question_answer1) A particle moving with kinetic energy E has de Broglie wavelength\[\lambda \]. If energy \[\Delta E\] is added to its energy, the wavelength become\[\lambda /2\]. Value of \[\Delta E\], is: [JEE MAIN Held on 09-01-2020 Morning]
A) 4E done clear
B) E done clear
C) 2E done clear
D) 3E done clear
View Answer play_arrowquestion_answer2)
Consider a force\[\vec{F}=-x\hat{i}+y\hat{j}\]. The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is: (all quantities are in SI units) |
A) 2 done clear
B) 1 done clear
C) \[\frac{1}{2}\] done clear
D) \[\frac{3}{2}\] done clear
View Answer play_arrowquestion_answer3) The electric fields of two plane electromagnetic plane waves in vacuum are given by \[{{\vec{E}}_{1}}={{E}_{0}}\hat{j}\cos \left( \omega t-kx \right)\] and \[{{\vec{E}}_{2}}={{E}_{0}}\hat{k}\cos \left( \omega t-ky \right)\] At t = 0, a particle of chcarge q is at origin with a velocity \[\vec{v}=0.8c\hat{j}\] (c is the speed of light in vaccum). The instantaneous force experienced by the particle is: [JEE MAIN Held on 09-01-2020 Morning]
A) \[{{E}_{0}}q\left( 0.4\hat{i}-3\hat{j}+0.8\hat{k} \right)\] done clear
B) \[{{E}_{0}}q\left( -\,0.8\hat{i}+\hat{j}+\hat{k} \right)\] done clear
C) \[{{E}_{0}}q\left( 0.8\hat{i}+\hat{j}+0.2\hat{k} \right)\] done clear
D) \[{{E}_{0}}q\left( 0.8\hat{i}-\hat{j}+0.4\hat{k} \right)\] done clear
View Answer play_arrowquestion_answer4)
Water flows in a horizontal tube (see figure). The pressure of water changes by 700 \[N{{m}^{2}}\] between A and B where the area of cross section are 40 \[c{{m}^{2}}\]and 20\[c{{m}^{2}}\], respectively. Find the rate of flow of water through the tube. |
(density of water = 1000\[kg{{m}^{3}}\]) |
A) \[3020c{{m}^{3}}/s\] done clear
B) \[1810c{{m}^{3}}/s\] done clear
C) \[2720c{{m}^{3}}/s\] done clear
D) \[2420c{{m}^{3}}/s\] done clear
View Answer play_arrowquestion_answer5) Two particles of equal mass m have respective initial velocities \[u\hat{i}\]and u \[\left( \frac{\hat{i}+\hat{j}}{2} \right)\].They collide completely inelastically. The energy lost in the process is: [JEE MAIN Held on 09-01-2020 Morning]
A) \[\sqrt{\frac{2}{3}}m{{u}^{2}}\] done clear
B) \[\frac{3}{4}m{{u}^{2}}\] done clear
C) \[\frac{1}{8}m{{u}^{2}}\] done clear
D) \[\frac{1}{3}m{{u}^{2}}\] done clear
View Answer play_arrowquestion_answer6) Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass\[\frac{m}{4}\]. The ratio of the specific heats \[\left( C_{V}^{A}\,\,\text{and}\,\,C_{V}^{B} \right)\] of gas A and B, respectively is: [JEE MAIN Held on 09-01-2020 Morning]
A) 3 : 5 done clear
B) 7 : 9 done clear
C) 5 : 7 done clear
D) 5 : 9 done clear
View Answer play_arrowquestion_answer7)
A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field \[E\hat{i}\] and a uniform magnetic field \[B\hat{k}\] follows a trajectory from point P to Q as shown in figure. |
The velocities at P and Q are respectively, \[v\vec{i}\]and\[-2v\hat{j}\]. Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale) |
A. \[E=\frac{3}{4}\left( \frac{m{{v}^{2}}}{qa} \right)\] |
B. Rate of work done by the electric field at P is \[\frac{3}{4}\left( \frac{m{{v}^{3}}}{a} \right)\] |
C. Rate of work done by both the fields at Q is zero |
D. The difference between the magnitude of angular momentum of the particle at P and Q is 2 mav. |
A) A, B, C done clear
B) A, C, D done clear
C) A, B, C, D done clear
D) B, C, D done clear
