Solved papers for JEE Main & Advanced JEE Main Paper Phase-I (Held on 08-1-2020 Morning)

done JEE Main Paper Phase-I (Held on 08-1-2020 Morning) Total Questions - 75

• question_answer1) When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${{T}_{A}}$eV and de-Broglie wavelength${{\lambda }_{A}}.$ The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy $4.50\text{ }eV$is ${{T}_{B}}=\left( {{T}_{A}}1.5 \right)eV.$ If the de-Broglie wavelength of these photoelectrons ${{\lambda }_{B}}=2{{\lambda }_{A}},$ then the work function of metal B is: [JEE MAIN Held On 08-01-2020 Morning]

A)
$1.5\text{ }eV$

B)
$4\text{ }eV$

C)
$\text{3 }eV$

D)
$\text{2 }eV$

• question_answer2) The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a cell of emf 5 V and internal resistance of $20,\Omega$the null point on it is found to be at 1000 cm. The resistance of whole wire is : [JEE MAIN Held On 08-01-2020 Morning]

A)
$80\,\Omega$

B)
$100\,\Omega$

C)
$60\,\Omega$

D)
$120\,\Omega$

• question_answer3) Effective capacitance of parallel combination of two capacitors ${{C}_{1}}$and ${{C}_{2}}$is$10\mu F$. When these capacitors are individually connected to a voltage source of 1 V, the energy stored in the capacitor ${{C}_{2}}$is 4 times that of${{C}_{1}}$. If these capacitors are connected in series, their effective capacitance will be: [JEE MAIN Held On 08-01-2020 Morning]

A)
1.6 $\mu F$

B)
3.2 $\mu F$

C)
4.2 $\mu F$

D)
8.4 $\mu F$

• question_answer4) A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is             [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{ml{{\omega }^{2}}}{k-\omega m}$

B)
$\frac{ml{{\omega }^{2}}}{k+m{{\omega }^{2}}}$

C)
$\frac{ml{{\omega }^{2}}}{k+m\omega }$

D)
$\frac{ml{{\omega }^{2}}}{k-m{{\omega }^{2}}}$

• question_answer5) Boolean relation at the output stage-Y for the Following circuit is:  [JEE MAIN Held On 08-01-2020 Morning] A)
$\overline{A}.\overline{B}$

B)
$A.B$

C)
$A+B$

D)
$\overline{A}+\overline{B}$

• question_answer6) Consider a solid sphere of radius R and mass Density$\rho (r)={{\rho }_{0}}\left( 1\frac{{{r}^{2}}}{{{R}^{2}}} \right),0<r\le R.$ the minimum density of a liquid in which it will float is: [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{2{{\rho }_{0}}}{5}$

B)
$\frac{{{\rho }_{0}}}{3}$

C)
$\frac{{{\rho }_{0}}}{5}$

D)
$\frac{2{{\rho }_{0}}}{3}$

• question_answer7) Proton with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of ${{10}^{12}}m/{{s}^{2}}$ by an applied magnetic field (west to east). The value of magnetic field: (Rest mass of proton is$1.6\times {{10}^{27}}kg$)                        [JEE MAIN Held On 08-01-2020 Morning]

A)
$0.071\text{ }mT$

B)
$0.71\text{ }mT$

C)
$71\text{ }mT$

D)
$7.1\text{ }mT$

• question_answer8) The dimension of stopping potential ${{V}_{0}}$ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is:                              [JEE MAIN Held On 08-01-2020 Morning]

A)
${{h}^{1/3}}{{G}^{2/3}}{{c}^{1/3}}{{A}^{1}}$

B)
${{h}^{2/3}}{{c}^{5/3}}{{G}^{1/3}}{{A}^{1}}$

C)
${{h}^{2/3}}{{c}^{1/3}}{{G}^{4/3}}{{A}^{1}}$

D)
${{h}^{2}}{{G}^{3/2}}{{c}^{1/3}}{{A}^{1}}$

• question_answer9) A thermodynamic cycle xyzx is shown on a V-T diagram The P-V diagram that best describes this cycle is: (Diagrams are schematic and not to scale)  [JEE MAIN Held On 08-01-2020 Morning]

