# Solved papers for JEE Main & Advanced JEE Main Paper Phase-I Held on 07-1-2020 Morning

### done JEE Main Paper Phase-I Held on 07-1-2020 Morning

• question_answer1) A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as $k(x)=K(1+\alpha x)$ where 'x' is the distance measured from one of the plates. If $(\alpha d)<<1$, the total capacitance of the system is best given by the expression [JEE MAIN Held on 07-01-2020 Morning] A) $\frac{AK{{\varepsilon }_{0}}}{d}(1+\alpha d)$

B) $\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+\frac{{{\alpha }^{2}}{{d}^{2}}}{2} \right)$

C) $\frac{AK{{\varepsilon }_{0}}}{d}\left( 1+\frac{\alpha d}{2} \right)$

D) $\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+{{\left( \frac{\alpha d}{2} \right)}^{2}} \right)$

• question_answer2) If the magnetic field in a plane electromagnetic wave is given by $\overline{B}=3\times {{10}^{-8}}\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{j}T$, then what will be expression for electric field? [JEE MAIN Held on 07-01-2020 Morning]

A) $\vec{E}=\left( 60\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)$

B) $\vec{E}=\left( 3\times {{10}^{-8}}\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{i}V/m \right)$

C) $\vec{E}=\left( 9\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)$

D) $\vec{E}=\left( 3\times {{10}^{-8}}sin(1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{j}V/m \right)$

• question_answer3) 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 $\left( {{3}^{1.4}}=4.6555 \right)$ [Take air to be an ideal gas] [JEE MAIN Held on 07-01-2020 Morning]

A) 90.5 J

B) 60.7 J

C) 48 J

D) 100.8 J

• question_answer4) The radius of gyration of a uniform rod of length l, about an axis passing through a point $\frac{l}{\text{4}}$ away from the centre of the rod, and perpendicular to it, is:                                               [JEE MAIN Held on 07-01-2020 Morning]

A) $\sqrt{\frac{\text{7}}{\text{48}}}l$

B) $\frac{\text{1}}{\text{8}}l$

C) $\frac{1}{4}l$

D) $\sqrt{\frac{\text{3}}{\text{8}}}l$

• question_answer5) 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 $\frac{m}{10}$ 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): [JEE MAIN Held on 07-01-2020 Morning]

A) $5m\left( {{u}^{2}}-\frac{119}{200}\frac{GM}{R} \right)$

B) $\frac{3m}{8}{{\left( u+\sqrt{\frac{5GM}{6R}} \right)}^{2}}$

C) $\frac{m}{20}{{\left( u-\sqrt{\frac{2GM}{3R}} \right)}^{2}}$

D) $\frac{m}{20}\left( {{u}^{2}}+\frac{113}{200}\frac{GM}{R} \right)$

• question_answer6) A long solenoid of radius R carries a time (t) - dependent current $I(t)={{I}_{0}}t(1-t)$. 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: [JEE MAIN Held on 07-01-2020 Morning]

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 = 0.5 direction of ${{I}_{R}}$ reverses and ${{V}_{R}}$is zero

D) At t = 0.25 direction of ${{I}_{R}}$ reverses and ${{V}_{R}}$ is maximum

• question_answer7) Speed of transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross section$1.0\,\,m{{m}^{2}}$) is $90\text{ }m{{s}^{1}}$. If the Young?s modulus of wire is $16\times {{10}^{11}}\text{ }N{{m}^{2}}$, the extension of wire over its natural length is: [JEE MAIN Held on 07-01-2020 Morning]

A) 0.01 mm

B) 0.02 mm

C) 0.04 mm

D) 0.03 mm

• question_answer8) 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: $(1\text{ }HP=746\text{ }W,\text{ }g=10\text{ }m{{s}^{2}})$ [JEE MAIN Held on 07-01-2020 Morning]

