Class XII Physics

਀                            㰀椀渀瀀甀琀 琀礀瀀攀㴀∀挀栀攀挀欀戀漀砀∀ 椀搀㴀∀挀栀愀瀀琀攀爀㄀㈀∀ 渀愀洀攀㴀∀挀栀愀瀀琀攀爀∀ 瘀愀氀甀攀㴀∀䌀栀愀瀀琀攀爀 ㄀㈀∀㸀 12. Atoms਀                        㰀⼀搀椀瘀㸀 ਀    㰀⼀搀椀瘀㸀 ਀    㰀搀椀瘀 挀氀愀猀猀㴀∀挀漀渀琀愀椀渀攀爀 栀椀搀搀攀渀∀ 椀搀㴀∀最攀渀攀爀愀琀攀搀倀愀瀀攀爀䌀漀渀琀愀椀渀攀爀∀㸀㰀⼀搀椀瘀㸀 ਀    㰀猀挀爀椀瀀琀㸀 // Initialize jsPDF਀        挀漀渀猀琀 笀 樀猀倀䐀䘀 紀 㴀 眀椀渀搀漀眀⸀樀猀瀀搀昀㬀 ਀        氀攀琀 猀挀栀漀漀氀一愀洀攀 㴀 ✀✀㬀 let questionCounter = 1;਀        氀攀琀 猀攀猀猀椀漀渀夀攀愀爀 㴀 ✀✀㬀 ਀        挀漀渀猀琀 焀甀攀猀琀椀漀渀猀 㴀 笀 physics: {਀                ∀䌀栀愀瀀琀攀爀 ㄀∀㨀 笀 mcq: [ ਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀䄀 甀渀椀昀漀爀洀 攀氀攀挀琀爀椀挀 昀椀攀氀搀 瀀漀椀渀琀椀渀最 椀渀 瀀漀猀椀琀椀瘀攀 堀ⴀ搀椀爀攀挀琀椀漀渀 攀砀椀猀琀猀 椀渀 愀 爀攀最椀漀渀⸀ 䰀攀琀 䄀 戀攀 琀栀攀 漀爀椀最椀渀Ⰰ 䈀 戀攀 琀栀攀 瀀漀椀渀琀 漀渀 琀栀攀 堀ⴀ愀砀椀猀 愀琀 砀 㴀 ⬀㄀ 挀洀 愀渀搀 䌀 戀攀 琀栀攀 瀀漀椀渀琀 漀渀 琀栀攀 夀ⴀ愀砀椀猀 愀琀 礀 㴀 ⬀㄀ 挀洀⸀ 吀栀攀渀 琀栀攀 瀀漀琀攀渀琀椀愀氀 愀琀 瀀漀椀渀琀猀 䄀Ⰰ 䈀 愀渀搀 䌀 猀愀琀椀猀昀礀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀嘀开䄀 㰀 嘀开䈀∀Ⰰ ∀嘀开䄀 㸀 嘀开䈀∀Ⰰ ∀嘀开䄀 㰀 嘀开䌀∀Ⰰ ∀嘀开䄀 㸀 嘀开䌀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀嘀开䄀 㰀 嘀开䈀∀ 紀Ⰰ { question: "A conducting wire connects two charged conducting spheres of radii r₁ and r₂ such that they attain equilibrium with respect to each other. The distance of separation between the two spheres is very large as compared to either of their radii. The ratio of the magnitudes of the electric fields at the surfaces of the spheres of radii r₁ and r₂ is:", options: ["r₁/r₂", "r₂/r₁", "r₂²/r₁²", "r₁²/r₂²"], answer: "r₂/r₁" },਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀吀栀攀 搀椀昀昀爀愀挀琀椀漀渀 攀昀昀攀挀琀 挀愀渀 戀攀 漀戀猀攀爀瘀攀搀 椀渀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀猀漀甀渀搀 眀愀瘀攀猀 漀渀氀礀∀Ⰰ ∀氀椀最栀琀 眀愀瘀攀猀 漀渀氀礀∀Ⰰ ∀甀氀琀爀愀猀漀渀椀挀 眀愀瘀攀猀 漀渀氀礀∀Ⰰ ∀猀漀甀渀搀 眀愀瘀攀猀 愀猀 眀攀氀氀 愀猀 氀椀最栀琀 眀愀瘀攀猀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀猀漀甀渀搀 眀愀瘀攀猀 愀猀 眀攀氀氀 愀猀 氀椀最栀琀 眀愀瘀攀猀∀ 紀Ⰰ { question: "A capacitor consists of two parallel plates, with an area of