View Answer play_arrowquestion_answer8) If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is: [JEE MAIN Held on 09-01-2020 Morning]
A) 0.01 cm done clear
B) 0.001 mm done clear
C) 0.001 cm done clear
D) 0.02 mm done clear
View Answer play_arrowquestion_answer9)
In the given circuit diagram, a wire is joining points B and D. The current in this wire is: |
A) 0.4 A done clear
B) 4 A done clear
C) 2 A done clear
D) zero done clear
View Answer play_arrowquestion_answer10) The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is\[4\times {{10}^{5}}\text{ }km\]. With light of wavelength of 5500\[\overset{\text{o}}{\mathop{\text{A}}}\,\], the minimum separation between objects on the surface of moon, so that they are just resolved, is close to: [JEE MAIN Held on 09-01-2020 Morning]
A) 20 m done clear
B) 200 m done clear
C) 600 m done clear
D) 60 m done clear
View Answer play_arrowquestion_answer11)
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio \[{{I}_{0}}/{{I}_{A}}\] of moment of inertia \[{{I}_{0}}\]of the system about an axis passing the centroid and about center of any of the spheres \[{{I}_{A}}\] and perpendicular to the plane of the triangle is: |
A) \[\frac{23}{13}\] done clear
B) \[\frac{15}{13}\] done clear
C) \[\frac{13}{15}\] done clear
D) \[\frac{13}{23}\] done clear
View Answer play_arrowquestion_answer12) Consider a sphere of radius R which carries a uniform charge density\[\rho \]. If a sphere of radius \[\frac{R}{2}\]is carved out of it, as shown, the ratio \[\frac{\left| {{{\vec{E}}}_{A}} \right|}{\left| {{{\vec{E}}}_{B}} \right|}\] of magnitude of electric field \[{{\vec{E}}_{A}}\] and \[{{\vec{E}}_{B}}\]respectively, at points A and B due to the remaining portion is: [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{18}{34}\] done clear
B) \[\frac{18}{54}\] done clear
C) \[\frac{21}{34}\] done clear
D) \[\frac{9}{17}\] done clear
View Answer play_arrowquestion_answer13) Radiation, with wavelength 6561\[\overset{\text{o}}{\mathop{\text{A}}}\,\] falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of \[3\text{ }\times \text{ }{{10}^{4}}\]T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to [JEE MAIN Held on 09-01-2020 Morning]
A) 1.6 eV done clear
B) 1.1 eV done clear
C) 0.8 eV done clear
D) 1.8 Ev done clear
View Answer play_arrowquestion_answer14) A long straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance \[\frac{a}{3}\] and 2a, respectively from the axis of the wire is [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{1}{2}\] done clear
B) \[\frac{3}{2}\] done clear
C) \[2\] done clear
D) \[\frac{2}{3}\] done clear
View Answer play_arrowquestion_answer15) A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass \[\frac{m}{2}\] collides with A with a velocity which is half \[\left( \frac{{\vec{v}}}{2} \right)\] the instantaneous velocity \[\vec{v}\]of A. The collision is completely inelastic. Then the combined body [JEE MAIN Held on 09-01-2020 Morning]
A) Escapes from the Planet's Gravitational field done clear
B) Continues to move in a circular orbit done clear
C) Falls vertically downwards towards the planet done clear
D) Starts moving in an elliptical orbit around the planet done clear
View Answer play_arrowquestion_answer16) A vessel of depth 2h is half filled with a liquid of refractive index \[2\sqrt{2}\] and the upper half with another liquid of refractive index\[\sqrt{2}\]. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{h}{\sqrt{2}}\] done clear
B) \[\frac{h}{2\left( \sqrt{2}+1 \right)}\] done clear