A) $1.5\text{ }m{{s}^{1}}$

B) $1.9\text{ }m{{s}^{1}}$

C) $1.7\text{ }m{{s}^{1}}$

D) $2.0\text{ }m{{s}^{1}}$

• question_answer9) The time period of revolution of electron in its 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: [JEE MAIN Held on 07-01-2020 Morning]

A) $1.6\times {{10}^{14}}$

B) $7.8\times {{10}^{14}}$

C) $5.6\times {{10}^{12}}$

D) $6.2\times {{10}^{15}}$

• question_answer10) Two moles of an ideal gas with $\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{{{C}_{P}}}{{{C}_{V}}}=\frac{4}{3}$. The value of $\frac{{{C}_{P}}}{{{C}_{V}}}$ for the mixture is: [JEE MAIN Held on 07-01-2020 Morning]

A) 1.47

B) 1.42

C) 1.50

D) 1.45

• question_answer11) The current ${{I}_{1}}$ (in A) flowing through $1\Omega$ resistor in the following circuit is: [JEE MAIN Held on 07-01-2020 Morning] A) 0.5

B) 0.4

C) 0.25

D) 0.2

• question_answer12) As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be: [JEE MAIN Held on 07-01-2020 Morning] A) $r\sqrt{\frac{3}{2gh}}$

B) $r\sqrt{\frac{3}{4gh}}$

C) $\frac{1}{r}\sqrt{\frac{4gh}{3}}$

D) $\frac{1}{r}\sqrt{\frac{2gh}{3}}$

• question_answer13) Visible light of wavelength $6000\times {{10}^{8}}\text{ }cm$ falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at $60{}^\circ$ from the central maximum. If the first minimum is produced at ${{\theta }_{1}}$, then ${{\theta }_{1}}$ is close to [JEE MAIN Held on 07-01-2020 Morning]

A) $25{}^\circ$

B) $30{}^\circ$

C) $20{}^\circ$

D) $45{}^\circ$

• question_answer14) 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 system is at a point [JEE MAIN Held on 07-01-2020 Morning] A) 1.5 cm right and 1.2 cm above 1 kg mass

B) 2.0 cm right and 0.9 cm above 1 kg mass

C) 0.9 cm right and 2.0 cm above 1 kg mass

D) 0.6 cm right and 2.0 cm above 1 kg mass

• question_answer15) 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 [JEE MAIN Held on 07-01-2020 Morning]

A) 2 mm

B) 33 mm

C) 22 mm

D) 12 mm

• question_answer16) 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? [JEE MAIN Held on 07-01-2020 Morning]

A) ${{\phi }_{i}}=-{{\phi }_{0}}$

B) ${{\phi }_{i}}<{{\phi }_{0}}$

C) ${{\phi }_{i}}={{\phi }_{0}}$

D) ${{\phi }_{i}}>{{\phi }_{0}}$

• question_answer17) 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 the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduced the output intensity to be zero, is [JEE MAIN Held on 07-01-2020 Morning]

A) $71.6{}^\circ$

B) $45{}^\circ$

C) $90{}^\circ$

D) $18.4{}^\circ$

• question_answer18) Which of the following gives a reversible operation? [JEE MAIN Held on 07-01-2020 Morning]

A) B) C) D) • question_answer19) 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 [JEE MAIN Held on 07-01-2020 Morning]

A) $L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b$

B) $L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m$

C) $L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}$

D) $L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b$

• question_answer20) Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30{}^\circ$. The electric field in the region shown between them is given by [JEE MAIN Held on 07-01-2020 Morning] A) $\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]$

B) $\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]$

C) $\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1-\frac{\sqrt{3}}{2} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]$

D) $\frac{\sigma }{{{\varepsilon }_{0}}}\left[ \left( 1+\frac{\sqrt{3}}{2} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]$