cross-section of 0.001 m², separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of 10⁸ V/s, then the value of displacement current through the capacitor is:", options: ["8.85 × 10⁻³ A", "8.85 × 10⁻⁴ A", "7.85 × 10⁻³ A", "9.85 × 10⁻³ A"], answer: "8.85 × 10⁻³ A" },਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀䤀渀 愀 猀攀爀椀攀猀 䰀䌀刀 挀椀爀挀甀椀琀Ⰰ 琀栀攀 瘀漀氀琀愀最攀 愀挀爀漀猀猀 琀栀攀 爀攀猀椀猀琀愀渀挀攀Ⰰ 挀愀瀀愀挀椀琀愀渀挀攀 愀渀搀 椀渀搀甀挀琀愀渀挀攀 椀猀 ㄀　 嘀 攀愀挀栀⸀ 䤀昀 琀栀攀 挀愀瀀愀挀椀琀愀渀挀攀 椀猀 猀栀漀爀琀 挀椀爀挀甀椀琀攀搀 琀栀攀 瘀漀氀琀愀最攀 愀挀爀漀猀猀 琀栀攀 椀渀搀甀挀琀愀渀挀攀 眀椀氀氀 戀攀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀㄀　 嘀∀Ⰰ ∀㄀　ᨀ㈢ 嘀∀Ⰰ ∀㄀　⼀ᨀ㈢ 嘀∀Ⰰ ∀㈀　 嘀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀㄀　ᨀ㈢ 嘀∀ 紀 ],਀                    愀猀猀攀爀琀椀漀渀㨀 嬀  { statement1: "On increasing the current sensitivity of a galvanometer by increasing the number of turns may not necessarily increase its voltage sensitivity.", statement2: "The resistance of the coil of the galvanometer increases on increasing the number of turns.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are true and Reason is the correct explanation of Assertion" },਀                        笀 猀琀愀琀攀洀攀渀琀㄀㨀 ∀䤀渀 愀 栀礀搀爀漀最攀渀 愀琀漀洀 琀栀攀爀攀 椀猀 漀渀氀礀 漀渀攀 攀氀攀挀琀爀漀渀 戀甀琀 椀琀猀 攀洀椀猀猀椀漀渀 猀瀀攀挀琀爀甀洀 猀栀漀眀猀 洀愀渀礀 氀椀渀攀猀⸀∀Ⰰ 猀琀愀琀攀洀攀渀琀㈀㨀 ∀䤀渀 愀 最椀瘀攀渀 猀愀洀瀀氀攀 漀昀 栀礀搀爀漀最攀渀 琀栀攀爀攀 愀爀攀 洀愀渀礀 愀琀漀洀猀 攀愀挀栀 挀漀渀琀愀椀渀椀渀最 漀渀攀 攀氀攀挀琀爀漀渀㬀 栀攀渀挀攀 洀愀渀礀 攀氀攀挀琀爀漀渀猀 椀渀 搀椀昀昀攀爀攀渀琀 愀琀漀洀猀 洀愀礀 戀攀 椀渀 搀椀昀昀攀爀攀渀琀 漀爀戀椀琀猀 猀漀 洀愀渀礀 琀爀愀渀猀椀琀椀漀渀猀 昀爀漀洀 栀椀最栀攀爀 琀漀 氀漀眀攀爀 漀爀戀椀琀猀 愀爀攀 瀀漀猀猀椀戀氀攀⸀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 愀渀搀 刀攀愀猀漀渀 椀猀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀Ⰰ ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 戀甀琀 刀攀愀猀漀渀 椀猀 渀漀琀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀Ⰰ ∀䄀猀猀攀爀琀椀漀渀 椀猀 琀爀甀攀 戀甀琀 刀攀愀猀漀渀 椀猀 昀愀氀猀攀∀Ⰰ ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 