Sample papers for JEE Main & Advanced JEE Main Sample Paper-5

1) The relation between the time periods in two cases =, if the spring of first case is cut into two equal parts and used as shown

A) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{1}{2}\]

B) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{2}{1}\]

C) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{1}{\sqrt{2}}\]

D) \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{\sqrt{2}}{1}\]

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2) Two Blocks are placed over a rough pulley of moment of inertia I when the block of mass m comes down by a distance h, the angular of the pulley is

A) \[\sqrt{\frac{2gh}{(M+m){{r}^{2}}+l}}\]

B) \[\sqrt{\frac{2(M+m)gh}{(M-m){{r}^{2}}+l}}\]

C) \[\sqrt{\frac{2Mgh}{(M-m){{r}^{2}}+l}}\]

D) \[\sqrt{\frac{2(M-m)gh}{(M+m){{r}^{2}}+l}}\]

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3) The equivalent capacitance between M and N is

A) \[8\mu F\]

B) \[2\mu F\]

C) \[4\mu F\]

D) \[6\mu F\]

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4) Poise is the CGS unit of coefficient of viscosity. Suppose we employ a system of units in which unit of mass is a kg, the unit of length is P metre and unit of time is y s. In this new system, 1Poise is equal to

A) \[1000\alpha {{\beta }^{-1}}{{\gamma }^{-1}}\]

B) \[10\alpha {{\beta }^{-1}}{{\gamma }^{-1}}\]

C) \[0.1{{\alpha }^{-1}}\beta \gamma \]

D) \[0.01{{\alpha }^{-1}}\beta \gamma \]

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5) A uniform metal disc of radius R is taken and out of it a disc of diameter R/2 is cut-off from the end. The centre of mass of the remaining part will be

A) \[\frac{R}{4}\]from the centre

B) \[\frac{R}{3}\]from the centre

C) \[\frac{R}{5}\]from the centre

D) \[\frac{R}{6}\]from the centre

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6) A milliammeter of range 10 mA has a coil of resistance\[1\Omega \]. To use it as an ammeter of range 1 A, the required shunt must have a resistance of

A) \[\frac{1}{101}\Omega \]

B) \[\frac{1}{100}\Omega \]

C) \[\frac{1}{99}\Omega \]

D) \[\frac{1}{9}\Omega \]

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7) The electron in a H-atom makes transition\[{{n}_{1}}\to {{n}_{2}}\]where, \[{{n}_{1}}\]and\[{{n}_{2}}\]are principal quantum numbers of two states. Assume the Bohr model to be valid. The time period of the electron in the initial state is eight times the final state. Then, the possible value of\[{{n}_{1}}\]and\[{{n}_{2}}\]are

A) \[{{n}_{1}}=4;{{n}_{2}}=1\]

B) \[{{n}_{1}}=8,{{n}_{2}}=2\]

C) \[{{n}_{1}}=6,{{n}_{2}}=2\]

D) \[{{n}_{1}}=4,{{n}_{2}}=2\]

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8) An ideal ammeter and an ideal voltmeter are connected as shown. The ammeter and voltmeter reading for the circuit having\[{{R}_{1}}=5\Omega \],\[{{R}_{2}}=15\Omega \],\[{{R}_{3}}=1.25\Omega \]and\[E=20\]V are given as

A) 6.25 A, 3.75 V

B) 3.00 A, 5 V

C) 3.75 A, 3.75V

D) 3.75 A, 6.25 V

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9) The gravitation field (g) inside the earth is proportional to r as (where, r is distance from the centre)

A) \[\frac{1}{r}\]

B) \[\frac{1}{{{r}^{2}}}\]

C) \[{{r}^{2}}\]

D) \[r\]

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10) Two blocks are placed on a wedge with coefficients of friction being different for two blocks. Choose the correct option (friction is not sufficient to prevent the motion)

A) if\[{{m}_{1}}<{{m}_{2}}\], then normal reaction between blocks will be non-zero

B) if\[{{m}_{1}}={{m}_{2}}\]then normal reaction between the blocks will be zero

C) if\[{{\mu }_{1}}={{\mu }_{2}}\], then normal reaction between the blocks will be zero

D) None of the above

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11) A rod of mass M which is non-uniformly distributed over its length L has been considered. Its linear mass density variation with distance x from left end is shown in the figure. From this information, we can conclude that the centre of mass of rod

A) is on left of its mid-point

B) is on right of its mid-point

C) is coinciding with its mid-point

D) information is insufficient

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12) For a system of two springs and block system, choose the correct option.