A) B) C) D) • question_answer10) Consider two solid spheres of radii ${{R}_{1}}=1\text{ }m,$ ${{R}_{2}}=2\text{ }m$ and masses ${{M}_{1}}$and ${{M}_{2}},$respectively. The gravitational field due to sphere and are shown. The value of$\frac{{{M}_{1}}}{{{M}_{2}}}$ is [JEE MAIN Held On 08-01-2020 Morning] A)
$\frac{1}{6}$

B)
$\frac{1}{2}$

C)
$\frac{2}{3}$

D)
$\frac{1}{3}$

• question_answer11) The plot that depicts the behavior of the mean Free time $\tau$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is (Graphs are schematic and not drawn to scale) [JEE MAIN Held On 08-01-2020 Morning]

A) B) C) D) • question_answer12) The graph which depicts the results of Rutherford gold foil experiment with $\alpha$-particle is $\theta$ : Scattering angle Y: Number of scattered $\alpha$-particles detected (Plots are schematic and not to scale) [JEE MAIN Held On 08-01-2020 Morning]

A) B) C) D) • question_answer13) Three charged particles A, B and C wit charges -4q, 2q and -2q are present on the circumference of a circle of radius d. The charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is                                                          [JEE MAIN Held On 08-01-2020 Morning] A)
$\frac{\sqrt{3}q}{\pi {{\varepsilon }_{0}}{{d}^{2}}}$

B)
$\frac{3\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

C)
$\frac{\sqrt{3}q}{4\pi {{\varepsilon }_{0}}{{d}^{2}}}$

D)
$\frac{2\sqrt{3}q}{\pi {{\varepsilon }_{0}}{{d}^{2}}}$

• question_answer14) In finding the electric field using Gauss law the Formula $\left| {\vec{E}} \right|=\frac{{{q}_{enc}}}{{{\varepsilon }_{0}}\left| A \right|}$ is applicable. In the formula${{\varepsilon }_{0}}$ is permittivity of free space, A is the area of Gaussian surface and ${{q}_{enc}}$is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation? [JEE MAIN Held On 08-01-2020 Morning]

A)
Only when the Gaussian surface is an equipotential surface and $\left| {\vec{E}} \right|$ is constant on The surface.

B)
Only when$\left| {\vec{E}} \right|=$ constant on the surface.

C)
Only when the Gaussian surface is a equipotential surface.

D)
For any choice of Gaussian surface.

• question_answer15) The coordinates of centre of mass of a uniform Flag shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown in figure) are [JEE MAIN Held On 08-01-2020 Morning] A)
$\left( 0.75\text{ }m,\text{ }1.75\text{ }m \right)$

B)
$\left( 1.25\text{ }m,\text{ }1.50\text{ }m \right)$

C)
$\left( 1\text{ }m,\text{ }1.75\text{ }m \right)$

D)
$\left( 0.75\text{ }m,\text{ }0.75\text{ }m \right)$

• question_answer16) At time t = 0 magnetic field of 1000 Gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to 500 Gauss, in the next 5 s, then induced EMF in the loop is                                                                                        [JEE MAIN Held On 08-01-2020 Morning] A)
$48\,\mu V$

B)
$36\text{ }\mu V$

C)
$56\text{ }\mu V$

D)
$28\text{ }\mu V$

• question_answer17) The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability$\frac{4}{3}$ for this wavelength, will be                [JEE MAIN Held On 08-01-2020 Morning]

A)
$60{}^\circ$

B)
$45{}^\circ$

C)
$15{}^\circ$

D)
$30{}^\circ$

• question_answer18) The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye piece? [JEE MAIN Held On 08-01-2020 Morning]