昀愀氀猀攀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 愀渀搀 刀攀愀猀漀渀 椀猀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀ 紀 ],਀                    琀眀漀䴀愀爀欀㨀 嬀  "A platinum surface having work function 5.63 eV is illuminated by a monochromatic source of 1.6 × 10¹⁵ Hz. What will be the minimum wavelength associated with the ejected electron?",਀                        ∀䄀 戀攀愀洀 漀昀 氀椀最栀琀 挀漀渀猀椀猀琀椀渀最 漀昀 琀眀漀 眀愀瘀攀氀攀渀最琀栀猀Ⰰ 㐀　　　 씀 愀渀搀 㘀　　　 씀Ⰰ 椀猀 甀猀攀搀 琀漀 漀戀琀愀椀渀 椀渀琀攀爀昀攀爀攀渀挀攀 昀爀椀渀最攀猀 椀渀 愀 夀漀甀渀最✀猀 搀漀甀戀氀攀ⴀ猀氀椀琀 攀砀瀀攀爀椀洀攀渀琀⸀ 圀栀愀琀 椀猀 琀栀攀 氀攀愀猀琀 搀椀猀琀愀渀挀攀 昀爀漀洀 琀栀攀 挀攀渀琀爀愀氀 洀愀砀椀洀甀洀 眀栀攀爀攀 琀栀攀 搀愀爀欀 昀爀椀渀最攀 椀猀 漀戀琀愀椀渀攀搀㼀∀Ⰰ "State Gauss's theorem in electrostatics. Using this theorem, derive an expression for the electric field due to an infinitely long straight wire of linear charge density λ.",਀                        ∀䐀攀昀椀渀攀 攀氀攀挀琀爀椀挀 昀氀甀砀 愀渀搀 眀爀椀琀攀 椀琀猀 匀䤀 甀渀椀琀⸀ 唀猀攀 䜀愀甀猀猀✀猀 氀愀眀 琀漀 漀戀琀愀椀渀 琀栀攀 攀砀瀀爀攀猀猀椀漀渀 昀漀爀 琀栀攀 攀氀攀挀琀爀椀挀 昀椀攀氀搀 搀甀攀 琀漀 愀 甀渀椀昀漀爀洀氀礀 挀栀愀爀最攀搀 椀渀昀椀渀椀琀攀 瀀氀愀渀攀 猀栀攀攀琀 漀昀 挀栀愀爀最攀⸀∀ ],਀                    琀栀爀攀攀䴀愀爀欀㨀 嬀  "Find the expression for the capacitance of a parallel plate capacitor of plate area A and plate separation d when (I) a dielectric slab of thickness t and (II) a metallic slab of thickness t, where (t < d) are introduced one by one between the plates of the capacitor. In which case would the capacitance be more and why?",਀                        ∀䐀爀愀眀 愀 爀愀礀 搀椀愀最爀愀洀 昀漀爀 琀栀攀 昀漀爀洀愀琀椀漀渀 漀昀 椀洀愀最攀 戀礀 愀 䌀愀猀猀攀最爀愀椀渀 琀攀氀攀猀挀漀瀀攀⸀ 圀栀礀 琀栀攀猀攀 琀礀瀀攀猀 漀昀 琀攀氀攀猀挀漀瀀攀猀 愀爀攀 瀀爀攀昀攀爀爀攀搀 漀瘀攀爀 爀攀昀爀愀挀琀椀渀最 琀礀瀀攀 琀攀氀攀猀挀漀瀀攀猀㼀 ⠀圀爀椀琀攀 ㈀ 瀀漀椀渀琀猀⤀∀Ⰰ "Draw the energy band diagram for P-type semiconductor at (i) T=0K and (ii) room temperature."