A) for the equilibrium position (about which oscillation occur), the stretch is\[x=\frac{mg}{k}\]

B) the time period of oscillation is\[2\pi \sqrt{\frac{m}{2k}}\]

C) Both [a] and [b] are correct

D) Both [c] and [b] are incorrect

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13) Figure shows an Amperian path ABCDA. Part ABC is in vertical plane PSTU while part CDA is in horizontal plane PQRS. Direction of circulation along the path is shown by an arrow near points B and D. \[\oint{\mathbf{B}dI\,\,l}\]for this path according to Ampere's law will be

A) \[(-{{i}_{1}}-{{i}_{2}}+{{i}_{3}}){{\mu }_{0}}\]

B) \[(-{{i}_{1}}+{{i}_{2}}){{\mu }_{0}}\]

C) \[{{i}_{3}}{{\mu }_{0}}\]

D) \[({{i}_{1}}+{{i}_{2}}){{\mu }_{0}}\]

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14) The relation between\[{{v}_{1}}\]and\[{{v}_{2}}\]is

A) \[{{v}_{1}}=\frac{{{v}_{2}}}{\sin \theta }\]

B) \[{{v}_{1}}={{v}_{2}}\]

C) \[{{v}_{2}}=\frac{{{v}_{1}}}{\sin \theta }\]

D) \[d{{v}_{1}}={{v}_{2}}\cos \theta \]

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15) In the figure shown, the magnetic field at the point P is

A) \[\frac{2{{\mu }_{0}}i}{3\pi a}\sqrt{4-{{\pi }^{2}}}\]

B) \[\frac{2{{\mu }_{0}}i}{3\pi a}\sqrt{4+{{\pi }^{2}}}\]

C) \[\frac{2{{\mu }_{0}}i}{3\pi a}(4+{{\pi }^{2}})\]

D) \[\frac{2{{\mu }_{0}}i}{3\pi a}(4-{{\pi }^{2}})\]

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16) Directions (Q. No. 16): A voltage source\[V={{V}_{0}}\sin \] (100 t) is connected to a black box in which there can be either one element out of L, C, R or any two of them connected in series. At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope as shown The element(s) present in black box is/are

A) only C

B) L and C

C) L and R

D) R and C

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17) Directions (Q. No. 16): A voltage source\[V={{V}_{0}}\sin \] (100 t) is connected to a black box in which there can be either one element out of L, C, R or any two of them connected in series. At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope as shown Values of the parameters of the elements, present in the black box are

A) \[R=50\Omega \,C=200\mu F\]

B) \[R=50\,\Omega \,L=2mH\]

C) \[R=400\,\Omega ,\,C=50\mu F\]

D) \[R=50\,\Omega ,\,L=02H\]

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18) Directions (Q. No. 16): A voltage source\[V={{V}_{0}}\sin \] (100 t) is connected to a black box in which there can be either one element out of L, C, R or any two of them connected in series. At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope as shown If AC source is removed, the circuit is shorted and then at t = 0, a battery of constant emf is connected across the black box. The current in the circuit will

A) increase exponentially with constant\[4\times {{10}^{-3}}\]s

B) decrease exponentially with time constant\[1\times {{10}^{-2}}\]

C) oscillate with angular frequency\[20\,{{s}^{-1}}\]

D) first increase and then decrease

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19) Two blocks of same masses are attached with two rough pulleys of moment of inertia\[{{I}_{1}}\]and\[{{I}_{2}}\]. If both the blocks left at the same instant and let after time t the angular speeds of two pulleys are\[{{\omega }_{1}}\]and\[{{\omega }_{2}}\]then

A) \[{{\omega }_{1}}={{\omega }_{2}}\]

B) \[{{\omega }_{1}}>{{\omega }_{2}}\]

C) \[{{\omega }_{1}}<{{\omega }_{2}}\]

D) Information insufficient

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20) Two mirrors, placed perpendicularly form two sides of a vessel filled with water. A light ray is incident on the water surface at an angle\[\alpha \]and emerges at an angle\[\beta \]after getting reflected from both the mirrors inside. The relation between\[\alpha \]and\[\beta \]is expressed as

A) \[\alpha =\beta \]

B) \[\alpha >\beta \]

C) \[\alpha <\beta \]

D) All are possible depending upon\[\alpha \]

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21) Two waves are represented as\[{{y}_{1}}=2a\,\sin \left( \omega t+\frac{\pi }{6} \right)\]and\[{{y}_{2}}=-2a\,\cos \left( \omega t+\frac{\pi }{6} \right)\]. The phase difference between the two waves is

A) \[\frac{\pi }{3}\]

B) \[\frac{4\pi }{3}\]

C) \[\frac{3\pi }{3}\]

D) \[\frac{5\pi }{6}\]

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22) For a capacitor Q = CV, so choose the correct option.

