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) \[\frac{AK{{\varepsilon }_{0}}}{d}(1+\alpha d)\] done clear
B) \[\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+\frac{{{\alpha }^{2}}{{d}^{2}}}{2} \right)\] done clear
C) \[\frac{AK{{\varepsilon }_{0}}}{d}\left( 1+\frac{\alpha d}{2} \right)\] done clear
D) \[\frac{A{{\varepsilon }_{0}}K}{d}\left( 1+{{\left( \frac{\alpha d}{2} \right)}^{2}} \right)\] done clear
View Answer play_arrowquestion_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) \[\vec{E}=\left( 60\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)\] done clear
B) \[\vec{E}=\left( 3\times {{10}^{-8}}\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{i}V/m \right)\] done clear
C) \[\vec{E}=\left( 9\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)\] done clear
D) \[\vec{E}=\left( 3\times {{10}^{-8}}sin(1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{j}V/m \right)\] done clear
View Answer play_arrowquestion_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 done clear
B) 60.7 J done clear
C) 48 J done clear
D) 100.8 J done clear
View Answer play_arrowquestion_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) \[\sqrt{\frac{\text{7}}{\text{48}}}l\] done clear
B) \[\frac{\text{1}}{\text{8}}l\] done clear
C) \[\frac{1}{4}l\] done clear
D) \[\sqrt{\frac{\text{3}}{\text{8}}}l\] done clear
View Answer play_arrowquestion_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) \[5m\left( {{u}^{2}}-\frac{119}{200}\frac{GM}{R} \right)\] done clear
B) \[\frac{3m}{8}{{\left( u+\sqrt{\frac{5GM}{6R}} \right)}^{2}}\] done clear
C) \[\frac{m}{20}{{\left( u-\sqrt{\frac{2GM}{3R}} \right)}^{2}}\] done clear
D) \[\frac{m}{20}\left( {{u}^{2}}+\frac{113}{200}\frac{GM}{R} \right)\] done clear
View Answer play_arrowquestion_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 done clear
B) Direction of \[{{I}_{R}}\] remains unchanged and \[{{V}_{R}}\] is maximum at t = 0.5 done clear
C) At t = 0.5 direction of \[{{I}_{R}}\] reverses and \[{{V}_{R}}\]is zero done clear
D) At t = 0.25 direction of \[{{I}_{R}}\] reverses and \[{{V}_{R}}\] is maximum done clear
View Answer play_arrowquestion_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 done clear
B) 0.02 mm done clear
C) 0.04 mm done clear
D) 0.03 mm done clear
View Answer play_arrowquestion_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) \[1.5\text{ }m{{s}^{1}}\] done clear
B) \[1.9\text{ }m{{s}^{1}}\] done clear
C) \[1.7\text{ }m{{s}^{1}}\] done clear
D) \[2.0\text{ }m{{s}^{1}}\] done clear
View Answer play_arrowquestion_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) \[1.6\times {{10}^{14}}\] done clear
B) \[7.8\times {{10}^{14}}\] done clear
C) \[5.6\times {{10}^{12}}\] done clear
D) \[6.2\times {{10}^{15}}\] done clear
View Answer play_arrowquestion_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 done clear
B) 1.42 done clear
C) 1.50 done clear
D) 1.45 done clear
View Answer play_arrowquestion_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 done clear
B) 0.4 done clear
C) 0.25 done clear
D) 0.2 done clear
View Answer play_arrowquestion_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) \[r\sqrt{\frac{3}{2gh}}\] done clear
B) \[r\sqrt{\frac{3}{4gh}}\] done clear
C) \[\frac{1}{r}\sqrt{\frac{4gh}{3}}\] done clear
D) \[\frac{1}{r}\sqrt{\frac{2gh}{3}}\] done clear
View Answer play_arrowquestion_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) \[25{}^\circ \] done clear
B) \[30{}^\circ \] done clear
C) \[20{}^\circ \] done clear
D) \[45{}^\circ \] done clear
View Answer play_arrowquestion_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 done clear
B) 2.0 cm right and 0.9 cm above 1 kg mass done clear
C) 0.9 cm right and 2.0 cm above 1 kg mass done clear
D) 0.6 cm right and 2.0 cm above 1 kg mass done clear
