22 January Shift 1 – JEE Main Paper Solution & Review

Q1. A projectile is thrown upward at an angle 60° with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is 45° with the horizontal. The initial speed of the particle is, (1) 40√2 (2) 40 (3) 20√2 (4) 20√3

Q2. Match the following LIST–I (a) Spring constant (b) Thermal conductivity (c) Boltzmann constant (d) Inductance LIST–II (i) ML²T⁻²K⁻¹ (ii) ML⁻¹T⁻³K⁻¹ (iii) ML²T⁻²A⁻² (iv) MLT⁻² (1) a→ii, b→iv, c→i, d→iii (2) a→iv, b→iii, c→ii, d→i (3) a→iii, b→ii, c→iv, d→i (4) a→i, b→ii, c→iii, d→iv

Q3. The escape velocity from a spherical planet A is 10 m/s. The escape velocity from another planet B whose density and radius are 10% of planet A is ____ m/s.

Q4. Two disc having same moment of inertia about their axis. Thickness is t₁ & t₂ and they have same densities. If R₁/R₂ = 1/R then find t₁/t₂.

Q5. Two solid spheres masses 5 kg and 10 kg with radius 10 cm and 20 cm respectively are in contact as shown. Find the moment of inertia of the system about common tangent.

Q6. A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains equilibrium is

Q7. The minimum frequency of photon required to break a particle of mass 15.348 amu into 4α-particle is ______.

Q8. 7.9 MeV α-particle scatters from a target material of atomic number 79. Estimate the distance of closest approach.

Q9. In series R–L circuit voltage of battery is 10 V. Resistance and inductance are 10 Ω and 10 mH respectively. Find the energy stored in inductor when current reaches 1/e times of maximum value. (1) 0.67 mJ (2) 1.33 mJ (3) 0.33 mJ (4) 0.50 mJ

Q10. Electric field in a region is given by E = Axi + Byj, where A = 10 V/m², B = 5 V/m². If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is (in V). (1) 2000 (2) 1000 (3) 500 (4) 0

Q11. During an adiabatic expansion the volume increases to 8 times and temperature reduces to 1/4th. What is the adiabatic constant for the gas?

Q1. Find the energy to excite electron from first Bohr orbit of hydrogen atom to 2nd Bohr’s orbit. (in eV)

Q2. Arrange the given metal ions in increasing order of number of unpaired electrons in low spin complex formed by Mn³⁺, Cr³⁺, Fe³⁺, Co³⁺. (1) Co³⁺ < Fe³⁺ < Mn³⁺ < Cr³⁺ (2) Co³⁺ < Mn³⁺ < Fe³⁺ < Cr³⁺ (3) Cr³⁺ < Mn³⁺ < Fe³⁺ < Co³⁺ (4) Cr³⁺ < Mn³⁺ < Co³⁺ < Fe³⁺

Q3. The order of electrophilic substitution when CHCl₃ and Methanol is added. (1) I⁻ < F⁻ < C₆H₅O⁻ < C₂H₅O⁻ (2) I⁻ > F⁻ > C₆H₅O⁻ > C₂H₅O⁻ (3) I⁻ > F⁻ > C₂H₅O⁻ > C₆H₅O⁻ (4) F⁻ < I⁻ < C₆H₅O⁻ < C₂H₅O⁻

Q4. K₂Cr₂O₇ is heated with KCl in presence of conc. H₂SO₄. Find the correct match of product with their oxidation state. (1) CrO₂Cl₂, +6 (2) Cr₂O₂Cl₂, +6 (3) Cr₂O₂Cl₂, +5 (4) CrO₂Cl₂, +5

Q5. Match the following Column-I with Column-II. Column-I (a) [Ag(NH₃)₂]⁺ (b) Zn–Hg/HCl (c) NH₂–NH₂/KOH (d) Cu²⁺/OH⁻ Column-II (i) Fehling’s solution (ii) Clemmenson’s reduction (iii) Tollen’s reagent (iv) Wolff-Kishner reduction (1) a(i), b(ii), c(iii), d(iv) (2) a(iv), b(iii), c(ii), d(i) (3) a(iii), b(ii), c(iv), d(i) (4) a(i), b(iii), c(iv), d(ii)

Q6. Given below are two statements. Statement I: HX bond length is higher in HCl than HF. Statement II: The lowest boiling point in hydride of group 15 element is having covalency 4. (1) Both statement-I and statement-II are correct (2) Both statement-I and statement-II are incorrect (3) Statement-I is correct and statement-II is incorrect (4) Statement-I is incorrect and statement-II is correct

Q7. When X and Y react with fluorine then it forms XF₃. The XF₃ is a Lewis acid and YF₃ is a Lewis base. Then hybridization of XF₃ and YF₃ is: (1) both sp² (2) both sp³ (3) sp² and sp³ (4) sp³ and sp²

Q8. Reactivity of following on the basis of SN1 mechanism. (1) IV > III > I > II (2) II > IV > III > I (3) III > IV > I > II (4) IV > III > II > I

Q9. A compound ‘A’ with molecular formula C₉H₁₁NO reacts with Br₂/NaOH to give (X). (X) on reaction with NaNO₂ in dil. HCl gives compound (Y). When (Y) is treated with CuCN, followed by hydrolysis gives (Z). The compound (A) on hydrolysis also gives compound (Z). Identify compound (A). (1) Option-1 (2) Option-2 (3) Option-3 (4) Option-4

Q10. Which of the following statement is correct regarding the nature and directive influence of –NO₂ group in nitration of benzene. (1) It is an activating group and ortho/para director (2) It is a deactivating group and ortho/para director (3) It is a deactivating group and meta director (4) It is an activating group and meta director

Q1. \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \beta\sqrt{5}}{2}

Q2. Random variable x has the probability distribution x : 0 1 2 3 4 5 6 7 P(x): 0, 2k, k, 3k, 2k², 2k, k²+k, 7k² Then P(3 < x < 6) is equal to (1) 0.22 (2) 0.64 (3) 0.34 (4) 0.33

Q3. If A = \begin{pmatrix} 2 & 3\\ 3 & 5 \end{pmatrix} (1) 12 (2) 16 (3) 24 (4) 28

Q4. The coefficient of x⁴⁸ in (1+x) + 2(1+x)^2 + 3(1+x)^3 + \dots + 100(1+x)^{100} (1) 100·¹⁰¹C₄₉ − ¹⁰¹C₅₀ (2) ¹⁰⁰C₅₀ + ¹⁰¹C₄₉ (3) 100·¹⁰⁰C₄₉ − ¹⁰⁰C₄₈ (4) 100·¹⁰⁰C₄₉ − ¹⁰⁰C₅₀

Q5. If the sum of the first 4 terms of an AP is 6 and the sum of 6 terms is 4, then the sum of the first 12 terms of an AP is (1) −22 (2) −21 (3) −23 (4) −24

Q6. The number of real solutions of the equation x|x+4| + 3|x+2| + 10 = 0 (1) 1 (2) 4 (3) 3 (4) 2