chloramphenicol is