View Answer play_arrowquestion_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 done clear
B) 33 mm done clear
C) 22 mm done clear
D) 12 mm done clear
View Answer play_arrowquestion_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) \[{{\phi }_{i}}=-{{\phi }_{0}}\] done clear
B) \[{{\phi }_{i}}<{{\phi }_{0}}\] done clear
C) \[{{\phi }_{i}}={{\phi }_{0}}\] done clear
D) \[{{\phi }_{i}}>{{\phi }_{0}}\] done clear
View Answer play_arrowquestion_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) \[71.6{}^\circ \] done clear
B) \[45{}^\circ \] done clear
C) \[90{}^\circ \] done clear
D) \[18.4{}^\circ \] done clear
View Answer play_arrowquestion_answer18) Which of the following gives a reversible operation? [JEE MAIN Held on 07-01-2020 Morning]
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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) \[L\leftrightarrow m,C\leftrightarrow \frac{1}{k},R\leftrightarrow b\] done clear
B) \[L\leftrightarrow k,C\leftrightarrow b,R\leftrightarrow m\] done clear
C) \[L\leftrightarrow \frac{1}{b},C\leftrightarrow \frac{1}{m},R\leftrightarrow \frac{1}{k}\] done clear
D) \[L\leftrightarrow m,C\leftrightarrow k,R\leftrightarrow b\] done clear
View Answer play_arrowquestion_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) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]\] done clear
B) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1+\sqrt{3} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]\] done clear
C) \[\frac{\sigma }{2{{\varepsilon }_{0}}}\left[ \left( 1-\frac{\sqrt{3}}{2} \right)\hat{y}-\frac{{\hat{x}}}{2} \right]\] done clear
D) \[\frac{\sigma }{{{\varepsilon }_{0}}}\left[ \left( 1+\frac{\sqrt{3}}{2} \right)\hat{y}+\frac{{\hat{x}}}{2} \right]\] done clear
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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 done clear
B) More efficient as it can exchange only cations done clear
C) More efficient as it can exchange both cations as well as anions done clear
D) Less efficient as the resins cannot be regenerated done clear
View Answer play_arrowquestion_answer27) The atomic radius of Ag is closest to [JEE MAIN Held on 07-01-2020 Morning]
A) Cu done clear
B) Au done clear
C) Hg done clear
D) Ni done clear
View Answer play_arrowquestion_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 done clear
B) -0.158 V done clear
C) -0.182 V done clear
D) 0.182 V done clear
View Answer play_arrowquestion_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 done clear
B) A mixture of \[100\text{ }mL\text{ }C{{S}_{2}}\] and \[100\text{ }mL\] acetone has a volume < 200 mL done clear
C) Heat must be absorbed in order to produce the solution at \[35{}^\circ C\] done clear
D) \[C{{S}_{2}}\] and acetone are less attracted to each other than to themselves done clear
View Answer play_arrowquestion_answer30) Match the following
(i) | Riboflavin | (a) | Beriberi |
(ii) | Thiamine | (b) | Scurvy |
(iii) | Pyridoxine | (c) | Cheilosis |
(iv) | Ascorbic acid | (d) | Convulsions |
A) (i)-(c), (ii)-(d),(iii)-(a), (iv)-(b) done clear
B) (i)-(c), (ii)-(a),(iii)-(d), (iv)-(b) done clear
C) (i)-(d), (ii)-(b),(iii)-(a), (iv)-(c) done clear
D) (i)-(a), (ii)-(d),(iii)-(c), (iv)-(b) done clear
View Answer play_arrowquestion_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) done clear
B) (B) < (A) < (C) done clear
C) (C) < (A) < (B) done clear
D) (A) < (B) < (C) done clear
View Answer play_arrowquestion_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) \[+1,\,\,+2\text{ }and+4\] done clear
B) \[+2,+1\text{ }and+\frac{1}{2}\] done clear
C) \[+1,\,\,+4\text{ }and+2\] done clear
D) \[+1,\,\,+1\text{ }and+1\] done clear
View Answer play_arrowquestion_answer33)