A) Q is the net charge on the capacitor

B) C depends on Q and V

C) C do not depend on Q

D) V is the potential of a single plate of the capacitor (if we assuming parallel plate capacitor)

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23) The value of time constant for given circuit is

A) 1s

B) 2 s

C) 3 s

D) 4 s

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24) If g be the acceleration due to gravity and K be the rotational kinetic energy of the earth. If the earth's radius increases by 2% keeping mass constant, then

A) Both decrease by 4%

B) g decrease by 4% and K decrease by 2%

C) Both decrease by 2%

D) g decrease by 4% and K increase by 4%

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25) A car accelerates from rest in the 1st part of its journey with a m/s2 and then it retards with 2a m/s2 so as to bring it to rest again. If t is the total time of journey, then the distance travelled by car is

A) \[\frac{a{{t}^{2}}}{3}\]

B) \[\frac{a{{t}^{2}}}{2}\]

C) \[a{{t}^{2}}\]

D) \[\frac{a{{t}^{2}}}{4}\]

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26) At rest, a liquid stands at the same level in the tubes. As the system is given an acceleration a towards the right. A height difference h occurs as shown in the figure. The value of h is

A) \[\frac{aL}{2g}\]

B) \[\frac{gL}{2a}\]

C) \[\frac{gL}{a}\]

D) \[\frac{aL}{g}\]

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27) Frequencies higher than 10 MHz were found not being reflected by the ionosphere on a particular day. The maximum electron density of the ionosphere on the day was near to

A) \[\tilde{\ }{{10}^{10}}/{{m}^{-3}}\]

B) \[\tilde{\ }{{10}^{11}}{{m}^{-3}}\]

C) \[\tilde{\ }{{10}^{12}}{{m}^{-3}}\]

D) \[\tilde{\ }{{10}^{13}}{{m}^{-3}}\]

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28) If the magnitude of tangential and normal accelerations of a particle moving on a curve in a plane be constant throughout, then which of the following represent the variation of radius of curvature with time?

A)

B)

C)

D)

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29)

Statement I Work done by static friction could be negative.

Statement II When static friction acts on a body that body must have zero KE.

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is true but Statement II is false

D) Both Statement I and Statement II are false

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30)

Statement I A ball is left from a tower. The ball will cover same distance in consecutive seconds.

Statement II The distance covered in a second for free fall\[=\frac{1}{2}g{{t}^{2}}\].

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is false but Statement II is true

D) Both Statement I and Statement II are false

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31) Which of the following have X-O-X linkage? (where, X is central atom) (i) Pyro silicate (ii) \[C{{r}_{2}}O_{7}^{2-}\] (iii) \[{{S}_{2}}O_{3}^{2-}\] (iv) Hyponitrous acid

A) (II), (III)

B) (II), (I)

C) (I), (III), (IV)

D) All have X-O-X linkage

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32) Associated colloids

A) raise both surface tension and viscosity

B) have greater concentration at the surface layer than the bulk of the solution

C) lower both the surface tension and viscosity

D) lower the surface tension and raise the viscosity of \[{{H}_{2}}O\]

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33) Which of the following compound does not formed during Lassaigne's test?

A) ferricferro cyanide

B) ferricthiocyanide

C) silver chloride

D) ferric cyanide

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34) A certain compound A when treated with copper sulphate solution yields a brown precipitate. On adding hypo solution, the precipitate turns white. The compound will be

A) \[{{K}_{3}}P{{O}_{4}}\]

B) \[KBr\]

C) \[{{K}_{2}}C{{O}_{3}}\]

D) Kl

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35) If \[{{a}_{0}}\] be the radius of first Bohr's orbit of H-atom, the de-Broglie's wavelength of an electron revolving in the third Bohr's orbit will be

A) \[6\pi {{a}_{0}}\]

B) \[4\pi {{a}_{0}}\]

C) \[2\pi {{a}_{0}}\]

D) \[\pi {{a}_{0}}\]

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36) How many isomeric forms are possible for a tripeptide equally composed of L-valine, L-tyrosine and L-analine?

A) 3

B) 4

C) 6

D) 8

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37) \[{{A}_{2}}{{B}_{3}}\]is sparingly soluble salt of molecular weight M and solubility x g/L. The ratio of the molar concentration of \[[{{B}^{2-}}]\]to the solubility product of the solution will be

A) \[\frac{7{{M}^{4}}}{54{{x}^{4}}}\]

B) \[\frac{3}{28\,}\frac{{{M}^{4}}}{{{x}^{4}}}\]

C) \[\frac{{{M}^{4}}}{36{{x}^{4}}}\]

D) \[\frac{36{{M}^{4}}}{{{x}^{4}}}\]

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38) A metal M readily forms water soluble sulphates and water soluble hydroxide M(OH)a. Its oxide MO is amphoteric, hard and possesses high melting point. The hydroxide is also amphoteric in nature. The alkaline earth's metal M will be

A) Ba

B) Mg

C) Be

D) Ca

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39) Arrange the following in decreasing order of their reactivity toward S^ reaction. 1. \[M{{e}_{3}}C{{O}^{-}}\] 2. \[Me{{O}^{-}}\] 3. \[MeC{{H}_{2}}{{O}^{-}}\] 4. \[M{{e}_{2}}CH{{O}^{-}}\] 5.