• question_answer21) 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 m), the kinetic energy of the particle (in J) is: (figure drawn is schematic and not to scale; take $g=10\text{ }m{{s}^{2}}$) [JEE MAIN Held on 07-01-2020 Morning] • question_answer22) 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_______. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer23) 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 $\overrightarrow{B}=\left( 3\hat{i}+4\hat{k} \right)T$. The quantity of flux through the loop ABCDEFA (in Wb) is ________.                                            [JEE MAIN Held on 07-01-2020 Morning]

• question_answer24) A non-isotropic solid metal cube has coefficients of linear expansion as: $5\times {{10}^{5}}/{}^\circ \,C$ along the x-axis and $5\times {{10}^{6}}/{}^\circ \,C$ along the y and the z-axis. If the coefficient of volume expansion of the solid is $C\times {{10}^{6}}/{}^\circ C$then the value of C is________.            [JEE MAIN Held on 07-01-2020 Morning]

• question_answer25) A beam of electromagnetic radiation of intensity $6.4\times {{10}^{5}}W/c{{m}^{2}}$ is comprised of wavelength, $\lambda =310\text{ }nm$. It falls normally on a metal (work function $\varphi =2\text{ }eV$) of surface area of $1\text{ }c{{m}^{2}}$. If one in ${{10}^{3}}$ photons ejects an electron, total number of electrons ejected in 1 s is ${{10}^{x}}$. $(hc=1240\text{ }eVnm,\text{ }1\text{ }eV=1.6\times {{10}^{19}}J)$, then x is _______. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer26) In comparison to the zeolite process for the removal of permanent hardness, the synthetic resins method is [JEE MAIN Held on 07-01-2020 Morning]

A) Less efficient as it exchanges only anions

B) More efficient as it can exchange only cations

C) More efficient as it can exchange both cations as well as anions

D) Less efficient as the resins cannot be regenerated

• question_answer27) The atomic radius of Ag is closest to [JEE MAIN Held on 07-01-2020 Morning]

A) Cu

B) Au

C) Hg

D) Ni

• question_answer28) Given that the standard potentials $(E{}^\circ )$ of $C{{u}^{2+}}\text{/}\,Cu\text{ }and\text{ }C{{u}^{+}}\text{/}\,Cu\text{ }are\text{ }0.34\text{ }V$and$0.522\text{ }V$respectively, the $E{}^\circ$ of $C{{u}^{2}}^{+}/C{{u}^{+}}$is: [JEE MAIN Held on 07-01-2020 Morning]

A) +0.158 V

B) -0.158 V

C) -0.182 V

D) 0.182 V

• question_answer29) At $35{}^\circ C$, the vapour pressure of $C{{S}_{2}}$ is 512 mm Hg and that of acetone is 344 mm Hg. A solution of $C{{S}_{2}}$ in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is [JEE MAIN Held on 07-01-2020 Morning]

A) Raoult?s law is not obeyed by this system

B) A mixture of $100\text{ }mL\text{ }C{{S}_{2}}$ and $100\text{ }mL$ acetone has a volume < 200 mL

C) Heat must be absorbed in order to produce the solution at $35{}^\circ C$

D) $C{{S}_{2}}$ and acetone are less attracted to each other than to themselves

 (i) Riboflavin (a) Beriberi (ii) Thiamine (b) Scurvy (iii) Pyridoxine (c) Cheilosis (iv) Ascorbic acid (d) Convulsions
[JEE MAIN Held on 07-01-2020 Morning]

A) (i)-(c), (ii)-(d),(iii)-(a), (iv)-(b)

B) (i)-(c), (ii)-(a),(iii)-(d), (iv)-(b)

C) (i)-(d), (ii)-(b),(iii)-(a), (iv)-(c)

D) (i)-(a), (ii)-(d),(iii)-(c), (iv)-(b)

• question_answer31) The increasing order of $p{{K}_{b}}$ for the following compounds will be [JEE MAIN Held on 07-01-2020 Morning] A) (B) < (C) < (A)

B) (B) < (A) < (C)

C) (C) < (A) < (B)