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 done clear
B) In protein estimation as an alternative to ninhydrin done clear
C) In laboratory test for phenols done clear
D) As food grade colourant done clear
View Answer play_arrowquestion_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 done clear
B) ion-dipole > dipole-dipole > ion-ion done clear
C) ion-dipole > ion-ion > dipole-dipole done clear
D) dipole-dipole > ion-dipole > ion-ion done clear
View Answer play_arrowquestion_answer35) What is the product of following reaction? [JEE MAIN Held on 07-01-2020 Morning]
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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 done clear
B) m-chlorophenol, m-chlorobenzoic acid and m-chloroaniline done clear
C) m-chlorobenzoic acid, m-chlorophenol and m-chloroaniline done clear
D) m-chlorobenzoic acid, m-chloroaniline and m-chlorophenol done clear
View Answer play_arrowquestion_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 done clear
B) Matter consists of indivisible atoms. done clear
C) Chemical reactions involve reorganization of atoms. These are neither created nor destroyed in a chemical reaction. done clear
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. done clear
View Answer play_arrowquestion_answer38) The purest form of commercial iron is [JEE MAIN Held on 07-01-2020 Morning]
A) Scrap iron and pig iron done clear
B) Cast iron done clear
C) Wrought iron done clear
D) Pig iron done clear
View Answer play_arrowquestion_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) \[{{(C{{H}_{3}})}_{2}}\underset{OH}{\mathop{\underset{|}{\mathop{C}}\,}}\,-C{{H}_{2}}-CHO\xrightarrow{\Delta }\] |
A) (A), (C) and (D) done clear
B) (C) only done clear
C) (B) and (D) done clear
D) (D) only done clear
View Answer play_arrowquestion_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 done clear
B) -333, -325, -349 and -296 done clear
C) -349, -333, -325 and -296 done clear
D) -333, -349, -325 and -296 done clear
View Answer play_arrowquestion_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 done clear
B) Diammine (methanamine) chloride platinum (II) Chloride done clear
C) Bisammine (methanamine) chloride platinum (II) chloride done clear
D) Diammine chlorido (aminomethane) platinum (II) chloride done clear
View Answer play_arrowquestion_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 done clear
B) Werner's theory done clear
C) Valence bond theory done clear
D) Molecular orbital theory done clear
View Answer play_arrowquestion_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 done clear
B) 50 done clear
C) 25 done clear
D) 11 done clear
View Answer play_arrowquestion_answer44) 1-methylethylene oxide when treated with an excess of HBr produces: [JEE MAIN Held on 07-01-2020 Morning]
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_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) \[CC{{l}_{4}}<C{{H}_{4}}<CHC{{l}_{3}}\] done clear
B) \[CHC{{l}_{3}}<C{{H}_{4}}=CC{{l}_{4}}\] done clear
C) \[C{{H}_{4}}=CC{{l}_{4}}<CHC{{l}_{3}}\] done clear
D) \[C{{H}_{4}}<CC{{l}_{4}}<CHC{{l}_{3}}\] done clear
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_answer48) The number of chiral carbons in chloramphenicol is ___________. [JEE MAIN Held on 07-01-2020 Morning]
View Answer play_arrowquestion_answer49)
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]
View Answer play_arrowquestion_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 done clear
B) p done clear
C) q done clear
D) ~p done clear
View Answer play_arrowquestion_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 done clear
B) 60 done clear
C) 32 done clear
D) 63 done clear
View Answer play_arrowquestion_answer53)
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. done clear