A) 2 > 3 > 5 > 4 > 1

B) 5 > 3 > 2 > 1 > 4

C) 1 > 5 > 2 > 3 > 4

D) 3 > 5 > 1 > 2 > 3

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40) A vessel of uniform cross-section of length 250 cm as shown in figure is divided in two parts by a weightless and frictionless piston. One part contains 5 moles of He (g) and other part 2 moles of \[{{\text{H}}_{\text{2}}}\] (g) and 10 moles of \[{{\text{O}}_{\text{2}}}\] (g) added at the same temperature and pressure. In which reaction takes place, finally vessel cooled to 350 K and 1 atm. What is length of compartment? (Assume piston volume and \[{{H}_{2}}O(l)\] volume is negligible)

A) 89.28cm

B) 200 cm

C) 250 cm

D) 312.5 cm

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41) When \[Ca{{C}_{2}}\]is hydrolysed it produces a gas which when treated with red hot tube it produces an organic compound A which on reaction with excess of \[C{{l}_{2}}\] produces a chemical compound which is used to kill insecticide [B]. Identify B

A) benzene

B) BHC (Benzene Hexa Chloride)

C) chloro benzene

D) trichloro benzene

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42) In the extraction of aluminium, Process X applied for red bauxite to remove iron oxide (main impurity). Process Y (Serpech's process) Applied for white bauxite to remove Z (main impurity), then Process X and impurity Z are

A) X = Serpech's process and\[Z=F{{e}_{2}}{{O}_{3}}\]

B) X = Bayer's process and \[Z=FeO\]

C) X = Hall and Heroullt's process and\[Z=Si{{O}_{2}}\]

D) X = Bayer's process and \[Z=Si{{O}_{2}}\]

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43) x g of non-electrolyte compound of molecular mass 200, when dissolved in 1L of 0.05 M NaCl solution, the osmotic pressure of the resulting solution is found to be 4.92 atm at \[27{}^\circ C\]. Assuming the complete dissociation of NaCI and ideal behaviour of solution, the value of x would be

A) 10 g

B) 20.0g

C) 40.0 g

D) 80.0 g

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44) Compound X and Y are treated with dilute \[{{H}_{2}}S{{O}_{4}}\] separately. The gases liberated are P and Q. P turns acidified \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] paper green while gas Q turns lead acetate paper black. The compounds X and y are

A) \[N{{a}_{2}}S{{O}_{3}}\]and\[N{{a}_{2}}S\]

B) \[N{{a}_{2}}C{{O}_{3}}\]and\[N{{a}_{2}}S\]

C) \[NaCl\]and\[N{{a}_{2}}S{{O}_{3}}\]

D) \[N{{a}_{2}}S{{O}_{3}}\]and\[N{{a}_{2}}S{{O}_{4}}\]

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45) Identify the correct product of following reaction.

A)

B)

C)

D)

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46) Some half-cell reaction and their standard potentials are given as below \[MnO_{4}^{-}(aq)+8{{H}^{+}}(aq)+5{{e}^{-}}\xrightarrow[{}]{{}}\]\[M{{n}^{2+}}(aq)+4{{H}_{2}}O(l);\] \[{{E}^{0}}=-1.51\text{V}\] \[C{{r}_{2}}O_{7}^{2-}(aq)+14{{H}^{+}}(aq)+6{{e}^{-}}\xrightarrow[{}]{{}}\] \[2C{{r}^{3+}}(aq)+7{{H}_{2}}O(l);\] \[{{E}^{0}}=-1.38\text{V}\] \[F{{e}^{3+}}(aq)+{{e}^{-}}\xrightarrow[{}]{{}}F{{e}^{2+}}(aq);\] \[{{E}^{0}}=0.77\,\text{V}\] \[C{{l}_{2}}(g)+2{{e}^{-}}\xrightarrow[{}]{{}}2C{{l}^{-}}(aq);\] \[{{E}^{0}}=1.40\,\text{V}\] Identify the incorrect statement.

A) \[MnO_{4}^{-}\]is weaker oxidising agent than \[C{{l}_{2}}\]

B) \[C{{r}_{2}}O_{7}^{2-}\] is weaker oxidising agent than \[C{{l}_{2}}\]

C) \[MnO_{4}^{-}\] is stronger oxidising agent than \[F{{e}^{3+}}\]

D) \[C{{r}_{2}}O_{7}^{2-}\]is weaker oxidising agent than\[MnO_{4}^{-}\]

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47) What will be the degree of un saturation in the product when a compound having molecular formula \[{{C}_{4}}{{H}_{6}}BrCl\] is treated with metallic sodium in ether? Given that halogens are present on opposite comer in a cyclic compound.