A)
30 cm

B)
10 cm

C)
20 cm

D)
40 cm

• question_answer19) Consider a uniform rod of mass M = 4 m and length l pivoted about its centre. A mass moving with velocity v making angle$\theta =\frac{\pi }{4}$to the rod?s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is                                              [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{4}{7}\frac{V}{l}$

B)
$\frac{3}{7}\frac{V}{l}$

C)
$\frac{3}{7\sqrt{2}}\frac{V}{l}$

D)
$\frac{3\sqrt{2}}{7}\frac{V}{l}$

• question_answer20) A leak proof cylinder of length 1 m, made of a Metal which has very low coefficient of expansion is floating vertically in water at $0{}^\circ C$such that its height above the water surface is 20 cm. When the temperature of water is increased to $4{}^\circ C,$ the height of the cylinder above the water surface becomes 21 cm. The density of water at $T=4{}^\circ C,$relative to the density at $T=0{}^\circ C$is close to                  [JEE MAIN Held On 08-01-2020 Morning]

A)
1.04

B)
1.03

C)
1.26

D)
1.01

• question_answer21) Four resistances of 15 $\Omega$, 12 $\Omega$, 4 $\Omega$ and 10 $\Omega$ Respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10 $\Omega$ to balance the network is _________ $\Omega$.   [JEE MAIN Held On 08-01-2020 Morning]

• question_answer22) A one meter long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is _______ Hz.                                           [JEE MAIN Held On 08-01-2020 Morning]

• question_answer23) A body A, of mass $m\text{ }=\text{ }0.1\text{ }kg$ has an initial velocity of $3\hat{i}\,m{{s}^{1}}$. It collides elastically with another body, B of the same mass which has an initial velocity of$5\hat{j}\text{ }m{{s}^{1}}$. After collision, A moves with a velocity $\vec{v}=4\left( \hat{i}+\hat{j} \right)$ . The energy of B after collision is written as $\frac{x}{10}J.$  the value of x is ________.  [JEE MAIN Held On 08-01-2020 Morning]

• question_answer24) A particle is moving along the x-axis with its coordinate with time 't' given by $x\left( t \right)=10+8t3{{t}^{2}}.$ Another particle is moving along the y-axis with its coordinate as a function of time given by $y\left( t \right)=58{{t}^{3}}.$ $At\text{ }t=1\text{ }s,$ the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$ . Then v (in m/s) is ________.                                                               [JEE MAIN Held On 08-01-2020 Morning]

• question_answer25) A point object in air is in front of the curved surface of a Plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, Then the focal length of the lens (in cm) is ______.                                                                         [JEE MAIN Held On 08-01-2020 Morning]

• question_answer26) The complex that can show fac-and merisomers is                     [JEE MAIN Held On 08-01-2020 Morning]

A)
$\left[ CoC{{l}_{2}}{{\left( en \right)}_{2}} \right]$

B)
$\left[ Co{{\left( N{{H}_{3}} \right)}_{3}}{{\left( N{{O}_{2}} \right)}_{3}} \right]$

C)
$\left[ Pt{{\left( N{{H}_{3}} \right)}_{2}}C{{l}_{2}} \right]$

D)
${{\left[ Co{{\left( N{{H}_{3}} \right)}_{4}}C{{l}_{2}} \right]}^{+}}$

• question_answer27) As per Hardy-Schulze formulation, the flocculation values of the following for ferric hydroxide sol are in the order [JEE MAIN Held On 08-01-2020 Morning]

A)
$AlC{{l}_{3}}>{{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]>{{K}_{2}}Cr{{O}_{4}}>KBr=KN{{O}_{3}}$

B)
${{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]<{{K}_{2}}Cr{{O}_{4}}<KBr=KN{{O}_{3}}=AlC{{l}_{3}}$

C)
${{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]>AlC{{l}_{3}}>{{K}_{2}}Cr{{O}_{4}}>KBr>KN{{O}_{3}}$

