JEE Main 2023 Question Paper Jan 31 Shift 1- Download PDF

The number of real roots of the equation \(\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}\), is:

• (1) 2
• (2) 3
• (3) 1
• (4) 0

A bag contains 6 balls Two balls are drawn from it at random and both are found to be black The probability that the bag contains at least 5 black balls is

• (1) \(\frac{2}{7}\)
• (2) \(\frac{3}{7}\)
• (3) \(\frac{5}{7}\)
• (4) \(\frac{5}{6}\)

If \(\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13\), then \(\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)\) is equal to

• (1) \(16-5 \pi\)
• (2) 16
• (3) 0
• (4) \(\pi\)

If the sum and product of four positive consecutive terms of a GP, are 126 and 1296, respectively, then the sum of common ratios of all such GPs is

• (1) \(\frac{9}{2}\)
• (2) 3
• (3) 7
• (4) 14

For the system of linear equations 
\(x+y+z=6\) 
\(\alpha x+\beta y+7 z=3\) 
\(x+2 y+3 z=14\). 
which of the following is NOT true ?

• (1) The system in inconsistent for α =−5 and β = 8
• (2) The system has a unique solution for α =−5 and β = 8
• (3) The system has infinitely many solutions for α =−6 and β = 9
• (4) The system has infinitely many solutions for α =−5 and β = 9

Let \(R\) be a relation on \(N \times N\) defined by \((a, b) R (c, d)\) if and only if \(a d(b-c)=b c(a-d)\) Then \(R\) is

• (1) transitive but neither reflexive nor symmetric
• (2) symmetric but neither reflexive nor transitive
• (3) symmetric and transitive but not reflexive
• (4) reflexive and symmetric but not transitive

If the domain of the function \(f(x)=\frac{[x]}{1+x^2}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

• (1) \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
• (2) \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
• (3) \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
• (4) \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)

A wire of length \(20 m\) is to be cut into two pieces A piece of length \(l_1\) is bent to make a square of area \(A_1\) and the other piece of length \(l_2\) is made into a circle of area \(A_2\) If \(2 A_1+3 A_2\) is minimum then \(\left(\pi l_1\right): l_2\) is equal to:

• (1) \(6: 1\)
• (2) \(3: 1\)
• (3) \(4: 1\)
• (4) \(1: 6\)

Let \(\alpha \in(0,1)\) and \(\beta=\log _e(1-\alpha)\) Let \(P_n(x)=x+\frac{x^2}{2}+\frac{x^3}{3}+\ldots+\frac{x^n}{n}, x \in(0,1)\) Then the integral \(\int\limits_0^\alpha \frac{t^{50}}{1-t} d t\) is equal to

• (1) \(P_{50}(\alpha)-\beta\)
• (2) \(-\left(\beta+P_{50}(\alpha)\right)\)
• (3) \(\beta+P_{50}(a)\)
• (4) \(\beta-P_{50}(\alpha)\)

Let the shortest distance between the lines \(L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0\) and \(L_1: x+1=y-1=4-z\) be \(2 \sqrt{6}\) If \((\alpha, \beta, \gamma)\) lies on \(L\), then which of the following is NOT possible?

• (1) \(\alpha+2 y=24\)
• (2) \(2 \alpha+\gamma=7\)
• (3) \(\alpha-2 \gamma=19\)
• (4) \(2 \alpha-\gamma=9\)

Let \(\vec{a}=2 \hat{i}+\hat{j}+\hat{k}\), and \(\vec{b}\) and \(\vec{c}\) be two nonzero vectors such that \(|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|\) and \(\vec{b} \cdot \vec{c}=0\). Consider the following two statements: 

(A) \(|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|\) for all \(\lambda \in R\) 

(B) \(\vec{a}\) and \(\vec{c}\) are always parallel. Then. is

• (1) both (A) and (B) are correct
• (2) only \(( A )\) is correct
• (3) only (B) is correct
• (4) neither \(( A )\) nor \((B)\) is correct

Let \(A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}\) Then the sum of the diagonal elements of the matrix \((A+I)^{11}\) is equal to :