A) 2

B) 1

C) 0

D) 3

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48) \[\underset{\begin{smallmatrix} \text{Imparts}\,\text{violet} \\ \text{colour}\,\text{to}\,\text{flame} \end{smallmatrix}}{\mathop{\text{A}}}\,\xrightarrow[{}]{\text{compound}\,\text{(P)+conc}\text{.}{{\text{H}}_{\text{2}}}\text{S}{{\text{O}}_{\text{4}}}}\underset{\text{Red}\,\text{gas}}{\mathop{\text{B}}}\,\xrightarrow[{}]{\text{NaOH+AgN}{{\text{O}}_{\text{3}}}}\]\[\underset{\text{Red}\,\text{ppt,}}{\mathop{\text{C}}}\,\xrightarrow[\text{solution}]{\text{N}{{\text{H}}_{\text{3}}}}\text{D}\]\[\text{C}\xrightarrow[{}]{\text{Dil}\,\text{HCl}}\text{X}\]white ppt. \[\text{P}\xrightarrow[\text{Heat}]{\text{NaOH}}\text{Q}\]Gas (gives white fumes with HCl) Then, A, B, C, D, X , P and Q are

A) \[{{K}_{2}}C{{r}_{2}}{{O}_{7}},Cr{{O}_{2}}C{{l}_{2}},A{{g}_{2}}Cr{{O}_{4}},{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}},\]\[AgCl,N{{H}_{4}}Cl\]and\[N{{H}_{3}}\]

B) \[{{K}_{2}}Cr{{O}_{4}},C{{l}_{2}},A{{g}_{2}}Cr{{O}_{4}},AgN{{O}_{3}},AgCl,N{{H}_{4}}Cl\]and\[N{{H}_{3}}\]

C) \[KMn{{O}_{4}},C{{l}_{2}},A{{g}_{2}}Cr{{O}_{4}},{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}},\]\[AgCl{{(N{{H}_{4}})}_{2}}S{{O}_{4}},\]and\[{{N}_{2}}\]

D) \[KMn{{O}_{4}},Cr{{O}_{2}}C{{l}_{2}},A{{g}_{2}}(Cr{{O}_{4}}),{{[Ag{{(N{{H}_{3}})}_{2}}]}^{+}},\]\[AgN{{O}_{3}},N{{H}_{4}}Cl\]and\[{{N}_{2}}\]

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49) Which of the catalyst is used to preparation of polymer having specific stereochemistry?

A) \[TiC{{l}_{3}}+Al{{({{C}_{2}}{{H}_{5}})}_{3}}\]

B) \[TiC{{l}_{4}}+Al{{({{C}_{2}}{{H}_{5}})}_{3}}\]

C) \[Ti{{({{C}_{2}}{{H}_{5}})}_{4}}+AlC{{l}_{3}}\]

D) \[Ti{{({{C}_{2}}{{H}_{5}})}_{3}}+AlC{{l}_{3}}\]

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50) The best hydride donor intermediate in Cannizaro reaction will be

A)

B)

C)

D)

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51) If in this reaction two isomers of the product are obtained. Which statement is true for the initial (reactant) complex? \[{{[CoC{{l}_{2}}{{(N{{H}_{3}})}_{4}}]}^{+}}+C{{l}^{-}}\xrightarrow[{}]{{}}[CoC{{l}_{3}}{{(N{{H}_{3}})}_{3}}]\]\[+N{{H}_{3}}\]

A) Compound is in transform

B) Compound is in cis-form

C) Compound is in both (cis and trans)-form

D) Cannot be predicted

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52) In an iodometric estimation, following reactions occur. \[2C{{u}^{2}}+4{{I}^{-}}\xrightarrow[{}]{{}}C{{u}_{2}}{{I}_{2}}+{{I}_{2}}\] \[{{I}_{2}}+2N{{a}_{2}}{{S}_{2}}{{O}_{3}}\xrightarrow[{}]{{}}2NaI+N{{a}_{2}}{{S}_{4}}{{O}_{6}}\] 0.24 mole of \[CuS{{O}_{4}}\] was added to excess of KI solution and the liberated iodine required 240 mL of hypo. Then, find the molarity of hypo solution.

A) 5.0

B) 3.0

C) 1.0

D) 5.5

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53) Which of the following statement is correct regarding given figure.

A) This figure represents an emulsion of phase II in phase I

B) Two immiscible, liquid, not yet emulsified

C) this figure represents associated colloid

D) this can be separated using elect osmosis

View Answer

54) For reaction \[A\to B\]the rate constant \[{{k}_{1}}={{A}_{1}}{{e}^{-{{E}_{{{a}_{1}}}}/RT}}\] and for the reaction \[X\to Y\] the rate constant \[{{k}_{1}}={{A}_{2}}\,{{e}^{-{{E}_{{{a}_{2}}}}/RT}}\], if \[{{A}_{1}}={{10}^{10}}\],\[{{A}_{2}}={{10}^{12}}\] and \[{{E}_{{{a}_{1}}}}=800\,\text{cal/mol}\],\[{{E}_{{{a}_{2}}}}=1600\,\text{cal/mol}\], then temperature at which \[{{k}_{1}}={{k}_{2}}\] is (given R = 2 cal/K-mol)