D)
${{K}_{3}}\left[ Fe{{\left( CN \right)}_{6}} \right]<{{K}_{2}}Cr{{O}_{4}}<AlC{{l}_{3}}<KBr<KN{{O}_{3}}$

• question_answer28)  The decreasing order of reactivity towards dehydrohalogenation $\left( {{E}_{1}} \right)$ reaction of the following compounds is (A) (B) (C) (D) [JEE MAIN Held On 08-01-2020 Morning]

A)
B > A > D > C

B)
B > D > A > C

C)
B > D > C > A

D)
D > B > C > A

• question_answer29)  For the Balmer series in the spectrum of H atom,$\overline{V}={{R}_{^{H}}}\left\{ \frac{1}{{{n}^{2}}_{1}}-\frac{1}{{{n}^{2}}_{2}} \right\},$ the correct statements among (I) to (VI) are (I) as wavelength decreases, the lines in the series converge (II) The integer ${{n}_{1}}$ is equal to 2 (III)The lines of longest wavelength corresponds to ${{n}_{2}}=3$ (IV)The ionization energy of hydrogen can be calculated from wave number of these lines
[JEE MAIN Held On 08-01-2020 Morning]

A)
(I), (II), (III)

B)
(II), (III), (IV)

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

D)
(I), (II), (IV)

• question_answer30) The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are [JEE MAIN Held On 08-01-2020 Morning]

A)
786, 737, 577, 496

B)
496, 577, 786, 737

C)
496, 737, 577, 786

D)
496, 577, 737, 786

• question_answer31) The predominant intermolecular forces present in ethyl acetate, a liquid, are [JEE MAIN Held On 08-01-2020 Morning]

A)
Dipole-dipole and hydrogen bonding

B)
London dispersion and dipole-dipole

C)
Hydrogen bonding and London dispersion

D)
London dispersion, dipole-dipole and hydrogen bonding

• question_answer32)  A graph of vapour pressure and temperature for three different liquids X, Y, and Z is shown below The following inferences are made (A) X has higher intermolecular interactions compared to Y. (B) X has lower intermolecular interactions compared to Y (C) Z has lower intermolecular interactions compared to Y. The correct inferences is/are
[JEE MAIN Held On 08-01-2020 Morning]

A)
(B)

B)
(C)

C)
(A) and (C)

D)
(A)

• question_answer33) The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively [JEE MAIN Held On 08-01-2020 Morning] A)
${{X}_{2}}Y,\text{ }2\times {{10}^{9}}\text{ }{{M}^{3}}$

B)
$X{{Y}_{2}},\text{ }4\times {{10}^{9}}\text{ }{{M}^{3}}$

C)
$X{{Y}_{2}},\text{ }1\times {{10}^{9}}\text{ }{{M}^{3}}$

D)
$XY,2\times {{10}^{6}}\text{ }{{M}^{3}}$

• question_answer34) When gypsum is heated to 393 K, it forms                               [JEE MAIN Held On 08-01-2020 Morning]

A)
Anhydrous $CaS{{O}_{4}}$

B)

C)
$CaS{{O}_{4}}\cdot 5{{H}_{2}}O$

D)
$CaS{{O}_{4}}\cdot 0.5{{H}_{2}}O$

• question_answer35) Arrange the following compounds in increasing Order of C - OH bond length Methanol, phenol, p-ethoxyphenol [JEE MAIN Held On 08-01-2020 Morning]

A)
phenol < p-ethoxyphenol < methanol

B)
methanol < phenol < p-ethoxyphenol

C)
methanol < p-ethoxyphenol < phenol

D)
phenol < methanol < p-ethoxyphenol

• question_answer36) The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than without. The change in the activation energy upon adding enzyme is [JEE MAIN Held On 08-01-2020 Morning]