• (1) 2050
• (2) 4094
• (3) 6144
• (4) 4097

For all \(z \in C\) on the curve \(C_1:|z|=4\), let the locus of the point \(z+\frac{1}{z}\) be the curve \(C_2\) Then:

• (1) the curve \(C_1\) lies inside \(C_2\)
• (2) the curves \(C_1\) and \(C_2\) intersect at 4 points
• (3) the curve \(C_2\) lies inside \(C_1\)
• (4) the curves \(C_1\) and \(C_2\) intersect at 2 points

The value of \(\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x\) is equal to

• (1) \(\frac{7}{2}-\sqrt{3}-\log _e \sqrt{3}\)
• (2) \(\frac{10}{3}-\sqrt{3}-\log _e \sqrt{3}\)
• (3) \(\frac{10}{3}-\sqrt{3}+\log _e \sqrt{3}\)
• (4) \(-2+3 \sqrt{3}+\log _e \sqrt{3}\)

Let \(y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)\) Then, at \(x=1\)

• (1) \(2 y^{\prime}+\sqrt{3} \pi^2 y=0\)
• (2) \(\sqrt{2} y^{\prime}-3 \pi^2 y=0\)
• (3) \(2 y^{\prime}+3 \pi^2 y=0\)
• (4) \(y^{\prime}+3 \pi^2 y=0\)

Let a differentiable function \(f\) satisfy \(f(x)+\int\limits_3^x \frac{f(t)}{t} d t=\sqrt{x+1}, x \geq 3\) Then \(12 f(8)\) is equal to :

• (1) 19
• (2) 1
• (3) 17
• (4) 34

Let a circle \(C_1\) be obtained on rolling the circle \(x^2+y^2-4 x-6 y+11=0\) upwards 4 units on the tangent \(T\) to it at the point \((3,2)\) Let \(C_2\) be the image of \(C_1\) in \(T\) Let \(A\) and \(B\) be the centers of circles \(C_1\) and \(C_2\) respectively, and \(M\) and \(N\) be respectively the feet of perpendiculars drawn from \(A\) and \(B\) on the \(x\)-axis. Then the area of the trapezium AMNB is:

• (1) \(2(2+\sqrt{2})\)
• (2) \(2(1+\sqrt{2})\)
• (3) \(4(1+\sqrt{2})\)
• (4) \(3+2 \sqrt{2}\)

If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b<2\), from the origin is 1 , then the eccentricity of the ellipse is 

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

\(( S 1)(p \Rightarrow q) \vee(p \wedge(\sim q))\) is a tautology(S2) \(((\sim p) \Rightarrow(\sim q)) \wedge((\sim p) \vee q)\) is a contradictionThen

• (1) both (S1) and (S2) are correct
• (2) only (S2) is correct
• (3) only ( \(S 1)\) is correct
• (4) both ( \(S 1)\) and (S2) are wrong

Let \(y=f(x)\) represent a parabola with focus \(\left(-\frac{1}{2}, 0\right)\) and directrix \(y=-\frac{1}{2}\) Then \(S=\left\{x \in R : \tan ^{-1}(\sqrt{f(x)})+\sin ^{-1}(\sqrt{f(x)+1})=\frac{\pi}{2}\right\}\) :

• (1) is an empty set
• (2) contains exactly one element
• (3) contains exactly two elements
• (4) is an infinite set

The remainder on dividing \(5^{99}\) by 11 is

Let 5 digit numbers be constructed using the digits \(0,2,3,4,7,9\) with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

Let \(\alpha>0\), be the smallest number such that the expansion of \(\left(x^{\frac{2}{3}}+\frac{2}{x^3}\right)^{30}\) has a term \(\beta x^{-a}, \beta \in N\).
Then \(α\) is equal to _________. 