A) \[\left( \frac{200}{0.693} \right)K\]

B) \[200\times 0.693K\]

C) \[\left( \frac{400}{0.693} \right)K\]

D) \[400\times 0.693K\]

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55) Benzaldehyde undergo Claisen condensation to give cinnamaldehyde on reaction with \[[\alpha ]\] in presence of base, \[[\alpha ]\]and degree of unsaturation in cinnamaldehyde is

A) formaldehyde, 3

B) acetaldehyde, 6

C) crotonaldehyde, 4

D) propanaldehyde, 6

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56) Consider the following reaction.\[N{{O}_{2}}+NaOH\xrightarrow[{}]{{}}X+Y+{{H}_{2}}O\]. Which of the following statement is correct?

A) Both X and Y on treatment with Zn and NaON produce \[{{N}_{2}}\]

B) Both X and Y on heating with Na form \[{{N}_{2}}\]

C) Both [a] and [b] are correct

D) None of the above

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57) Determine \[\Delta {{U}^{o}}\]at 400 K for the following reaction using the listed enthalpies of reaction. \[4CO(g)+8{{H}_{2}}(g)\xrightarrow[{}]{{}}\] \[3C{{H}_{4}}(g)+C{{O}_{2}}(g)+2{{H}_{2}}O(l)\]

\[C\,\text{(graphite)+}\frac{1}{2}{{O}_{2}}\xrightarrow[{}]{{}}CO(g),\]	\[\Delta H_{1}^{o}=-110.5\,\text{kJ}\]
\[CO\,\text{(g)}\,\text{+}\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}CO(g),\]	\[\Delta H_{2}^{o}=-282.9\,\text{kJ}\]
\[{{H}_{2}}\,\text{(g)}\,\text{+}\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}{{H}_{2}}O(l),\]	\[\Delta H_{3}^{o}=-285.8\,\text{kJ}\]
\[C\,\text{(graphite)}\,+2{{H}_{2}}(g)\xrightarrow[{}]{{}}C{{H}_{4}}(g),\]	\[\Delta H_{4}^{o}=-74.8\,\text{kJ}\]

A) - 750.69 kJ

B) - 820.79 kJ

C) - 720.79 kJ

D) - 1000.79 kJ

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58) The major product obtained after reaction and number of chiral centre is

A)

B)

C)

D)

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59)

Statement I Central atom of peroxy disulphuric acid is sp3 hybridised.

Statement II This is due to the presence of peroxy linkage (-O-O-) is peroxy disulphuric agent.

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is true but Statement II is false

D) Both Statement I and Statement II are false

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60)

Statement I All the values \[\Delta G,\Delta H,\Delta S\]must have negative value for adsorption.

Statement II Adsorption is a spontaneous as well as exothermic process in which randomness decreases. The decrease in randomness is due to increase in attraction between adsorbate and adsorbent.

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is true but statement II is false

D) Both Statement I and Statement II are false

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61) The volume of tetrahedron with one of the vertex at origin and the others 3 at points A (3, 4, 2) B (0, 4, 1) and C (1, 0, 0) is

A) \[\frac{1}{3}\]cubic unit

B) \[\frac{1}{4}\]cubic unit

C) \[\frac{2}{5}\]cubic unit

D) \[\frac{2}{3}\]cubic unit

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62) \[\alpha \]and \[\beta \]are cube roots of unity, then \[{{\alpha }^{4}}+{{\beta }^{4}}+{{\alpha }^{-1}}{{\beta }^{-1}}\]is equal to

A) 1

B) 0

C) -1

D) None of these

View Answer

63) \[\int_{{}}^{{}}{\frac{{{x}^{8}}+4}{{{x}^{4}}-2{{x}^{2}}+2}dx,}\]then which of the following is correct?

A) \[\frac{{{x}^{5}}}{5}-\frac{2{{x}^{3}}}{3}+2x+C\]

B) \[\frac{{{x}^{5}}}{5}-\frac{2{{x}^{3}}}{3}-2x+C\]

C) \[\frac{{{x}^{5}}}{5}+\frac{2{{x}^{3}}}{3}-2x+C\]

D) \[\frac{{{x}^{5}}}{5}+\frac{2{{x}^{3}}}{3}+2x+C\]

View Answer

64) The value of \[\theta \] in \[[0,2\pi ]\] such that the matrix \[\left[ \begin{matrix} 2\sin \theta -1 & \sin \theta & \cos \theta \\ \sin (\theta +\pi ) & 2\cos \theta -\sqrt{3} & \tan \theta \\ \cos (\theta -\pi ) & \tan (\pi -\theta ) & 0 \\ \end{matrix} \right]\] is a skew symmetric is

A) \[\frac{\pi }{2}\]

B) \[\frac{\pi }{3}\]

C) \[\frac{\pi }{4}\]

D) \[\frac{\pi }{6}\]