਀                    崀Ⰰ fiveMark: [ ਀                        ∀䔀砀瀀氀愀椀渀 戀爀椀攀昀氀礀Ⰰ 眀椀琀栀 琀栀攀 栀攀氀瀀 漀昀 愀 氀愀戀攀氀氀攀搀 搀椀愀最爀愀洀Ⰰ 琀栀攀 戀愀猀椀挀 瀀爀椀渀挀椀瀀氀攀 漀昀 琀栀攀 眀漀爀欀椀渀最 漀昀 愀渀 愀⸀挀⸀ 最攀渀攀爀愀琀漀爀⸀ 䤀渀 愀渀 愀⸀挀⸀ 最攀渀攀爀愀琀漀爀Ⰰ 挀漀椀氀 漀昀 一 琀甀爀渀猀 愀渀搀 愀爀攀愀 䄀 椀猀 爀漀琀愀琀攀搀 愀琀 愀渀 愀渀最甀氀愀爀 瘀攀氀漀挀椀琀礀 준 椀渀 愀 甀渀椀昀漀爀洀 洀愀最渀攀琀椀挀 昀椀攀氀搀 䈀⸀ 䐀攀爀椀瘀攀 愀渀 攀砀瀀爀攀猀猀椀漀渀 昀漀爀 琀栀攀 椀渀猀琀愀渀琀愀渀攀漀甀猀 瘀愀氀甀攀 漀昀 琀栀攀 攀洀昀 椀渀搀甀挀攀搀 椀渀 挀漀椀氀⸀ 圀栀愀琀 椀猀 琀栀攀 猀漀甀爀挀攀 漀昀 攀渀攀爀最礀 最攀渀攀爀愀琀椀漀渀 椀渀 琀栀椀猀 搀攀瘀椀挀攀㼀∀Ⰰ "A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is angular magnification of the telescope in normal adjustment? If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 10⁶ m, and the radius of lunar orbit is 3.8 × 10⁸ m."਀                    崀Ⰰ caseStudy: [ ਀                        笀 挀愀猀攀㨀 ∀䌀愀猀攀 匀琀甀搀礀 䈀愀猀攀搀 儀甀攀猀琀椀漀渀㨀 䴀漀琀椀漀渀 漀昀 䌀栀愀爀最攀 椀渀 䴀愀最渀攀琀椀挀 䘀椀攀氀搀尀渀䄀渀 攀氀攀挀琀爀漀渀 眀椀琀栀 猀瀀攀攀搀 瘀耀†㰀㰀 挀 洀漀瘀攀猀 椀渀 愀 挀椀爀挀氀攀 漀昀 爀愀搀椀甀猀 爀耀†椀渀 愀 甀渀椀昀漀爀洀 洀愀最渀攀琀椀挀 昀椀攀氀搀⸀ 吀栀椀猀 攀氀攀挀琀爀漀渀 椀猀 愀戀氀攀 琀漀 琀爀愀瘀攀爀猀攀 愀 挀椀爀挀甀氀愀爀 瀀愀琀栀 愀猀 琀栀攀 洀愀最渀攀琀椀挀 昀漀爀挀攀 愀挀琀椀渀最 漀渀 琀栀攀 攀氀攀挀琀爀漀渀 椀猀 瀀攀爀瀀攀渀搀椀挀甀氀愀爀 琀漀 戀漀琀栀 瘀耀†愀渀搀 䈀Ⰰ 愀猀 猀栀漀眀渀 椀渀 琀栀攀 昀椀最甀爀攀⸀ 吀栀椀猀 昀漀爀挀攀 挀漀渀琀椀渀甀漀甀猀氀礀 搀攀昀氀攀挀琀猀 琀栀攀 瀀愀爀琀椀挀氀攀 猀椀搀攀眀愀礀猀 眀椀琀栀漀甀琀 挀栀愀渀最椀渀最 椀琀猀 猀瀀攀攀搀 愀渀搀 琀栀攀 瀀愀爀琀椀挀氀攀 眀椀氀氀 洀漀瘀攀 愀氀漀渀最 愀 挀椀爀挀氀攀 瀀攀爀瀀攀渀搀椀挀甀氀愀爀 琀漀 琀栀攀 昀椀攀氀搀⸀ 吀栀攀 琀椀洀攀 爀攀焀甀椀爀攀搀 昀漀爀 漀渀攀 爀攀瘀漀氀甀琀椀漀渀 漀昀 琀栀攀 攀氀攀挀琀爀漀渀 椀猀 吀耀⸠∀Ⰰ 焀甀攀猀琀椀漀渀猀㨀 嬀∀䤀昀 瘀 㴀 ㈀瘀耀Ⱐ 琀栀攀渀 琀栀攀 爀愀搀椀甀猀 漀昀 琀栀攀 挀椀爀挀甀氀愀爀 瀀愀琀栀 渀漀眀 戀攀挀漀洀攀猀∀Ⰰ ∀䤀昀 瘀 㴀 ㈀瘀耀Ⱐ 琀栀攀渀 琀栀攀 琀椀洀攀 爀攀焀甀椀爀攀搀 昀漀爀 漀渀攀 爀攀瘀漀氀甀琀椀漀渀 漀昀 琀栀攀 攀氀攀挀琀爀漀渀 ⠀吀耀⤠ 眀椀氀氀 挀栀愀渀最攀 琀漀∀Ⰰ ∀䄀 挀栀愀爀最攀搀 瀀愀爀琀椀挀氀攀 椀猀 瀀爀漀樀攀挀琀攀搀 椀渀 愀 洀愀最渀攀琀椀挀 昀椀攀氀搀 䈀 㴀 ⠀㈀椀 ⬀ 㐀樀⤀ 휀 ㄀　눀 吀⸀ 吀栀攀 愀挀挀攀氀攀爀愀琀椀漀渀 漀昀 琀栀攀 瀀愀爀琀椀挀氀攀 椀猀 昀漀甀渀搀 琀漀 戀攀 愀 㴀 ⠀砀椀 ⬀ ㈀樀⤀ 洀⼀猀눀⸀ 䘀椀渀搀 琀栀攀 瘀愀氀甀攀 漀昀 砀⸀∀Ⰰ ∀䤀昀 琀栀攀 最椀瘀攀渀 攀氀攀挀琀爀漀渀 栀愀猀 愀 瘀攀氀漀挀椀琀礀 渀漀琀 瀀攀爀瀀攀渀搀椀挀甀氀愀爀 琀漀 䈀Ⰰ 琀栀攀渀 琀爀愀樀攀挀琀漀爀礀 漀昀 琀栀攀 攀氀攀挀琀爀漀渀 椀猀∀崀 紀Ⰰ { case: "Case Study Based Question: Photoelectric effect\nIt is the phenomenon of emission of electrons from a metallic surface when light of a suitable frequency is incident on it. The emitted electrons are called photoelectrons. Nearly all metals exhibit this effect with ultraviolet light but alkali