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

Let \(a_1, a_2, \ldots, a_n\) be in AP If \(a_5=2 a_7\) and \(a_{11}=18\), then \(12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)\) is equal to

Let \(\vec{a}\) and \(\vec{b}\) be two vectors such that \(|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}\) and \(|\vec{a} \times \vec{b}|=\sqrt{48}\) Then \((\vec{a} \cdot \vec{b})^2\) is equal to

Let for \(x \in R\) \(f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} \) 

Then area bounded by the curve \(y=(f \circ g)(x)\) and the lines \(y=0,2 y-x=15\) is equal to

If the variance of the frequency distribution

is 3 , then \(\alpha\) is equal to

Let the line \(L: \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-3}{1}\) intersect the plane \(2 x+y+3 z=16\) at the point \(P\) Let the point \(Q\) be the foot of perpendicular from the point \(R(1,-1,-3)\) on the line \(L\) If \(\alpha\) is the area of triangle \(P Q R\), then \(\alpha^2\) is equal to

Let \(\theta\) be the angle between the planes \(P_1: \vec{r} \cdot(\hat{i}+\hat{j}+2 \hat{k})=9\) and \(P_2: \hat{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=15\) Let \(L\) be the line that meets \(P_2\) at the point \((4,-2,5)\) and makes an angle \(\theta\) with the normal of \(P_4\) If \(\alpha\) is the angle between \(L\) and \(P_2\), then \(\left(\tan ^2 \theta\right)\left(\cot ^2 \alpha\right)\) is equal to

The initial speed of a projectile fired from ground is \(u\) At the highest point during its motion, the speed of projectile is \(\frac{\sqrt{3}}{2} u\) The time of flight of the projectile is :

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

A bar magnet with a magnetic moment 50 \(Am ^2\) is placed in parallel position relative to a magnetic field of 0.4T. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is

• (1) \(4 J\)
• (2) \(1 J\)
• (3) \(2 J\)
• (4) Zero

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)

• (1) Both will reach the earth's surface simultaneously.
• (2) Insulating ball will reach the earth's surface earlier than the metal ball
• (3) Metal ball will reach the earth's surface earlier than the insulating ball
• (4) Time taken by them to reach the earth's surface will be independent of the properties of their materials

The effect of increase in temperature on the number of electrons in conduction band \(\left( n _{ e }\right)\) and resistance of a semiconductor will be as:

• (1) \(n _{ e }\) decreases, resistance increases
• (2) Both \(n _{ e }\) and resistance increase
• (3) \(n _{ e }\) increases, resistance decreases
• (4) Both \(n_e\) and resistance decrease

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

• (1)
• (2)
• (3)
• (4)

The drift velocity of electrons for a conductor connected in an electrical circuit is \(V _{ d }\) The conductor in now replaced by another conductor with same material and same length but double the area of cross section The applied voltage remains same The new drift velocity of electrons will be

• (1) \(\frac{V_{ d }}{4}\)
• (2) \(\frac{ V _{ d }}{2}\)
• (3) \(2 V _{ d }\)
• (4) \(V _{ d }\)

A rod with circular cross-section area \(2\, cm ^2\) and length \(40 cm\) is wound uniformly with \(400\) turns of an insulated wire If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is \(4 \pi \times 10^{-6}\, Wb\) The relative permeability of the rod is(Given : Permeability of vacuum \(\mu_0=4 \pi \times 10^{-7}\, NA ^{-2}\) )

• (1) \(125\)
• (2) \(12.5\)
• (3) \(\frac{5}{16}\)
• (4) \(\frac{32}{5}\)

At a certain depth "\(d\)" below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height \(3 R\) above earth surface Where \(R\) is Radius of earth (Take \(R =6400\, km\) ) The depth \(d\) is equal to

• (1) \(4800 \, km\)
• (2) \(640 \, km\)
• (3) \(2560\, km\)
• (4) \(5260\, km\)

Two polaroide \(A\) and \(B\) are placed in such a way that the pass-axis of polaroids are perpendicular to each other Now, another polaroid \(C\) is placed between \(A\) and \(B\) bisecting angle between them If intensity of unpolarized light is \(I _0\) then intensity of transmitted light after passing through polaroid \(B\) will be:

• (1) \(\frac{I_0}{8}\)
• (2) \(Z erO\)
• (3) \(\frac{I_0}{2}\)
• (4) \(\frac{I_0}{4}\)

100 balls each of mass \(m\) moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(t s\) The total force exerted by the balls on the wall is