B) a, b, c are in A.P. done clear
C) a + b + c = 0 done clear
D) a, b, c are in G.P. done clear
View Answer play_arrowquestion_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) \[\frac{1}{6}(24\pi -1)\] done clear
B) \[\frac{1}{6}(12\pi -1)\] done clear
C) \[\frac{1}{3}(12\pi -1)\] done clear
D) \[\frac{1}{3}(6\pi -1)\] done clear
View Answer play_arrowquestion_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) done clear
B) (4, 3, 2) done clear
C) (3, 4, -2) done clear
D) (6, 5, -2) done clear
View Answer play_arrowquestion_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) \[{{A}^{2}}\] done clear
B) A done clear
C) \[{{I}_{3}}\] done clear
D) \[{{A}^{3}}\] done clear
View Answer play_arrowquestion_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) \[-\frac{1}{2}\] done clear
B) \[\frac{3}{2}\] done clear
C) \[\frac{1}{2}\] done clear
D) \[-\frac{3}{2}\] done clear
View Answer play_arrowquestion_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) \[\frac{3}{2}\] done clear
B) \[\frac{1}{3}\] done clear
C) \[\frac{4}{3}\] done clear
D) \[\frac{2}{3}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[10\sqrt{2}\] done clear
C) 5 done clear
D) \[5\sqrt{2}\] done clear
View Answer play_arrowquestion_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) \[\vec{a}\cdot \hat{i}+3=0\] done clear
B) \[\vec{a}\cdot \hat{i}+1=0\] done clear
C) \[\vec{a}\cdot \hat{k}+2=0\] done clear
D) \[\vec{a}\cdot \hat{k}+4=0\] done clear
View Answer play_arrowquestion_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) \[\frac{21}{2}\] done clear
B) 7 done clear
C) 27 done clear
D) 16 done clear
View Answer play_arrowquestion_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 done clear
B) 128 done clear
C) -32 done clear
D) -128 done clear
View Answer play_arrowquestion_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) \[\frac{3}{16}\] done clear
B) \[-\frac{1}{8}\] done clear
C) \[-\frac{3}{16}\] done clear
D) \[\frac{1}{8}\] done clear
View Answer play_arrowquestion_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 done clear
B) \[lo{{g}_{e}}2\] done clear
C) \[2+lo{{g}_{e}}2\] done clear
D) \[1+lo{{g}_{e}}2\] done clear
View Answer play_arrowquestion_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 \[\left( -\frac{1}{2},-\frac{3}{2} \right)\] done clear
B) Straight line whose slope is \[-\frac{2}{3}\] done clear
C) Circle whose diameter is \[\frac{\sqrt{5}}{2}\] done clear
D) Straight line whose slope is \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_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) \[\frac{1}{2}(6!)\] done clear
B) \[\frac{5}{2}(6!)\] done clear
C) \[{{5}^{6}}\] done clear
D) 6! done clear
View Answer play_arrowquestion_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) \[[-3,\,\,11]\] done clear
B) \[(-\infty ,\,\,20]\] done clear
C) \[(-\infty ,\,\,11]\] done clear
D) \[[-6,\,\,20]\] done clear
View Answer play_arrowquestion_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 done clear
B) \[\frac{4}{3}\] done clear
C) \[-\frac{1}{4}\] done clear
D) -4 done clear
View Answer play_arrowquestion_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) \[\int_{a-1}^{b-1}{f(x)dx}\] done clear
B) \[\int_{a+1}^{b+1}{f(x)dx}\] done clear
C) \[\int_{a-1}^{b-1}{f(x+1)dx}\] done clear
D) \[\int_{a+1}^{b+1}{f(x+1)dx}\] done clear
View Answer play_arrowquestion_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) \[\frac{3}{\sqrt{2}}\] done clear
B) \[\sqrt{3}\] done clear
C) \[3\sqrt{2}\] done clear
D) \[2\sqrt{3}\] done clear
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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]
View Answer play_arrowquestion_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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