C) \[\frac{h}{3\sqrt{2}}\] done clear
D) \[\frac{3}{4}h\sqrt{2}\] done clear
View Answer play_arrowquestion_answer17) An electric dipole of moment \[\vec{p}-=\left( -\hat{i}-3\hat{j}+2\hat{k} \right)\times {{10}^{-29}}\]C.m is at the origin (0, 0, 0). The electric field due to this dipole at \[\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}\](note that \[\vec{r}.\vec{p}=0\]) is paralled to [JEE MAIN Held on 09-01-2020 Morning]
A) \[\left( -\hat{i}-3\hat{j}+2\hat{k} \right)\] done clear
B) \[\left( +\hat{i}-3\hat{j}-2\hat{k} \right)\] done clear
C) \[\left( -\hat{i}+3\hat{j}-2\hat{k} \right)\] done clear
D) \[\left( +\hat{i}+3\hat{j}-2\hat{k} \right)\] done clear
View Answer play_arrowquestion_answer18) A quantity f is given by \[f=\sqrt{\frac{h{{c}^{5}}}{G}}\] where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of [JEE MAIN Held on 09-01-2020 Morning]
A) Energy done clear
B) Area done clear
C) Volume done clear
D) Momentum done clear
View Answer play_arrowquestion_answer19) Three harmonic waves having equal frequency \[\nu \]and same intensity\[{{I}_{0}}\], have phase angles \[0,\frac{\pi }{4}\] and \[-\frac{\pi }{4}\] respectively. When they are superimposed the intensity of the resultant wave is close to [JEE MAIN Held on 09-01-2020 Morning]
A) \[3{{I}_{0}}\] done clear
B) \[~5.8{{I}_{0}}\] done clear
C) \[0.2{{I}_{0}}\] done clear
D) \[{{I}_{0}}\] done clear
View Answer play_arrowquestion_answer20)
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? where, \[1\to 2\] is adiabatic. (Graphs are schematic and are not to scale) |
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer21) The distance x covered by a particle in one dimensional motion varies with time t as \[{{x}^{2}}\text{ }=\text{ }a{{t}^{2}}\text{ }+\text{ }2bt\text{ }+\text{ }c\]. If the acceleration of the particle depends on x as\[{{x}^{n}}\], where n is an integer, the value of n is _____. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer22) In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be _______ [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer23) One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle \[30{}^\circ \] from the horizontal (see figure). Its angular speed when it hits the table is given as \[\sqrt{n}\]\[{{s}^{-1}}\], where n is an integer. The value of n is ______ [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer24) Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown in the figure, the voltage (in Volts) at point A is ___________ [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer25) A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad \[{{s}^{-1}}\]) with which it can be rotated about its other end in space station in (Breaking stress of wire =\[4.8\text{ }\times \text{ }{{10}^{7}}\text{ }N{{m}^{2}}\] and area of cross-section of the wire = \[{{10}^{2}}\text{ }c{{m}^{2}}\]) is [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer26)
\[{{\left[ Pd\left( F \right)\left( Cl \right)\left( Br \right)\left( I \right) \right]}^{2}}\] has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of \[{{\left[ Fe{{\left( CN \right)}_{6}} \right]}^{n\text{ }\text{ }6}}\], respectively, are |
[Note: Ignore the pairing energy] |
A) 0 BM and -2.4 \[{{\Delta }_{0}}\] done clear
B) 5.92 BM and 0 done clear
C) 1.73 BM and -2.0 \[{{\Delta }_{0}}\] done clear
D) 2.84 BM and -1.6 \[{{\Delta }_{0}}\] done clear