• (1) \(\frac{100 m v}{t}\)
• (2) \(200 m v t\)
• (3) \(\frac{200 m v}{t}\)
• (4) \(\frac{m v}{100 t}\)

If \(R , X _{ L }\), and \(X _{ C }\) represent resistance, inductive reactance and capacitive reactance Then which of the following is dimensionless :

• (1) \(R X_L \quad X_C\)
• (2) \(\frac{R}{\sqrt{X_L X_C}}\)
• (3) \(\frac{R}{X_L X_C}\)
• (4) \(R \frac{X_L}{X_C}\)

The maximum potential energy of a block executing simple harmonic motion is \(25 J\) A is amplitude of oscillation At \(A / 2\), the kinetic energy of the block is

• (1) \(18.75 J\)
• (2) \(37.5 J\)
• (3) \(9.75 J\)
• (4) \(12.5 J\)

If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop In the process the released surface energy is - (Take π=\(\frac {22}{7}\))
 

• (1) \(8.8 \times 10^{-5} J\)
• (2) \(7.92 \times 10^{-4} J\)
• (3) \(7.92 \times 10^{-6} J\)
• (4) \(9.68 \times 10^{-4} J\)

As shown in figure, a \(70 kg\) garden roller is pushed with a force of \(\vec{F}=200 N\) at an angle of \(30^{\circ}\) with horizontal. The normal reaction on the roller is (Given \(g=10 m s ^{-2}\) )

• (1) \(800 N\)
• (2) \(600 N\)
• (3) \(200 \sqrt{3} N\)
• (4) \(800 \sqrt{2} N\)

The pressure of a gas changes linearly with volume from \(A\) to \(B\) as shown in figure If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be Is

• (1) \(4.5 J\)
• (2) \(-4.5 J\)
• (3) zero
• (4) \(6 J\)

The correct relation between \(\gamma=\frac{ c _{ p }}{ c _{ v }}\) and temperature \(T\) is :

• (1) \(\gamma \alpha T ^{\circ}\)
• (2) \(\gamma \alpha \frac{1}{T}\)
• (3) \(\gamma \alpha T\)
• (4) \(\gamma \alpha \frac{1}{\sqrt{T}}\)

If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is(Take Planck constant \(h =6 \times 10^{-34} Js\) )

• (1) Micro waves
• (2) Radio waves
• (3) Gamma rays
• (4) Ultraviolet rays

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\)

Assertion (A) : The beam of electrons show wave nature and exhibit interference and diffraction 

Reason (R) : Davisson Germer Experimentally verified the wave nature of electrons

In the light of the above statements, choose the most appropriate answer from the options given below :

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

The amplitude of \(15 \sin (1000 \pi t )\) is modulated by \(10 \sin (4 \pi t )\) signal The amplitude modulated signal contains frequency (ies) of 
A \(500\,Hz\) 
B \(2\, Hz\) 
C \(250\, Hz\) 
D \(498\, Hz\) 
E \(502\, Hz\) 
Choose the correct answer from the options given below:

• (1) B Only
• (2) A and B Only
• (3) A, D and E Only
• (4) A Only

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

• (1) neutron is an uncharged particle
• (2) neutron has larger rest mass than proton
• (3) neutron is a composite particle made of a proton and an electron
• (4) proton is a charged particle

A lift of mass \(M =500 kg\) is descending with speed of \(2 ms ^{-1}\) Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of \(2 ms ^{-2}\) The kinetic energy of the lift at the end of fall through to a distance of \(6 m\) will be ___ \(kJ\)

For hydrogen atom, \(\lambda_1\) and \(\lambda_2\) are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure The ratio of \(\lambda_1\) and \(\lambda_2\) is \(\frac{x}{32}\) The value of \(x\) is

In the figure given below, a block of mass \(M=490 g\) placed on a frictionless table is connected with two springs having same spring constant \(\left( K =2 N m ^{-1}\right)\) If the block is horizontally displaced through ' \(X\) ' \(m\) then the number of complete oscillations it will make in \(14 \pi\) seconds will be

The speed of a swimmer is \(4 km h ^{-1}\) in still water If the swimmer makes his strokes normal to the flow of river of width \(1 km\), he reaches a point \(750 m\) down the stream on the opposite bank.The speed of the river water is ___ \(km h ^{-1}\)

A solid sphere of mass \(1 \,kg\) rolls without slipping on a plane surface Its kinetic energy is \(7 \times 10^{-3} J\). The speed of the centre of mass of the sphere is ___\(cm s ^{-1}\).