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

• question_answer32) Oxidation number of potassium in ${{K}_{2}}O,\text{ }{{K}_{2}}{{O}_{2}}$and $K{{O}_{2}}$, respectively, is [JEE MAIN Held on 07-01-2020 Morning]

A) $+1,\,\,+2\text{ }and+4$

B) $+2,+1\text{ }and+\frac{1}{2}$

C) $+1,\,\,+4\text{ }and+2$

D) $+1,\,\,+1\text{ }and+1$

 Consider the following reaction: $\xrightarrow{O{{H}^{-}}}$ $'\,X\,'$ The product 'X' is used [JEE MAIN Held on 07-01-2020 Morning]

A) In acid base titration as an indicator

B) In protein estimation as an alternative to ninhydrin

C) In laboratory test for phenols

• question_answer34) The relative strength of interionic/ intermolecular forces in decreasing order is: [JEE MAIN Held on 07-01-2020 Morning]

A) ion-ion > ion-dipole > dipole-dipole

B) ion-dipole > dipole-dipole > ion-ion

C) ion-dipole > ion-ion > dipole-dipole

D) dipole-dipole > ion-dipole > ion-ion

• question_answer35) What is the product of following reaction? [JEE MAIN Held on 07-01-2020 Morning] A) B) C) D) • question_answer36) A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of $NaHC{{O}_{3}}$ to give fraction A. The left over organic phase was extracted with dilute $NaOH$solution to give fraction B. The final organic layer was labelled as fraction C. Fractions A, B and C, contain respectively: [JEE MAIN Held on 07-01-2020 Morning]

A) m-chloroaniline, m-chlorobenzoic acid and m-chlorophenol

B) m-chlorophenol, m-chlorobenzoic acid and m-chloroaniline

C) m-chlorobenzoic acid, m-chlorophenol and m-chloroaniline

D) m-chlorobenzoic acid, m-chloroaniline and m-chlorophenol

• question_answer37) Amongst the following statements, that which was not proposed by Dalton was: [JEE MAIN Held on 07-01-2020 Morning]

A) All the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass

B) Matter consists of indivisible atoms.

C) Chemical reactions involve reorganization of atoms. These are neither created nor destroyed in a chemical reaction.

D) When gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same T & P.

• question_answer38) The purest form of commercial iron is [JEE MAIN Held on 07-01-2020 Morning]

A) Scrap iron and pig iron

B) Cast iron

C) Wrought iron

D) Pig iron

• question_answer39) Consider the following reactions: [JEE MAIN Held on 07-01-2020 Morning]

 (A) ${{(C{{H}_{3}})}_{3}}CCH(OH)C{{H}_{3}}\xrightarrow{conc.{{H}_{2}}S{{O}_{4}}}$ (B) ${{(C{{H}_{3}})}_{2}}CHCH(Br)C{{H}_{3}}\xrightarrow{alc.KOH}$ (C) ${{(C{{H}_{3}})}_{2}}CHCH(Br)C{{H}_{3}}\xrightarrow{{{(C{{H}_{3}})}_{3}}{{O}^{\Theta }}{{K}^{\oplus }}}$ (D) ${{(C{{H}_{3}})}_{2}}\underset{OH}{\mathop{\underset{|}{\mathop{C}}\,}}\,-C{{H}_{2}}-CHO\xrightarrow{\Delta }$
Which of these reaction(s) will not produce Saytzeff product?

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

B) (C) only

C) (B) and (D)

D) (D) only

• question_answer40) The electron gain enthalpy (in kJ/mol) of fluorine, chlorine, bromine and iodine, respectively, are: [JEE MAIN Held on 07-01-2020 Morning]

A) -296, -325, -333 and -349

B) -333, -325, -349 and -296

C) -349, -333, -325 and -296

D) -333, -349, -325 and -296

• question_answer41) The IUPAC name of the complex $[Pt{{(N{{H}_{3}})}_{2}}Cl(N{{H}_{2}}C{{H}_{3}})]Cl$ is: [JEE MAIN Held on 07-01-2020 Morning]