A)
- 6RT

B)
+ 6RT

C)
+ 6(2.303) RT

D)
- 6(2.303) RT

• question_answer37) The strength of an aqueous $NaOH$solution is most accurately determined by titrating (Note: consider that an appropriate indicator is Used)                 [JEE MAIN Held On 08-01-2020 Morning]

A)
Aq. $NaOH$in a pipette and aqueous oxalic acid in a burette

B)
Aq. $NaOH$ in a burette and aqueous oxalic acid in a conical flask

C)
Aq. $NaOH$ in a burette and concentrated ${{H}_{2}}S{{O}_{4}}$in a conical flask

D)
Aq. $NaOH$ in a volumetric flask and concentrated ${{H}_{2}}S{{O}_{4}}$in a conical flask

• question_answer38) The most suitable reagent for the given conversion is               [JEE MAIN Held On 08-01-2020 Morning] A)
$LiAl{{H}_{4}}$

B)
$NaB{{H}_{4}}$

C)
${{H}_{2}}\text{/}Pd$

D)
${{B}_{2}}{{H}_{6}}$

• question_answer39) Which of the following statement is not true for Glucose?      [JEE MAIN Held On 08-01-2020 Morning]

A)
Glucose reacts with hydroxylamine to form Oxime

B)
The pentaacetate of glucose does not react With hydroxylamine to give oxime

C)
Glucose exists in two crystalline forms $\alpha$ and $\beta$

D)
Glucose gives Schiff's test for aldehyde

• question_answer40) The third ionization enthalpy is minimum for                          [JEE MAIN Held On 08-01-2020 Morning]

A)
Mn

B)
Fe

C)
Co

D)
Ni

• question_answer41)  Among the gases - (e), the gases that cause Greenhouse effect are (A) $C{{O}_{2}}$ (B) ${{H}_{2}}O$ (C) $CFCs$ (D) ${{O}_{2}}$ (E) ${{O}_{3}}$
[JEE MAIN Held On 08-01-2020 Morning]

A)
(A), (B), (C) and (D)

B)
(A), (C), (D) and (E)

C)
(A), (B), (C) and (E)

D)
(A) and (D)

• question_answer42) The major product of the following reaction is                     [JEE MAIN Held On 08-01-2020 Morning] A) B) C) D) • question_answer43) A flask contains a mixture of isohexane and 3-methylpentane. One of the liquids boils at $63{}^\circ C$While the other boils at $60{}^\circ C$. What is the best way to separate the two liquids and which One will be distilled out first? [JEE MAIN Held On 08-01-2020 Morning]

A)
Simple distillation, isohexane

B)
Fractional distillation, isohexane

C)
Simple distillation, 3-methylpentane

D)
Fractional distillation, 3-methylpentane

• question_answer44) The major products A and B in the following reactions are       [JEE MAIN Held On 08-01-2020 Morning] A) B) C) D) • question_answer45) The number of bonds between sulphur and oxygen atoms in ${{S}_{2}}O_{8}^{2-}$ and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are             [JEE MAIN Held On 08-01-2020 Morning]

A)
4 and 6

B)
8 and 8

C)
8 and 6

D)
4 and 8

• question_answer46) The magnitude of work done by a gas that undergoes reversible expansion along the path ABC shown in the figure is _____________.            [JEE MAIN Held On 08-01-2020 Morning] • question_answer47)  The volume (in mL) of $0.125\text{ }M\text{ }AgN{{O}_{3}}$required to quantitatively precipitate chloride ions in $0.3\text{ }g\text{ }of\text{ }\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]C{{l}_{3}}$is _____________. $^{M}\left[ Co{{\left( N{{H}_{3}} \right)}_{6}} \right]C{{l}_{3}}=267.46\text{ }g\text{/}mol$ $^{M}AgN{{O}_{3}}=169.87\text{ }g\text{/}mol$
[JEE MAIN Held On 08-01-2020 Morning]

• question_answer48) The number of chiral centres in penicillin is __________.          [JEE MAIN Held On 08-01-2020 Morning]

