Practice Questions

Q16.The magnetic field vector of an electromagnetic wave is given by 𝐵= 𝐵0 ^i √2 represents unit vector along 𝑥 and 𝑦-axis respectively. At 𝑡= 0 s, two electric charges 𝑞1 of 4𝜋 coulomb and 𝜋 3𝜋 of 2𝜋 coulomb located at 0, 0, and 0, 0, respectively, have the same velocity of 0 . 5c ^i, (where 𝑞2 𝑘 𝑘, 𝑐 is the velocity of light ). The ratio of the force acting on charge 𝑞1 to 𝑞2 is : (1) 1 : √2 (2) 2√2 : 1 (3) √2 : 1 (4) 2 : 1

Q17.There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is 1: 1. The magnetic field at point 𝑃 is_________ . (1) 𝜇0I + 𝑦2 - (𝑥+ 𝑦) (2) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 - (𝑥+ 𝑦) 4πxy√𝑥2 4π (3) 𝜇0I + 𝑦2 + (𝑥+ 𝑦) (4) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 + (𝑥+ 𝑦) 4πxy√𝑥2 4π

Q35.Which of the following equation depicts the oxidizing nature of H2O2 ? (1) 2I−+ H2O2 + 2H+ →I2 + 2H2O (2) I2 + H2O2 + 2 OH−→2I−+ 2H2O + O2 (3) Cl2 + H2O2 →2HCl + O2 (4) KIO4 + H2O2 →KIO3 + H2O + O2

Q36. Correct statement about the given chemical reaction is (1) Reaction is possible and compound (A) will be (2) −¨NH2 group is ortho and para directive, so major product. product (B) is not possible. (3) Reaction is possible and compound (B) will be (4) The reaction will form sulphonated product the major product. instead of nitration.

Q37.What is the correct sequence of reagents used for converting nitrobenzene into m -dibromobenzene? (1) Sn / HCl KBr Br2 H+ (2) Br2 / Fe Sn / HCl NaNO2 / HCl CuBr / HBr−−−−−−→ / → / →/ → → / → / → / → (3) NaNO2 HCl KBr H+ (4) Sn / HCl Br2 NaNO2 NaBr−−−−−−→ / → / → / → → / →/ → / →

Q38.The correct sequence of correct reagents for the following transformation is :- (1) (i) Fe, HCl (2) (i) Fe, HCl (ii) Cl2, HCl, (ii) NaNO2, HCl, 0°C (iii) NaNO2, HCl, 0°C (iii) H2O/H+ (iv) H2O/H+ (iv) Cl2, FeCl3 (3) (i) Cl2, FeCl3 (4) (i) Cl2, FeCl3 (ii) Fe, HCl (ii) NaNO2, HCl, 0°C (iii) NaNO2, HCl, 0°C (iii) Fe, HCl (iv) H2O/H+ (iv) H2O/H+

Q38.The correct sequence of reagents used in the preparation of 4 -bromo- 2-nitroethylbenzene from benzene is : JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper (1) CH3 COCl / AlCl3, Br2 / AlBr3, HNO3 /H2 SO4, Zn / HCl (2) CH3 COCl / AlCl3, Zn −Hg / HCl, Br2 / AlBr3, HNO3 /H2 SO4 (3) HNO3 /H2 SO4, Br2 / AlCl3, CH3 COCl / AlCl3, Zn −Hg / HCl (4) Br2 / AlBr3, CH3 COCl / AlCl3, HNO3 /H2 SO4, Zn / HCl

Q38. Consider the given reaction, percentage yield of : (1) C > A > B (2) B > C > A (3) A > C > B (4) C > B > A

Q44.The Crystal Field Stabilization Energy (CFSE) and magnetic moment (spin-only) of an octahedral aqua complex of a metal ion M𝑍+ are -0 . 8Δ0 and 3 . 87 BM, respectively. Identify M𝑍+ : (1) V3 + (2) Co2 + (3) Cr3 + (4) Mn4 +

Q44.The correct order of intensity of colors of the compounds is: (1) [Ni(CN)4]2−> [NiCl4]2−> [Ni (H2O)6]2+ (2) [Ni (H2O)6]2+ > [NiCl4]2−> [Ni(CN)4]2− (3) [NiCl4]2−> [Ni (H2O)6]2+ > [Ni(CN)4]2− (4) [NiCl4]2−> [Ni(CN)4]2−> [Ni (H2O)6]2+ C2H5 OH −

Q45.Which one of the following complexes is violet in colour? (1) Fe4 [Fe(CN)6]3 ⋅H2O (2) [Fe(CN)5 NOS]4− (3) [Fe(SCN)6]4− (4) [Fe(CN)6]4−