A) Diammine chlorido (methanamine) platinum (II) chloride

B) Diammine (methanamine) chloride platinum (II) Chloride

C) Bisammine (methanamine) chloride platinum (II) chloride

D) Diammine chlorido (aminomethane) platinum (II) chloride

• question_answer42) The theory that can completely/properly explain the nature of bonding in $[Ni{{(CO)}_{4}}]$is: [JEE MAIN Held on 07-01-2020 Morning]

A) Crystal field theory

B) Werner's theory

C) Valence bond theory

D) Molecular orbital theory

• question_answer43) The number of orbitals associated with quantum numbers $n=5,\,{{m}_{s}}=+\frac{1}{2}$ is: [JEE MAIN Held on 07-01-2020 Morning]

A) 15

B) 50

C) 25

D) 11

• question_answer44) 1-methylethylene oxide when treated with an excess of HBr produces: [JEE MAIN Held on 07-01-2020 Morning]

A) B) C) D) • question_answer45) The dipole moments of $CC{{l}_{4}},\text{ }CHC{{l}_{3}}$ and $C{{H}_{4}}$are in the order:  [JEE MAIN Held on 07-01-2020 Morning]

A) $CC{{l}_{4}}<C{{H}_{4}}<CHC{{l}_{3}}$

B) $CHC{{l}_{3}}<C{{H}_{4}}=CC{{l}_{4}}$

C) $C{{H}_{4}}=CC{{l}_{4}}<CHC{{l}_{3}}$

D) $C{{H}_{4}}<CC{{l}_{4}}<CHC{{l}_{3}}$

• question_answer46) Two solutions, A and B, each of 100 L was made by dissolving 4 g of $NaOH$and 9.8 g of ${{H}_{2}}S{{O}_{4}}$in water, respectively. The pH of the resultant solution obtained from mixing 40 L of solution A and 10 L of solution B is________.                                                                                [JEE MAIN Held on 07-01-2020 Morning]

• question_answer47) During the nuclear explosion, one of the products is $^{90}Sr$ with half life of 6.93 years. If $1\,\,\mu g$ of  $^{90}Sr$was absorbed in the bones of a  newly born baby in place of Ca, how much time, in years, is required to reduce it by 90% if it is not lost metabolically _________.                                                      [JEE MAIN Held on 07-01-2020 Morning]

• question_answer48) The number of chiral carbons in chloramphenicol is ___________.    [JEE MAIN Held on 07-01-2020 Morning]

 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___________. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer50) 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 Cl and O atoms in (Y) is _________. [JEE MAIN Held on 07-01-2020 Morning]

• question_answer51) The logical statement $(p\Rightarrow q)\wedge (q\Rightarrow \,\tilde{\ }p)$ is equivalent to [JEE MAIN Held on 07-01-2020 Morning]

A) ~q

B) p

C) q

D) ~p

• question_answer52) The greatest positive integer k, for which ${{49}^{k}}+1$ is a factor of the sum ${{49}^{125}}+{{49}^{124}}+.....+{{49}^{2}}+49+1,$ is [JEE MAIN Held on 07-01-2020 Morning]

A) 65

B) 60

C) 32

D) 63

 If the system of linear equations $2x+2ay+az=0$ $2x+3by+bz=0$ $2x+4cy+cz=0,$ where $a,\text{ }b,\text{ }c\,\in R$ are non-zero and distinct; has a non-zero solution, then [JEE MAIN Held on 07-01-2020 Morning]

A) $\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P.

B) a, b, c are in A.P.

C) a + b + c = 0

D) a, b, c are in G.P.