View Answer play_arrowquestion_answer27) If enthalpy of atomisation for \[B{{r}_{2\left( I \right)}}\] is x kJ/mol and bond enthalpy for \[B{{r}_{2}}\]is y kJ/mol, the relation between them [JEE MAIN Held on 09-01-2020 Morning]
A) is x > y done clear
B) does not exist done clear
C) is x = y done clear
D) is x < y done clear
View Answer play_arrowquestion_answer28)
The major product Z obtained in the following reaction scheme is |
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer29) Complex X of composition \[Cr{{\left( {{H}_{2}}O \right)}_{6}}C{{l}_{n}}\] has a spin only magnetic moment of 3.83 BM. It reacts with \[AgN{{O}_{3}}\] and shows geometrical isomerism. The IUPAC nomenclature of X is [JEE MAIN Held on 09-01-2020 Morning]
A) Tetraaquadichlorido chromium(III) chloride dehydrate done clear
B) Hexaaqua chromium (III) chloride done clear
C) Tetraaquadichlorido chromium (IV) Chloride dehydrate done clear
D) Dichloridotetraaqua chromium (IV) chloride dehydrate done clear
View Answer play_arrowquestion_answer30) The electronic configurations of bivalent europium and trivalent cerium are (atomic number: Xe = 54, Ce = 58, Eu = 63) [JEE MAIN Held on 09-01-2020 Morning]
A) [Xe] \[4{{f}^{7}}\]and [Xe] \[4{{f}^{1}}\] done clear
B) [Xe] \[4{{f}^{7}}\]\[6{{s}^{2}}\] and [Xe] \[4{{f}^{2}}\text{ }6{{s}^{2}}\] done clear
C) [Xe] \[4{{f}^{2}}\]and [Xe] \[4{{f}^{7}}\] done clear
D) [Xe] \[4{{f}^{4}}\]and [Xe] \[4{{f}^{9}}\] done clear
View Answer play_arrowquestion_answer31) The de Broglie wavelength of an electron in the \[{{4}^{th}}\] Bohr orbit is [JEE MAIN Held on 09-01-2020 Morning]
A) \[4\pi {{a}_{0}}\] done clear
B) \[6\pi {{a}_{0}}\] done clear
C) \[8\pi {{a}_{0}}\] done clear
D) \[2\pi {{a}_{0}}\] done clear
View Answer play_arrowquestion_answer32)
Identify in the following reaction sequence. |
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer33)
The major product (Y) in the following reaction is |
A) \[C{{H}_{3}}-\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{CH}}\,}}\,-\underset{C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,=CH-C{{H}_{3}}\] done clear
B) \[C{{H}_{3}}-\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{C}}\,}}\,=\underset{C{{H}_{2}}C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,-C{{H}_{3}}\] done clear
C) \[{{H}_{3}}C-\overset{C{{H}_{2}}}{\mathop{\overset{||}{\mathop{C}}\,}}\,-\underset{{{C}_{2}}{{H}_{5}}}{\mathop{\underset{|}{\mathop{CH}}\,}}\,-C{{H}_{3}}\] done clear
D) \[C{{H}_{3}}-\overset{C{{H}_{3}}}{\mathop{\overset{|}{\mathop{CH}}\,}}\,-\underset{C{{H}_{2}}C{{H}_{3}}}{\mathop{\underset{|}{\mathop{C}}\,}}\,=C{{H}_{2}}\] done clear
View Answer play_arrowquestion_answer34)
A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following observations : |
(i) A and D both form blue-violet colour with ninhydrin. |
(ii) Lassaigne extract of C gives positive \[AgN{{O}_{3}}\] test and negative \[F{{e}_{4}}{{\left[ Fe{{\left( CN \right)}_{6}} \right]}_{3}}\]test. |
(iii) Lassaigne extract of B and D gives positive sodium nitroprusside test. |
Based on these observations which option is correct? |
A)
A : Aspartame; | B : Alitame; |
C : Saccharin; | D : Sucralose |
B)
A : Saccharin; | B : Alitame; |
C : Sucralose; | D : Aspartame |
C)
A : Alitame; | B : Saccharin; |
C : Aspartame; | D : Sucralose |
D)
A : Aspartame; | B : Saccharin; |
C : Sucralose; | D : Alitame |
question_answer35) If the magnetic moment of a dioxygen species is 1.73 B.M, it may be [JEE MAIN Held on 09-01-2020 Morning]