View Answer

65) If letup rectum of the ellipse x2 tan2 \[\alpha \] + y2 sec2 \[\alpha \] = 1 is 1/2, then \[\alpha \] \[(0<\alpha <\pi /3)\] is equal to

A) \[\pi /6\]

B) \[\pi /12\]

C) \[\pi /4\]

D) \[3\pi /4\]

View Answer

66) The interval of a for which (a, a2, a) and (3, 2,1) lies on same side of\[x+y-4z+2=0\]is

A) \[(\infty ,1]\cup (2,\infty ]\]

B) \[[-\infty ,1)\cup [2,\infty )\]

C) \[(-\infty ,2]\cup (3,\infty ]\]

D) \[(-\infty ,2)\cup [3,\infty )\]

View Answer

67) The set of points of continuity of the function \[f(x)=\sqrt{\frac{1}{2}-{{\cos }^{2}}x,}\] is

A) \[\left\{ x:\frac{\pi }{4}+2n\,\pi \le x\le \frac{3\pi }{4}+2n\pi ;n\in l \right\}\]

B) \[\left\{ x:\frac{5\pi }{4}+2n\,\pi \le x\le \frac{7\pi }{4}+2n\,\pi ;n\in l \right\}\]

C) \[\left\{ x:\frac{\pi }{4}+2n\,\pi \le x\le \frac{3\pi }{4}+2n\,\pi \right\}\cup \]\[\left\{ x:\frac{5\pi }{4}+2n\,\pi \le x\le \frac{7\pi }{4}+2n\,\pi \right\}\]

D) None of the above

View Answer

68) The solution of differential equation (x2 - 2xy] dy + [x2 - 3xy + 2y2) dx = 0, is

A) \[kx={{e}^{-y/x}}\]

B) \[kx={{e}^{y/x}}\]

C) \[kx={{e}^{x/y}}\]

D) \[kx={{e}^{-x/y}}\]

View Answer

69) A pack of playing cards was found to contain only 51 cards. If the first 13 cards, which are examined are all red, the probability that the missing card is black is

A) \[\frac{2}{3}\]

B) \[\frac{1}{3}\]

C) \[\frac{2}{9}\]

D) None of these

View Answer

70) The angle of intersection of the curves x2 - y2 = a2 and \[{{x}^{2}}+{{y}^{2}}={{\sqrt{2a}}^{2}}\] is

A) \[3\pi /4\]

B) \[\pi /2\]

C) \[\pi /6\]

D) \[\pi /4\]

View Answer

71) Area of a triangle formed by the lines x2 + 4xy + y2 = 0 and x + y = 1 is

A) \[\sqrt{3}\]

B) 2

C) 1

D) \[\frac{\sqrt{3}}{2}\]

View Answer

72) \[\sum\limits_{r=1}^{20}{\,\,\sum\limits_{p=1}^{r}{{{p}^{2}}}}\]is equal to

A) 16170

B) 13300

C) 16100

D) None of these

View Answer

73) If p, q and r are false statements, then which among the following is false?

A) \[\tilde{\ }q\vee r\] is true

B) \[\tilde{\ }r\vee q\]is true

C) \[\tilde{\ }(q\vee r)\wedge (\tilde{\ }r\,\vee q)\]is false

D) \[p\wedge [\tilde{\ }q\vee r)\wedge (\tilde{\ }r\,\vee q)]\]is false

View Answer

74) The graph of the function y = f[x} = cos x cos [x + 2) - cos2 [x + 1) is

A) a straight line through \[(0,-{{\sin }^{2}}1)\] with slope 2

B) a straight line through (0, 0)

C) a parabola with vertex \[(1,-{{\sin }^{2}}1)\]

D) a straight line through \[\left( \frac{\pi }{2},-{{\sin }^{2}}1 \right)\] and parallel to x-axis

View Answer

75) The point of intersection of less than ogive and greater than ogive is known as

A) median

B) mode

C) mean

D) None of these

View Answer

76) 10 different letters of english alphabet are given words of 5 letters are formed from these given letters. How many words are formed when at least one letter is repeated?

A) 69760

B) 2912

C) 98748

D) 987147

View Answer

77) The unit digit of \[{{17}^{1983}}+{{11}^{1983}}-{{7}^{1983}}\] is equal to

A) 2

B) 3

C) 5

D) 1

View Answer

78) If \[(\sqrt{3})bx+ay=2ab\]touches the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1,\]then the eccentric angle \[\theta \] of the point of contact is

A) \[\pi /6\]

B) \[\pi /2\]

C) \[3\pi /4\]

D) \[2\pi /3\]

View Answer

79) If a, b are positive quantities and if \[{{a}_{1}}=\frac{a+b}{2},{{b}_{1}}=\sqrt{{{a}_{1}}b,}{{a}_{2}}=\frac{{{a}_{1}}+{{b}_{1}}}{2},{{b}_{2}}=\sqrt{{{a}_{2}}{{b}_{1}}}\]... and so on, then