Expression for an electric field is given by \(\overrightarrow{ E }=4000 x^2 i \frac{ V }{ m }\) The electric flux through the cube of side \(20 cm\) when placed in electric field (as shown in the figure) is ___\(V cm\)

A thin rod having a length of \(1 m\) and area of cross-section \(3 \times 10^{-6} m ^2\) is suspended vertically from one end. The rod is cooled from \(210^{\circ} C\) to \(160^{\circ} C\) After cooling, a mass \(M\) is attached at the lower end of the rod such that the length of rod again becomes \(1m\). Young's modulus and coefficient of linear expansion of the rod are \(2 \times 10^{11} N m ^{-2}\) and \(2 \times 10^{-5} K ^{-1}\), respectively. The value of \(M\) is ____ \(kg\). (Take \(g =10 \ m s ^{-2}\))

In a medium the speed of light wave decreases to \(0.2\) times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is \(x: 1\) The value of \(x\) is(Given speed of light in free space \(=3 \times 10^8 m s ^{-1}\) and for the given medium \(\mu =1\))

Two identical cells, when connected either in parallel or in series gives same current in an external resistance \(5 \Omega\) The internal resistance of each cell will be__ \(\Omega\)

An inductor of \(0.5 mH\), a capacitor of \(20 \mu F\) and resistance of \(20 \Omega\) are connected in series with a \(220 V\) ac source If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x}\) A The value of \(x\) is -

When \(Cu ^{2+}\) ion is treated with \(KI\), a white precipitate, \(X\) appears in solution The solution is titrated with sodium thiosulphate, the compound \(Y\) is formed \(X\) and \(Y\) respectively are

• (1) \(X = CuI _2 \,\,\,Y = Na _2 S _2 O _3\)
• (2) \(X = CuI _2 \,\,\, Y = Na _2 S _4 O _6\)
• (3) \(X = Cu _2 I _2 \,\,\,Y = Na _2 S _4 O _6\)
• (4) \(X = Cu _2 I _2 \,\,\, Y = Na _2 S _4 O _5\)

Match items of column I and II

Column I (Mixture of compounds)		Column II (Separation Technique)
A	H2​O/CH2​Cl2​	i	Crystallization
B		ii	Differential solvent extraction
C	Kerosene/Naphthalene	iii	Column chromatography
D	C6​H12​O6​/NaCl	iv	Fractional Distillation

• (1) A-(iii), B-(iv), C-(ii), D-(i)
• (2) A-(i), B-(iii), C-(ii), D-(iv)
• (3) A-(ii), B-(iv), C-(i), D-(iii)
• (4) A-(ii), B-(iii), C-(iv), D-(i)

• (1) optically active and adds one mole of bromine
• (2) optically active alcohol and is neutral
• (3) racemic mixture and gives a gas with saturated \(NaHCO _3\) solution
• (4) racemic mixture and is neutral

\(Nd ^{2+}=\) ___________

• (1) \(4 f ^3\)
• (2) \(4 f^4 6 s^2\)
• (3) \(4 f ^2 6 s ^2\)
• (4) \(4 f ^4\)

The correct order of basicity of oxides of vanadium is

• (1) \(V _2 O _3\gt V _2 O _5\gt V _2 O _4\)
• (2) \(V _2 O _4\gt V _2 O _3\gt V _2 O _5\)
• (3) \(V _2 O _3\gt V _2 O _4\gt V _2 O _5\)
• (4) \(V _2 O _5\gt V _2 O _4\gt V _2 O _3\)

The correct increasing order of the ionic radii is

• (1) \(Ca ^{2+}\lt K ^{+}\lt Cl ^{-}\lt S ^{2-}\)
• (2) \(S ^{2-}\lt Cl ^{-}\lt Ca ^{2+}\lt K ^{+}\)
• (3) \(K ^{+}\lt S ^{2-}\lt Ca ^{2+}\lt Cl ^{-}\)
• (4) \(Cl ^{-}\lt Ca ^{2+}\lt K ^{+}\lt S ^{2-}\)

The correct order of melting points of dichlorobenzenes is

• (1)
• (2)
• (3)
• (4)

Consider the above reaction and identify the product B.