A) \[O_{2}^{-}\] or \[O_{2}^{+}\] done clear
B) \[{{O}_{2}},O_{2}^{-}\] or \[O_{2}^{+}\] done clear
C) \[{{O}_{2}}\] or \[O_{2}^{+}\] done clear
D) \[{{O}_{2}}\] or \[O_{2}^{-}\] done clear
View Answer play_arrowquestion_answer36)
The increasing order of basicity for the following intermediates is (from weak to strong) |
A) (v) < (i) < (iv) < (ii) < (iii) done clear
B) (iii) < (iv) < (ii) < (i) < (v) done clear
C) (v) < (iii) < (ii) < (iv) < (i) done clear
D) (iii) < (i) < (ii) < (iv) < (v) done clear
View Answer play_arrowquestion_answer37) According to the following diagram, A reduces \[B{{O}_{2}}\]when the temperature is [JEE MAIN Held on 09-01-2020 Morning]
A) \[>\text{ }1400{}^\circ C\] done clear
B) \[>\text{ }1200{}^\circ C\] but \[<\text{ }1400{}^\circ C\] done clear
C) \[<\text{ }1200{}^\circ C\] done clear
D) \[<\text{ }1400{}^\circ C\] done clear
View Answer play_arrowquestion_answer38) The acidic, basic and amphoteric oxides, respectively, are [JEE MAIN Held on 09-01-2020 Morning]
A) \[N{{a}_{2}}O,\text{ }S{{O}_{3}},\text{ }A{{l}_{2}}{{O}_{3}}\] done clear
B) \[C{{l}_{2}}O,\text{ }CaO,\text{ }{{P}_{4}}{{O}_{10}}\] done clear
C) \[MgO,\text{ }C{{l}_{2}}O,\text{ }A{{l}_{2}}{{O}_{3}}\] done clear
D) \[{{N}_{2}}{{O}_{3}},\text{ }L{{i}_{2}}O,\text{ }A{{l}_{2}}{{O}_{3}}\] done clear
View Answer play_arrowquestion_answer39) Which of these will produce the highest yield in Friedel Crafts reaction?
A) done clear
B) done clear
C) done clear
D) done clear
View Answer play_arrowquestion_answer40) The \[{{K}_{sp}}\] for the following dissociation is \[1.6\text{ }\times \text{ }{{10}^{5}}\] \[PbC{{l}_{2\left( s \right)}}\rightleftharpoons Pb_{\left( aq \right)}^{2+}+2Cl_{\left( aq \right)}^{-}\] Which of the following choices is correct for a mixture of 300 mL 0.134 M \[Pb{{\left( N{{O}_{3}} \right)}_{2}}\]and 100 mL 0.4 M NaCl? [JEE MAIN Held on 09-01-2020 Morning]
A) \[Q\text{ }<\text{ }{{K}_{sp}}\] done clear
B) \[Q\text{ }=\text{ }{{K}_{sp}}\] done clear
C) Not enough data provided done clear
D) \[Q\text{ }>\text{ }{{K}_{sp}}\] done clear
View Answer play_arrowquestion_answer41) The compound that cannot act both as oxidising and reducing agent is [JEE MAIN Held on 09-01-2020 Morning]
A) \[{{H}_{3}}P{{O}_{4}}\] done clear
B) \[{{H}_{2}}S{{O}_{3}}\] done clear
C) \[{{H}_{2}}{{O}_{2}}\] done clear
D) \[HN{{O}_{2}}\] done clear
View Answer play_arrowquestion_answer42) 'X' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is [JEE MAIN Held on 09-01-2020 Morning]
A) Zinc sulphide done clear
B) Carbon tetrachloride done clear
C) Mercury done clear
D) Silicon carbide done clear
View Answer play_arrowquestion_answer43)
B has a smaller first ionization enthalpy than Be. Consider the following statements. |
(I) It is easier to remove 2p electron than 2s electron |
(II) 2p electron of B is more shielded from the nucleus by the inner core of electrons than the 2s electrons of Be |
(III) 2s electron has more penetration power than 2p electron |
(IV) Atomic radius of B is more than Be (atomic number B = 5, Be = 4) |
The correct statements are |
A) (I), (II) and (IV) done clear
B) (I), (III) and (IV) done clear
C) (I), (II) and (III) done clear
D) (II), (III) and (IV) done clear
View Answer play_arrowquestion_answer44)
For following reactions |
\[A\xrightarrow{700K}\] Product |
\[A\xrightarrow[catalyst]{500K}\] Product |