• question_answer49) What would be the electrode potential for the given half-cell reaction at pH = 5? _________. $2{{H}_{2}}\text{ }O\to {{O}_{2}}+4{{H}^{\oplus }}+4{{e}^{-}}\text{ };\text{ }{{E}^{0}}_{red}=1.23\text{ }V$ ($R\text{ }=\text{ }8.314\text{ }J\text{ }mo{{l}^{1}}{{K}^{1}};$Temp = 298 K; oxygen Under std. atm. pressure of 1 bar)                                     [JEE MAIN Held On 08-01-2020 Morning]

• question_answer50) Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is _____________. [JEE MAIN Held On 08-01-2020 Morning] Atomic weight: $Fe=55.85;\text{ }S=32.00;\text{ }O\text{ }=16.00$

• question_answer51) If c is a point at which Rolle's theorem holds for the function, $f(x)=lo{{g}_{e}}\left( \frac{{{x}^{2}}+\alpha }{7x} \right)$ in the interval [3, 4], where $\alpha \in R,$ Then f"is equal to  [JEE MAIN Held On 08-01-2020 Morning]

A)
$-\frac{1}{24}$

B)
$\frac{1}{12}$

C)
$\frac{\sqrt{3}}{7}$

D)
$-\frac{1}{12}$

• question_answer52) Let A and B be two independent events such that $P(A)=\frac{1}{3}$ and $P(B)=\frac{1}{6}.$ Then, which of the following is TRUE? [JEE MAIN Held On 08-01-2020 Morning]

A)
$P(A/B)=\frac{2}{3}$

B)
$P(A'/B')=\frac{1}{3}$

C)
$P(A/B')=\frac{1}{3}$

D)
$P(A/(A\cup B))=\frac{1}{4}$

• question_answer53) The inverse function of $f(x)=\frac{{{8}^{2x}}-{{8}^{-2x}}}{{{8}^{2x}}+{{8}^{-2x}}},x\in (-1,1),$ is  [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{1}{4}{{\log }_{e}}\left( \frac{1-x}{1+x} \right)$

B)
$\frac{1}{4}(lo{{g}_{8}}e)lo{{g}_{e}}\left( \frac{1+x}{1-x} \right)$

C)
$\frac{1}{4}{{\log }_{e}}\left( \frac{1+x}{1-x} \right)$

D)
$\frac{1}{4}(lo{{g}_{8}}e)lo{{g}_{e}}\left( \frac{1-x}{1+x} \right)$

• question_answer54) Let two points be $A(1,-1)$ and$B(0,2)$. If a point $P(x',y')$be such that the area of $\Delta PAB=5sq.$units and it lies on the line, $3x+y-4\lambda =0,$then a value of $\lambda$is    [JEE MAIN Held On 08-01-2020 Morning]

A)
3

B)
4

C)
1

D)
-3

• question_answer55) Let $f(x)={{(sin(ta{{n}^{-1}}x)+sin(co{{t}^{-1}}x))}^{2}}-1,$$\left| x \right|>1.\,If\,\frac{dy}{dx}=\frac{1}{2}\frac{d}{dx}(si{{n}^{-1}}(f(x)))$ and $y(\sqrt{3})=\frac{\pi }{6},$ Then $y(-\sqrt{3})$is equal to [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{\pi }{3}$

B)
$-\frac{\pi }{6}$

C)
$\frac{2\pi }{3}$

D)
$\frac{5\pi }{6}$

• question_answer56) $\underset{x\to 0}{\mathop{\lim }}\,{{\left( \frac{3{{x}^{2}}+2}{7{{x}^{2}}+2} \right)}^{\frac{1}{{{x}^{2}}}}}$ is equal to   [JEE MAIN Held On 08-01-2020 Morning]