• (1)
• (2)
• (3)
• (4)

A protein ' \(X\) ' with molecular weight of \(70,000 u\), on hydrolysis gives amino acids One of these amino acid is

• (1)
• (2)
• (3)
• (4)

Choose the correct set of reagents for the following conversion trans \(\left( Ph - CH = CH - CH _3\right) \rightarrow \operatorname{cis}\left( Ph - CH = CH - CH _3\right)\)

• (1) \(Br _2\), alc \(\cdot KOH , NaNH _2, Na \left( Liq NH _3\right)\)
• (2) \(Br _2\), alc \(\cdot KOH , NaNH _2, H _2\) Lindlar Catalyst
• (3) \(Br _2\), aq \(\cdot KOH , NaNH _2, H _2\) Lindlar Catalyst
• (4) \(Br _2, aq \cdot KOH , NaNH _2, Na \left( Liq NH _3\right)\)

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from \(n =4\) to \(n =2\) of \(He ^{+}\)spectrum

• (1) \(n =1\) to \(n =3\)
• (2) \(n =1\) to \(n =2\)
• (3) \(n =2\) to \(n =1\)
• (4) \(n =3\) to \(n =4\)

Which one of the following statements is correct for electrolysis of brine solution?

• (1) \(OH ^{-}\)is formed at cathode
• (2) \(Cl _2\) is formed at cathode
• (3) \(O _2\) is formed at cathode
• (4) \(H _2\) is formed at anode

Cobalt chloride when dissolved in water forms pink colored complex \(X\) which has octahedral geometry. This solution on treating with cone \(HCl\) forms deep blue complex, \(\underline{Y}\) which has a \(\underline{Z}\) geometry \(X, Y\) and \(Z\), respectively, are

• (1) \(X =\left[ Co \left( H _2 O \right)_4 Cl _2\right]^{+}, Y =\left[ CoCl _4\right]^{2-}, Z =\) Tetrahedral
• (2) \(X =\left[ Co \left( H _2 O \right)_6\right]^{2+}, Y =\left[ CoCl _6\right]^{3-}, Z =\) Octahedral
• (3) \(X =\left[ Co \left( H _2 O \right)_6\right]^{2+}, Y =\left[ CoCl _4\right]^{2-}, Z =\) Tetrahedral
• (4) \(X =\left[ Co \left( H _2 O \right)_6\right]^{3+}, Y =\left[ CoCl _6\right]^{3-}, Z =\) Octahedral

An organic compound 'A' with emperical formula \(C _6 H _6 O\) gives sooty flame on burning Its reaction with bromine solution in low polarity solvent results in high yield of \(B .B\) is

• (1)
• (2)
• (3)
• (4)

Match List I with List II 

Choose the correct answer from the options given below :

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

The methods NOT involved in concentration of ore are
A Liquation
B Leaching
C Electrolysis
D Hydraulic washing
E Froth floatation
Choose the correct answer from the options given below :

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

Identify \(X , Y\) and \(Z\) in the following reaction (Equation not balanced) \(ClO + NO _2 \rightarrow \underline{ X } \stackrel{ H _2 O }{\longrightarrow} \underline{ Y }+\underline{Z}\)

• (1) \(X = ClNO _3, Y = Cl _2, Z = NO _2\)
• (2) \(X = ClONO _2, Y = HOCl , Z = HNO _3\)
• (3) \(X = ClONO _2, Y = HOCl , Z = NO _2\)
• (4) \(X = ClNO _2, Y = HCl , Z = HNO _3\)

Adding surfactants in non polar solvent, the micelles structure will look like

• (1) d
• (2) c
• (3) b
• (4) a

\(H _2 O _2\) acts as a reducing agent in

• (1) \(Na _2 S +4 H _2 O _2 \rightarrow Na _2 SO _4+4 H _2 O\)
• (2) \(Mn ^{2+}+2 H _2 O _2 \rightarrow MnO _2+2 H _2 O\)
• (3) \(2 Fe ^{2+}+2 H ^{+}+ H _2 O _2 \rightarrow 2 Fe ^{3+}+2 H _2 O\)
• (4) \(2 NaOCl + H _2 O _2 \rightarrow 2 NaCl + H _2 O + O _2\)

Which of the following artificial sweeteners has the highest sweetness value in comparison to cane sugar?