it was found that the \[{{E}_{a}}\]is decreased by 30 kJ/ mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponential factor is same) |
A) 75 kJ/mol done clear
B) 198 kJ/mol done clear
C) 105 kJ/mol done clear
D) 135 kJ/mol done clear
View Answer play_arrowquestion_answer45) The correct order of heat of combustion for following alkadienes is [JEE MAIN Held on 09-01-2020 Morning]
A) (c) < (b) < (a) done clear
B) (a) < (c) < (b) done clear
C) (b) < (c) < (a) done clear
D) (a) < (b) < (c) done clear
View Answer play_arrowquestion_answer46) How much amount of NaCl should be added to 600 g of water \[\left( \rho =1.00\text{ }g/mL \right)\] to decrease the freezing point of water to \[\,0.2{}^\circ C\]? ________. (The freezing point depression constant for water\[=\text{ }2\text{ }K\text{ }kg\text{ }mo{{l}^{1}}\]) [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer47) The molarity of \[HN{{O}_{3}}\]in a sample which has density 1.4 g/mL and mass percentage of 63% is _____. (Molecular Weight of \[HN{{O}_{3}}\]= 63) [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer48) The hardness of a water sample containing \[{{10}^{-3}}M\,\,\,MgS{{O}_{4}}\] expressed as \[CaC{{O}_{3}}\]equivalents (in ppm) is _____. (molar mass of \[MgS{{O}_{4}}\] is\[120.37\text{ }g/mol\]) [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer49) \[108\text{ }g\]of silver (molar mass \[108\text{ }g\text{ }mo{{l}^{1}}\]) is deposited at cathode from \[AgN{{O}_{3}}(aq)\] solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water by the same quantity of electricity is ______. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer50) The mass percentage of nitrogen in histamine is _____. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer51) Let z be a complex number such that \[\left| \frac{z-i}{z+2i} \right|=1\] and \[|z|=\frac{5}{2}.\]Then the value of \[|z+3i|\] is [JEE MAIN Held on 09-01-2020 Morning]
A) \[2\sqrt{3}\] done clear
B) \[\frac{7}{2}\] done clear
C) \[\sqrt{10}\] done clear
D) \[\frac{15}{4}\] done clear
View Answer play_arrowquestion_answer52)
If for some \[\alpha \] and \[\beta \] in R, the intersection of the following three planes |
\[x+4y-2z=1\] |
\[x+7y-5z=\beta \] |
\[x+5y+\alpha z=5\] |
is a line in \[{{R}^{3}},\] then \[\alpha +\beta \] is equal to |
A) \[-10\] done clear
B) \[0\] done clear
C) \[2\] done clear
D) 10 done clear
View Answer play_arrowquestion_answer53) A circle touches the y-axis at the point \[(0,4)\] and passes through the point. Which of the following lines is not a tangent to this circle? [JEE MAIN Held on 09-01-2020 Morning]
A) \[3x-4y-24=0\] done clear
B) \[4x-3y+17=0\] done clear
C) \[4x+3y-8=0\] done clear
D) \[3x+4y-6=0\] done clear
View Answer play_arrowquestion_answer54) In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obtained. The probability that the second A-card appears before the third B-card is [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{9}{16}\] done clear
B) \[\frac{13}{16}\] done clear
C) \[\frac{11}{16}\] done clear
D) \[\frac{15}{16}\] done clear
View Answer play_arrowquestion_answer55) Let f be any function continuous on \[[a,b]\]and twice differentiable on \[(a,b)\]. If for all \[x\in (a,b),\] \[f'(x)>0\] and \[f''(x)<0,\] then for any \[c\in (a,b),\frac{f(c)-f(a)}{f(b)-f(c)}\]is greater than [JEE MAIN Held on 09-01-2020 Morning]
A) \[1\] done clear
B) \[\frac{b+a}{b-a}\] done clear
C) \[\frac{c-a}{b-c}\] done clear
D) \[\frac{b-c}{c-a}\] done clear