• question_answer54) The area of the region, enclosed by the circle ${{x}^{2}}+{{y}^{2}}=2$ which is not common to the region bounded by the parabola ${{y}^{2}}=x$ and the straight line $y=x$, is [JEE MAIN Held on 07-01-2020 Morning]

A) $\frac{1}{6}(24\pi -1)$

B) $\frac{1}{6}(12\pi -1)$

C) $\frac{1}{3}(12\pi -1)$

D) $\frac{1}{3}(6\pi -1)$

• question_answer55) Let P be a plane 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 [JEE MAIN Held on 07-01-2020 Morning]

A) (6, 5, 2)

B) (4, 3, 2)

C) (3, 4, -2)

D) (6, 5, -2)

• question_answer56) Let $\alpha$ be a root of the equation ${{x}^{2}}+x+1=0$ and the matrix then matrix ${{A}^{31}}$ is equal to: [JEE MAIN Held on 07-01-2020 Morning]

A) ${{A}^{2}}$

B) A

C) ${{I}_{3}}$

D) ${{A}^{3}}$

• question_answer57) If $g(x)={{x}^{2}}+x-1$ and $(gof)(x)=4{{x}^{2}}-10x+5,$then $f\left( \frac{5}{4} \right)$ is equal to: [JEE MAIN Held on 07-01-2020 Morning]

A) $-\frac{1}{2}$

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

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

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

• question_answer58) Let ${{x}^{k}}+{{y}^{k}}={{a}^{k}},\text{ (}a,\text{ }k>0)$ and $\frac{dy}{dx}+{{\left( \frac{y}{x} \right)}^{\frac{1}{3}}}=0$, then k is: [JEE MAIN Held on 07-01-2020 Morning]

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

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

C) $\frac{4}{3}$

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

• question_answer59) Let $\alpha$ and $\beta$ be two real roots of the equation $(k+1)ta{{n}^{2}}x-\sqrt{2}\cdot \lambda \tan x=(1-k)$, where $k(\ne -1)$ and $\lambda$ are real numbers. If ${{\tan }^{2}}(\alpha +\beta )=50,$ then a value of $\lambda$ is: [JEE MAIN Held on 07-01-2020 Morning]

A) 10

B) $10\sqrt{2}$

C) 5

D) $5\sqrt{2}$

• question_answer60) A vector $\vec{a}=\alpha \hat{i}+2\hat{j}+\beta \hat{k}(\alpha ,\beta \in R)$ lies in the plane of the vectors, $\vec{b}=\hat{i}+\hat{j}$ and $\vec{c}=\hat{i}-\hat{j}+4\hat{k}.$If $\vec{a}$ bisects the angle between $\vec{b}$ and $\vec{c}$ , then: [JEE MAIN Held on 07-01-2020 Morning]

A) $\vec{a}\cdot \hat{i}+3=0$

B) $\vec{a}\cdot \hat{i}+1=0$

C) $\vec{a}\cdot \hat{k}+2=0$

D) $\vec{a}\cdot \hat{k}+4=0$

• question_answer61) Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is $-\frac{1}{2}$, then greatest number amongst them is: [JEE MAIN Held on 07-01-2020 Morning]

A) $\frac{21}{2}$

B) 7

C) 27

D) 16

• question_answer62) If $y=mx+4$ is a tangent to both the parabolas, ${{y}^{2}}=4x$ and ${{x}^{2}}=2by,$ then b is equal to [JEE MAIN Held on 07-01-2020 Morning]

A) -64

B) 128

C) -32

D) -128

• question_answer63) 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 [JEE MAIN Held on 07-01-2020 Morning]

A) $\frac{3}{16}$

B) $-\frac{1}{8}$

C) $-\frac{3}{16}$

D) $\frac{1}{8}$

• question_answer64) If $y=y(x)$ is the solution of the differential equation, ${{e}^{y}}\left( \frac{dy}{dx}-1 \right)={{e}^{x}}$ such that $y(0)=0,$then $y(1)$ is equal to [JEE MAIN Held on 07-01-2020 Morning]

A) 2e

B) $lo{{g}_{e}}2$

C) $2+lo{{g}_{e}}2$

D) $1+lo{{g}_{e}}2$

• question_answer65) If $\operatorname{Re}\left( \frac{z-1}{2z+i} \right)=1,$ where $z=x+iy,$ then the point $(x,\text{ }y)$ lies on a [JEE MAIN Held on 07-01-2020 Morning]