• (1) Alitane
• (2) Saccharin
• (3) Aspartame
• (4) Sucralose

Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride The volume of hydrogen gas produced at STP from the reaction of \(115 \, g\) of zine with excess \(HCl\) is ___\(L\) (Nearest integer)
(Given: Molar mass of \(Zn\) is \(654 \,g \,mol ^{-1}\) and Molar volume of \(H _2\) at \(STP =227 \,L\) )

The logarithm of equilibrium constant for the reaction \(Pd ^{2+}+4 Cl ^{-} \rightleftharpoons PdCl _4^{2-}\) is (Nearest integer) Given : \(\frac{230RT }{ F }=006 V\) \(Pd _{\text {(aq) }}^{2+}+2 e ^{-} \rightleftharpoons Pd ( s ) \quad E ^{\ominus}=083 V\) \(PdCl _4^{2-} \text { (aq) }+2 e ^{-} \rightleftharpoons Pd ( s )+4 Cl ^{-} \text {(aq) } E ^{\ominus}=065 V\)

The enthalpy change for the conversion of \(\frac{1}{2} Cl_2(g)\) to \(Cl^{-}(aq)\) is (-)_____________ \(KJ mol^{-1}\) (Nearest integer)
Given : \(\Delta_{\text {dis }} H _{ Cl _{2( g )}}^{\ominus}=240\, kJ \,mol ^{-1}\), \(\Delta_{ eg } H _{ Cl }^{\ominus}=-350\, kJ \,mol ^{-1}\), \(\Delta_{\text {hyd }} H ^\theta Cl _{( g )}^{-}=-380 \,kJ \,mol ^{-1}\)

On complete combustion, \(0.492\, g\) of an organic compound gave \(0.792 \,g\) of \(CO _2\) The \(\%\) of carbon in the organic compound is(Nearest integer)

At \(27^{\circ} C\), a solution containing \(25 \,g\) of solute in \(2500 \,mL\) of solution exerts an osmotic pressure of \(400 \,Pa\). The molar mass of the solute is ____ \(g\,mol ^{-1}\). (Nearest integer)
(Given : \(R =0.083 \,L\,bar\, K ^{-1} \,mol ^{-1}\) )

The oxidation state of phosphorus in hypophosphoric acid is + _____

How many of the transformations given below would result in aromatic amines?

\(A \rightarrow B\) The rate constants of the above reaction at \(200 K\) and \(300 K\) are \(0.03 \min ^{-1}\) and \(0.05 \min ^{-1}\) respectively The activation energy for the reaction is __\(J\) (Nearest integer) (Given \(: \ln 10=2.3\) 

\(R =8.3 \,JK ^{-1} \,mol ^{-1}\) 

\(\log 5=0.70\) 

\(\log 3=0.48\) 

\(\log 2=0.30)\)

For reaction : \(SO _2( g )+\frac{1}{2} O _2( g )= SO _3( g )\)\(K _{ p }=2 \times 10^{12}\) at \(27^{\circ} C\) and 1 atm pressure The \(K _{ c }\) for the same reaction is ____\(\times 10^{13}\) (Nearest integer)(Given \(R =0.082 \,L \,atm \,K ^{-1} \,mol ^{-1}\) )

The total pressure of a mixture of non-reacting gases \(X (0.6 \,g )\) and \(Y (0.45 \, g )\) in a vessel is \(740 mm\) of \(Hg\) The partial pressure of the gas \(X\) is ____\(mm\) of \(Hg\)(Nearest Integer)(Given : molar mass \(X =20\) and \(Y =45 \, g \, mol ^{-1}\) )