Q49.The correct sequential addition of reagents in the preparation of 3−nitrobenzoic acid from benzene is: JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper (1) Br2 / AlBr3, HNO3 /H2 SO4, Mg / ether, CO2, H3O+ (2) Br2 / AlBr3, NaCN, H3O+, HNO3 /H2 SO4 (3) Br2 / AlBr3, HNO3 /H2 SO4, NaCN, H3O+ (4) HNO3 /H2 SO4, Br2 / AlBr3, Mg / ether, CO2, H3O+

Q61.The number of pairs 𝑎, 𝑏 of real numbers, such that whenever 𝛼 is a root of the equation 𝑥2 + 𝑎𝑥+ 𝑏= 0, 𝛼2 - 2 is also a root of this equation, is : (1) 6 (2) 8 (3) 4 (4) 2

Q61.The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is: (1) 77 (2) 82 (3) 42 (4) 35

Q62.If 𝑏 is very small as compared to the value of 𝑎, so that the cube and other higher powers of 𝑏 can be neglected 𝑎 in the identity 1 1 1 1 … . + 𝛼𝑛+ 𝛽𝑛2 + 𝛾𝑛3 𝑎- 𝑏+ 𝑎- 2𝑏+ 𝑎- 3𝑏+ 𝑎- 𝑛𝑏= then the value of 𝛾 is : (1) 𝑎2 + 𝑏 (2) 𝑎+ 𝑏 3𝑎3 3𝑎2 (3) 𝑏2 (4) 𝑎+ 𝑏2 3𝑎3 3𝑎3

Q63. Let 𝑆𝑛= 1 · ( 𝑛- 1 ) + 2 · ( 𝑛- 2 ) + 3 · ( 𝑛- 3 ) + … + ( 𝑛- 1 ) · 1, 𝑛⩾4 . ∞ 2 Sn 1 The sum ∑n = 4 n! - ( n - 2 ) ! is equal to : 𝑒- 2 e - 1 (1) (2) 6 3 (3) e (4) e 6 3 20 1 4 = . If the sum of this 𝐴. 𝑃. is 189, then a6a16

Q63.If the greatest value of the term independent of x in the expansion of (x sin α + a cosx α )10 is (5!)210! value of a is equal to: (1) −1 (2) 1 (3) −2 (4) 2 10100 1

Q63.If 0 < a, b < 1 , and tan−1 a + tan−1 b = π4 , then the value of (a + b) −( a2+b22 ) ( a3+b33 ) −( a4+b44 ) is : (1) loge( 2e ) (2) e (3) e2 −1 (4) loge 2

Q64.Let [x] denote greatest integer less than or equal to x . If for n ∈N, (1 −x + x3) n = ∑3nj=0 ajxj , then [ 3n2 ] [ 3n−12 ] ∑ j=0 a2j + 4 ∑ j=0 a2j+1 is equal to : (1) 2 (2) 2n−1 (3) 1 (4) n

Q64.A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y −5 = 0 at two points P and Q such that PQ is a diameter of C1 . Then the diameter of C is : (1) 4√15 (2) √285 (3) 15 (4) 7√5 = 1 having eccentricity √52 . If the tangent and

Q64.Let r1 and r2 be the radii of the largest and smallest circles, respectively, which pass through the point (−4, 1) and having their centres on the circumference of the circle x2 + y2 + 2x + 4y −4 = 0. If r1 = a + b√2, then r2 a + b is equal to: (1) 3 (2) 11 (3) 5 (4) 7

Q64.If 0 < x, y < π and cos x + cos y −cos(x + y) = 23 , then sin x + cos y is equal to: (1) 1 (2) √3 2 2 (3) 1−√3 (4) 1+√3 2 2 JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

Q64.Let the circle S : 36x2 + 36y2 −108x + 120y + C = 0 be such that it neither intersects nor touches the co- ordinate axes. If the point of intersection of the lines, x −2y = 4 and 2x −y = 5 lies inside the circle S, then: (1) 25 9 < C < 133 (2) 100 < C < 165 (3) 81 < C < 156 (4) 100 < C < 156 = 1, a > b. Let E2 be another ellipse such that it touches the end points of major axis of E1

Q65.Let an ellipse 𝐸: 𝑥2 + 𝑦2 = 1, 𝑎2 > 𝑏2, passes through 3 1 and has eccentricity 1 If a circle, centered at √ 2, √3. 𝑎2 𝑏2 2 focus 𝐹( 𝛼, 0 ) , 𝛼> 0, of 𝐸 and radius √3, intersects 𝐸 at two points 𝑃 and 𝑄, then 𝑃𝑄2 is equal to : (1) 8 (2) 4 3 3 16 (3) (4) 3 3

Q65.The sum of solutions of the equation 1+sin x = |tan 2x|, x ∈(−π2 , π2 ) −{−π4 , π4 } is: (1) 10 π (2) −7π30 (3) −π15 (4) −11π30