View Answer play_arrowquestion_answer56) The number of real roots of the equation, \[{{e}^{4x}}+{{e}^{3x}}-4{{e}^{2x}}+{{e}^{x}}+1=0\] is [JEE MAIN Held on 09-01-2020 Morning]
A) 4 done clear
B) 2 done clear
C) 3 done clear
D) 1 done clear
View Answer play_arrowquestion_answer57) If \[{{e}_{1}}\] and \[{{e}_{2}}\] are the eccentricities of the ellipse, \[\frac{{{x}^{2}}}{18}+\frac{{{y}^{2}}}{4}=1\]and the hyperbola, \[\frac{{{x}^{2}}}{9}-\frac{{{y}^{2}}}{4}=1\] respectively and \[({{e}_{1}},{{e}_{2}})\]is a point on the ellipse, \[15{{x}^{2}}+3{{y}^{2}}=k,\]then k is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) 14 done clear
B) 15 done clear
C) 17 done clear
D) 16 done clear
View Answer play_arrowquestion_answer58) Let C be the centroid of the triangle with vertices \[(3,-1),\,\,(1,3)\] and \[(2,4)\]. Let P be the point of intersection of the lines \[x+3y-1=0\] and\[3x-y+1=0\]. Then the line passing through the points C and P also passes through the point [JEE MAIN Held on 09-01-2020 Morning]
A) \[(-9,-6)\] done clear
B) \[(-9,-7)\] done clear
C) \[(9,7)\] done clear
D) \[(7,6)\] done clear
View Answer play_arrowquestion_answer59) The integral \[\int{\frac{dx}{{{(x+4)}^{\frac{8}{7}}}{{(x-3)}^{\frac{6}{7}}}}}\] is equal to (where C is a constant of integration) [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{1}{2}\,\,{{\left( \frac{x-3}{x+4} \right)}^{3/7}}+C\] done clear
B) \[-\frac{1}{13}{{\left( \frac{x-3}{x+4} \right)}^{-13/7}}+C\] done clear
C) \[{{\left( \frac{x-3}{x+4} \right)}^{1/7}}+C\] done clear
D) \[-{{\left( \frac{x-3}{x+4} \right)}^{-1/7}}+C\] done clear
View Answer play_arrowquestion_answer60) If the matrices B = adj A and \[C=3A,\]then \[\frac{|adj\,B|}{|C|}\] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) 16 done clear
B) 2 done clear
C) 72 done clear
D) 8 done clear
View Answer play_arrowquestion_answer61) The value of \[\int\limits_{0}^{2\pi }{\frac{x{{\sin }^{8}}x}{{{\sin }^{8}}x+{{\cos }^{8}}x}}\,\,\,dx\] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[{{\pi }^{2}}\] done clear
B) \[2\pi \] done clear
C) \[2{{\pi }^{2}}\] done clear
D) \[4\pi \] done clear
View Answer play_arrowquestion_answer62) The product \[{{2}^{\frac{1}{4}}}.\,{{4}^{\frac{1}{16}}}.\,{{8}^{\frac{1}{48}}}.\,{{16}^{\frac{1}{128}}}.....\] to \[\infty \] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[{{2}^{\frac{1}{2}}}\] done clear
B) \[{{2}^{\frac{1}{4}}}\] done clear
C) \[2\] done clear
D) \[1\] done clear
View Answer play_arrowquestion_answer63) Negation of the statement: ?\[\sqrt{5}\] is an integer or 5 is irrational' is [JEE MAIN Held on 09-01-2020 Morning]
A) \[\sqrt{5}\] is not an integer and 5 is not irrational done clear
B) \[\sqrt{5}\] is an integer and 5 is irrational done clear
C) \[\sqrt{5}\] is not an integer or 5 is not irrational done clear
D) \[\sqrt{5}\] is irrational or 5 is an integer done clear
View Answer play_arrowquestion_answer64) Let the observations \[{{x}_{i}}(1\le i\le 10)\] satisfy the equations, \[\sum\limits_{i=1}^{10}{({{x}_{i}}-5)=10}\] and \[\sum\limits_{i=1}^{10}{{{({{x}_{i}}-5)}^{2}}=40}\] If \[\mu \] and \[\lambda \] are the mean and the variance of the observations, \[{{x}_{1}}-3,\] \[{{x}_{2}}-3,.....,{{x}_{10}}-3,\] then the ordered pair \[(\mu ,\lambda )\]is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[(6,\,3)\] done clear
B) \[(3,\,6)\] done clear
C) \[(3,\,3)\] done clear
D) \[(6,\,6)\] done clear