A)
e

B)
$\frac{1}{e}$

C)
$\frac{1}{{{e}^{2}}}$

D)
${{e}^{2}}$

• question_answer57) Let $f(x)=xco{{s}^{-1}}(-sin\left| x \right|),x\in \left[ -\frac{\pi }{2},\frac{\pi }{2} \right],$ then which of the following is true? [JEE MAIN Held On 08-01-2020 Morning]

A)
$f'(0)=-\frac{\pi }{2}$

B)
$f'$ is decreasing in $\left( -\frac{\pi }{2},0 \right)$ and increasing  in $\left( 0,\frac{\pi }{2} \right)$

C)
$f$ is not differentiable at x=0

D)
$f'$ is increasing in $\left( -\frac{\pi }{2},0 \right)$ and decreasing in $\left( 0,\frac{\pi }{2} \right)$

• question_answer58) Let f: $R\to R$ be such that for all $x\in R({{2}^{1+x}}+{{2}^{1-x}}),$ $f(x)$ and $({{3}^{x}}+{{3}^{-x}})$ are in A.P., then the minimum value of f(x) is              [JEE MAIN Held On 08-01-2020 Morning]

A)
2

B)
0

C)
3

D)
4

• question_answer59)   Let the volume of a parallelepiped whose coterminous edges are given by $\vec{u}=\vec{i}+\vec{j}+\lambda \hat{k},$$\vec{v}=\hat{i}+\hat{j}+3\hat{k}$ and $\vec{w}=2\hat{i}+\hat{j}+\hat{k}$ be 1 cu. Unit if $\theta$ be the angle between the edges $\vec{u}$ and $\vec{w}$, then $\cos \theta$can be [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{5}{7}$

B)
$\frac{5}{3\sqrt{3}}$

C)
$\frac{7}{6\sqrt{6}}$

D)
$\frac{7}{6\sqrt{3}}$

• question_answer60)              For which of the following ordered pairs $(\mu ,\delta )$, the system of linear equations $x+2y+3z=1$ $3x+4y+5z=\mu$ $4x+4y+4z=\delta$ Is inconsistent?
[JEE MAIN Held On 08-01-2020 Morning]

A)
$(4,3)$

B)
$(4,\,6)$

C)
$(3,4)$

D)
$(1,0)$

• question_answer61) Which one of the following is a tautology?

A)
$Q\to (P\wedge (P\to Q))$

B)
$P\vee (P\wedge Q)$

C)
$P\wedge (P\vee Q)$

D)
$(P\wedge (P\to Q))\to Q$

• question_answer62) If a, b and c are the greatest values of $^{19}{{C}_{p}}{{,}^{20}}{{C}_{q}}$ and $^{21}{{C}_{r}}$ respectively, then [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{a}{10}=\frac{b}{11}=\frac{c}{42}$

B)
$\frac{a}{11}=\frac{b}{22}=\frac{c}{42}$

C)
$\frac{a}{10}=\frac{b}{11}=\frac{c}{21}$

D)
$\frac{a}{11}=\frac{b}{22}=\frac{c}{21}$

• question_answer63) The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q, where $p\ne 0$ and$q\ne 0$. If the new mean and new s.d. become half of their original values, then q is equal to     [JEE MAIN Held On 08-01-2020 Morning]

A)
-10

B)
-20

C)
-5

D)
10

• question_answer64) The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{2}$ is [JEE MAIN Held On 08-01-2020 Morning]

A)
$2\sqrt{30}$

B)
$\frac{7}{2}\sqrt{30}$

C)
$3\sqrt{30}$

D)
3

• question_answer65) Let $y=y(x)$ be a solution of the differential Equation, $\sqrt{1-{{x}^{2}}}\frac{dy}{dx}+\sqrt{1-{{y}^{2}}}=0,\left| x \right|<1.$ If $y\left( \frac{1}{2} \right)=\frac{\sqrt{3}}{2},$ then $y\left( \frac{-1}{\sqrt{2}} \right)$ is equal to       [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{\sqrt{3}}{2}$