A) Circle whose centre is at $\left( -\frac{1}{2},-\frac{3}{2} \right)$

B) Straight line whose slope is $-\frac{2}{3}$

C) Circle whose diameter is $\frac{\sqrt{5}}{2}$

D) Straight line whose slope is $\frac{3}{2}$

• question_answer66) Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is [JEE MAIN Held on 07-01-2020 Morning]

A) $\frac{1}{2}(6!)$

B) $\frac{5}{2}(6!)$

C) ${{5}^{6}}$

D) 6!

• question_answer67) Let the function, $f:[-7,\text{ }0]\to R$ be continuous on $[-7,\text{ }0]$ and differentiable on $(-7,\text{ }0)$. If $f(-7)=-3$ and $f'(x)\le 2$, for all $x\in (-7,0)$ then for all such functions $f,\text{ }f(-1)+f(0)$ lies in the interval [JEE MAIN Held on 07-01-2020 Morning]

A) $[-3,\,\,11]$

B) $(-\infty ,\,\,20]$

C) $(-\infty ,\,\,11]$

D) $[-6,\,\,20]$

• question_answer68) lf $y(\alpha )=\sqrt{2\left( \frac{\tan \alpha +\cot \alpha }{1+{{\tan }^{2}}\alpha } \right)+\frac{1}{{{\sin }^{2}}\alpha },}\alpha \in \left( \frac{3\pi }{4},\pi \right),$ then $\frac{dy}{d\alpha }$ at $\alpha =\frac{5\pi }{6}$ is [JEE MAIN Held on 07-01-2020 Morning]

A) 4

B) $\frac{4}{3}$

C) $-\frac{1}{4}$

D) -4

• question_answer69) If f $(a+b+1-x)=f(x),$ for all x, where a and b are fixed positive real numbers, then $\frac{1}{a+b}\int_{a}^{b}{x(f(x)+f(x+1))dx}$ is equal to [JEE MAIN Held on 07-01-2020 Morning]

A) $\int_{a-1}^{b-1}{f(x)dx}$

B) $\int_{a+1}^{b+1}{f(x)dx}$

C) $\int_{a-1}^{b-1}{f(x+1)dx}$

D) $\int_{a+1}^{b+1}{f(x+1)dx}$

• question_answer70) 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   [JEE MAIN Held on 07-01-2020 Morning]

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

B) $\sqrt{3}$

C) $3\sqrt{2}$

D) $2\sqrt{3}$

• question_answer71) Let A (1, 0), B (6, 2) and $C\left( \frac{3}{2},6 \right)$ 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 $\left( -\frac{7}{6},-\frac{1}{3} \right),$ is _________.         [JEE MAIN Held on 07-01-2020 Morning]

• question_answer72) $\underset{x\to 2}{\mathop{\lim }}\,\frac{{{3}^{x}}+{{3}^{3-x}}-12}{{{3}^{-x/2}}-{{3}^{1-x}}}$ is equal to _________.       [JEE MAIN Held on 07-01-2020 Morning]

• question_answer73) 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 ____.                                                                [JEE MAIN Held on 07-01-2020 Morning]

• question_answer74) If the sum of the coefficients of all even powers of x in the product $\left( 1+x+{{x}^{2}}+...+{{x}^{2n}} \right)\left( 1-x+{{x}^{2}}-{{x}^{3}}+...+{{x}^{2n}} \right)$ is 61, then n is equal to________.                                                 [JEE MAIN Held on 07-01-2020 Morning]

• question_answer75) Let S be the set of points where the function, $f(x)=\left| 2-\left| x-3 \right| \right|,x\in R$, is not differentiable. Then $\sum\limits_{x\in S}{f(f(x))}$ is equal to_____.                                       [JEE MAIN Held on 07-01-2020 Morning]

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