A) \[{{a}_{\infty }}=\frac{\sqrt{{{b}^{2}}-{{a}^{2}}}}{{{\cos }^{-1}}\left( \frac{a}{b} \right)}\]

B) \[{{b}_{\infty }}=\frac{\sqrt{{{b}^{2}}-{{a}^{2}}}}{{{\cos }^{-1}}\left( \frac{a}{b} \right)}\]

C) \[{{b}_{\infty }}=\frac{\sqrt{{{a}^{2}}-{{b}^{2}}}}{{{\cos }^{-1}}\left( \frac{b}{a} \right)}\]

D) None of these

View Answer

80) The set of equations\[\lambda x-y+(\cos \theta )z=0\]\[3x+y+2z=0\]\[(\cos \theta )x+y+2z=0\] where\[0\le \theta <2\pi \], has non-trivial solutions.

A) for no value of \[\lambda \] and \[\theta \]

B) for all values of \[\lambda \] and \[\theta \]

C) for all values of \[\lambda \] and only two values of \[\theta \]

D) for only one value of \[\lambda \] and all values of \[\theta \]

View Answer

81) Let R be the relation on N defined by \[R=\{(x,y)|x={{2}^{n}}y;n\in N\}\]Then, R is

A) equivalence relation

B) not symmetric

C) reflexive only

D) transitive only

View Answer

82) If two events A and B are such that P (A') = 0.3, P = 0.4, and P \[(A\cap B')\] = 0.5. then \[P\left( \frac{B}{A\cup B'} \right)\]equals

A) \[\frac{1}{4}\]

B) \[\frac{1}{2}\]

C) \[\frac{1}{8}\]

D) \[\frac{1}{16}\]

View Answer

83) If (m3 - 3) x2 + 3mx + 3m +1=0 has roots which are reciprocal of each other, then the value of m can be

A) 4

B) 1

C) 2

D) None of these

View Answer

84) Let \[f(x)=\left\{ \begin{align} & \frac{1+\cos x}{{{(\pi /x)}^{2}}}.\frac{{{\sin }^{2}}x}{\log (1+{{\pi }^{2}}-2\pi x+{{x}^{2}})},x\ne \pi \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,x=\pi \\ \end{align} \right..\] If f (x) is continuous function at \[x=\pi ,\]then k is equal to

A) \[\frac{1}{4}\]

B) \[\frac{1}{2}\]

C) \[\frac{-1}{2}\]

D) \[-\frac{1}{4}\]

View Answer

85) The greater of the two angles \[A=2{{\tan }^{-1}}(2\sqrt{2}-1)\]and \[B=3{{\sin }^{-1}}\left( \frac{1}{3} \right)+\]\[{{\sin }^{-1}}\left( \frac{3}{5} \right)\] is

A) B

B) A

C) C

D) None of these

View Answer

86) The solution of differential equation \[ydx+(2\sqrt{xy}-x)\]\[dy=0\]is

A) \[Cy={{e}^{\sqrt{x/y}}}\]

B) \[Cy={{e}^{-\sqrt{x/y}}}\]

C) \[Cy={{e}^{x/y}}\]

D) \[Cy={{e}^{\sqrt{2x/y}}}\]

View Answer

87) The value of the integral\[\int_{-10}^{1}{\frac{\left| \frac{2[x]}{3x-[x]} \right|}{\frac{2[x]}{3x-[x]}}},\] where [ ] represents GIF

A) 0

B) 10

C) -10

D) \[10-\frac{2}{3}\]

View Answer

88) If the lines \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\]and \[\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}\]are coplanar. then k is equal to

A) \[\frac{3}{2}\]

B) \[\frac{5}{2}\]

C) \[\frac{7}{2}\]

D) \[\frac{9}{2}\]

View Answer

89)

Statement I The number of common tangents to the circle x2 + y2 = 4 and x2 + y2 - 8x - 6y - 24 = 0 is 4.

Statement II Circle with centre \[{{c}_{1}},{{c}_{2}}\] and radii \[{{r}_{1}},{{r}_{2}}\] and if \[|{{e}_{1}}{{e}_{2}}|>{{r}_{1}}+{{r}_{2}}\] , then circles have 4 common tangents.

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is true but Statement II is false

D) Statement I is false but Statement II is true

View Answer

90)

Statement I If \[a=2\hat{i}+3\hat{j}-\hat{k},b=-\hat{i}+3\hat{j}+4\hat{k},\] then projection of a on \[b=\frac{3}{\sqrt{26}}.\]

Statement II Projection of p on \[q=\frac{p\cdot q}{|q|}\]

A) Both Statement I and Statement II are true and the Statement II is the correct explanation of the Statement I

B) Both Statement I and Statement II are true but the Statement II is not the correct explanation of the Statement I

C) Statement I is true but Statement II is false

D) Statement I is false but Statement II is true

View Answer

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