B)
$\frac{1}{\sqrt{2}}$

C)
$-\frac{\sqrt{3}}{2}$

D)
$-\frac{1}{\sqrt{2}}$

• question_answer66) If the equation, ${{x}^{2}}+bx+45=0(b\in R)$ has conjugate complex roots and they satisfy $\left| z+1 \right|=2\sqrt{10},$ Then [JEE MAIN Held On 08-01-2020 Morning]

A)
${{b}^{2}}-b=42$

B)
${{b}^{2}}-b=30$

C)
${{b}^{2}}+b=12$

D)
${{b}^{2}}+b=72$

• question_answer67) The locus of a point which divides the line segment joining the point $(0,-1)$ and a point on the parabola, ${{x}^{2}}=4y,$ internally in the ratio $1:2,$ is     [JEE MAIN Held On 08-01-2020 Morning]

A)
$9{{x}^{2}}-12y=8$

B)
$4{{x}^{2}}-3y=2$

C)
${{x}^{2}}-3y=2$

D)
$9{{x}^{2}}-3y=2$

• question_answer68) For a>0, let the curves ${{C}_{1}}:{{y}^{2}}=ax$ and ${{C}_{2}}:{{x}^{2}}=ay$ intersect at origin 0 and a point P. let the line $x=b(0<b<a)$intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, ${{C}_{1}}$ and ${{C}_{2}}$, and the area of $\Delta OQR=\frac{1}{2},$ then 'a' satisfies the equation [JEE MAIN Held On 08-01-2020 Morning]

A)
${{x}^{6}}+6{{x}^{3}}-4=0$

B)
${{x}^{6}}-12{{x}^{3}}-4=0$

C)
${{x}^{6}}-6{{x}^{3}}+4=0$

D)
${{x}^{6}}-12{{x}^{3}}+4=0$

• question_answer69) If $\int{\frac{\cos xdx}{{{\sin }^{3}}x{{(1+si{{n}^{6}}x)}^{2/3}}}=f(x){{(1+si{{n}^{6}}x)}^{1/\lambda }}+c}$ Where c is a constant of integration, then $\lambda f\left( \frac{\pi }{3} \right)$ Is equal to   [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{9}{8}$

B)
$\frac{-9}{8}$

C)
$-2$

D)
2

• question_answer70) Let the line y = mx and the ellipse $2{{x}^{2}}+{{y}^{2}}=1$intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at $\left( -\frac{1}{3\sqrt{2}},0 \right)$ and $(0,\beta )$, then $\beta$ is equal to     [JEE MAIN Held On 08-01-2020 Morning]

A)
$\frac{\sqrt{2}}{3}$

B)
$\frac{2}{3}$

C)
$\frac{2}{\sqrt{3}}$

D)
$\frac{2\sqrt{2}}{3}$

• question_answer71) An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the moat three of them are red is ______ . [JEE MAIN Held On 08-01-2020 Morning]

• question_answer72) Let the normal at a point P on the curve ${{y}^{2}}-3{{x}^{2}}+y+10=0$ intersect the y-axis at$\left( 0,\frac{3}{2} \right)$. If m is the slope of the tangent at P to the curve, then $\left| m \right|$ is equal to _____.      [JEE MAIN Held On 08-01-2020 Morning]

• question_answer73) The sum $\sum\limits_{k=1}^{20}{(1+2+3+...+k)}$is _____. [JEE MAIN Held On 08-01-2020 Morning]

• question_answer74) The least positive value of 'a' for which the equation, $2{{x}^{2}}+(a-10)x+\frac{33}{2}=2a$has real roots is____. [JEE MAIN Held On 08-01-2020 Morning]

• question_answer75) The number of all $3\times 3$ matrices A, with entries form the set $\{-1,0,1\}$ such that the sum of the diagonal elements of $A{{A}^{T}}$is 3, is____.                                           [JEE MAIN Held On 08-01-2020 Morning]
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