View Answer play_arrowquestion_answer65) If for all real triplets (a, b, c), \[f(x)=a+bx+c{{x}^{2}};\]then \[\int_{0}^{1}{f(x)\,dx}\] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[2\left\{ 3f(1)+2f\left( \frac{1}{2} \right) \right\}\] done clear
B) \[\frac{1}{2}\left\{ f(1)+3f\left( \frac{1}{2} \right) \right\}\] done clear
C) \[\frac{1}{6}\left\{ f(0)+f(1)+4f\left( \frac{1}{2} \right) \right\}\] done clear
D) \[\frac{1}{3}\left\{ f(0)+f\left( \frac{1}{2} \right) \right\}\] done clear
View Answer play_arrowquestion_answer66) If \[f'(x)={{\tan }^{-1}}(\sec x+\tan x),\] \[-\frac{\pi }{2}<x<\frac{\pi }{2},\]and \[f(0)=0,\] then \[f(1)\] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{\pi +1}{4}\] done clear
B) \[\frac{1}{4}\] done clear
C) \[\frac{\pi +2}{4}\] done clear
D) \[\frac{\pi -1}{4}\] done clear
View Answer play_arrowquestion_answer67) The value of \[{{\cos }^{3}}\left( \frac{\pi }{8} \right).\cos \left( \frac{3\pi }{8} \right)+{{\sin }^{3}}\left( \frac{\pi }{8} \right).\sin \left( \frac{3\pi }{8} \right)\] is [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{1}{4}\] done clear
B) \[\frac{1}{2\sqrt{2}}\] done clear
C) \[\frac{1}{2}\] done clear
D) \[\frac{1}{\sqrt{2}}\] done clear
View Answer play_arrowquestion_answer68) If the number of five digit numbers with distinct digits and 2 at the 10th place is 336 k, then k is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) 8 done clear
B) 6 done clear
C) 7 done clear
D) 4 done clear
View Answer play_arrowquestion_answer69) If is continuous at \[x=0,\]then \[a+2b\] is equal to [JEE MAIN Held on 09-01-2020 Morning]
A) \[-1\] done clear
B) \[1\] done clear
C) \[0\] done clear
D) \[-2\] done clear
View Answer play_arrowquestion_answer70) A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of \[50\,\,c{{m}^{3}}/\min .\]When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the thickness of ice decreases, is [JEE MAIN Held on 09-01-2020 Morning]
A) \[\frac{1}{36\pi }\] done clear
B) \[\frac{1}{18\pi }\] done clear
C) \[\frac{1}{54\pi }\] done clear
D) \[\frac{5}{6\pi }\] done clear
View Answer play_arrowquestion_answer71) The projection of the line segment joining the points \[(1,-1,3)\] and \[(2,-4,11)\] on the line joining the points \[(-1,2,3)\] and \[(3,-2,10)\] is_______. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer72) The coefficient of \[{{x}^{4}}\] in the expansion of \[{{(1+x+{{x}^{2}})}^{10}}\]is _______. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer73) If the vectors, \[\overset{\to }{\mathop{p}}\,=(a+1)\hat{i}+a\hat{j}+a\hat{k},\] \[\overset{\to }{\mathop{q}}\,=a\,\,\hat{i}+(a+1)\hat{j}+a\hat{k},\] and \[\overset{\to }{\mathop{r}}\,=a\,\,\hat{i}+a\hat{j}+(a+1)\hat{k}\,\,(a\in R)\]are coplanar and \[3{{(\overset{\to }{\mathop{p}}\,.\overset{\to }{\mathop{q}}\,)}^{2}}-\lambda {{\left| \overset{\to }{\mathop{r}}\,\times \overset{\to }{\mathop{q}}\, \right|}^{2}}=0,\]then the value of \[\lambda \] is [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer74) The number of distinct solutions of the equation, \[{{\log }_{\frac{1}{2}}}|\sin x|=2-{{\log }_{\frac{1}{2}}}|\cos x|\] in the interval \[[0,\,\,2\pi ],\] is _______. [JEE MAIN Held on 09-01-2020 Morning]
View Answer play_arrowquestion_answer75) If for \[x\ge 0,\] \[y=y(x)\] is the solution of the differential equation, \[(x+1)dy=({{(x+1)}^{2}}+y-3)dx,\,\,y(2)=0,\]. then \[y(3)\] is equal to _______ [JEE MAIN Held on 09-01-2020 Morning]
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