metals like lithium, sodium, potassium, cesium etc. show this effect even with visible light. It is an instantaneous process i.e. photoelectrons are emitted as soon as the light is incident on the metal surface. The number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation. The maximum kinetic energy of the photoelectrons emitted from a given metal surface is independent of the intensity of the incident light and depends only on the frequency of the incident light. For a given metal surface there is a certain minimum value of the frequency of the incident light below which emission of photoelectrons does not occur.", questions: ["In a photoelectric experiment plate current is plotted against anode potential. Which statement is correct about the curves A, B and C?", "Photoelectrons are emitted when a zinc plate is", "The threshold frequency for photoelectric effect on sodium corresponds to a wavelength of 500 nm. Its work function is about", "The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV. The stopping potential is"] }਀                    崀 },਀                ∀䌀栀愀瀀琀攀爀 ㈀∀㨀 笀 mcq: [ ਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀䄀 氀漀渀最 猀琀爀愀椀最栀琀 眀椀爀攀 漀昀 挀椀爀挀甀氀愀爀 挀爀漀猀猀 猀攀挀琀椀漀渀 漀昀 爀愀搀椀甀猀 ✀愀✀ 挀愀爀爀椀攀猀 愀 猀琀攀愀搀礀 挀甀爀爀攀渀琀 䤀⸀ 吀栀攀 挀甀爀爀攀渀琀 椀猀 甀渀椀昀漀爀洀氀礀 搀椀猀琀爀椀戀甀琀攀搀 愀挀爀漀猀猀 椀琀猀 挀爀漀猀猀 猀攀挀琀椀漀渀⸀ 吀栀攀 爀愀琀椀漀 漀昀 洀愀最渀椀琀甀搀攀猀 漀昀 琀栀攀 洀愀最渀攀琀椀挀 昀椀攀氀搀 愀琀 愀 瀀漀椀渀琀 愀⼀㈀ 愀戀漀瘀攀 琀栀攀 猀甀爀昀愀挀攀 漀昀 眀椀爀攀 琀漀 琀栀愀琀 漀昀 愀 瀀漀椀渀琀 愀⼀㈀ 戀攀氀漀眀 椀琀猀 猀甀爀昀愀挀攀 椀猀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀㐀㨀㄀∀Ⰰ ∀㄀㨀㄀∀Ⰰ ∀㐀㨀㌀∀Ⰰ ∀㌀㨀㐀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀㄀㨀㄀∀ 紀Ⰰ { question: "The distance of closest approach of an alpha particle is d when it moves with a speed V towards a nucleus. Another alpha particle is projected with higher energy such that the new distance of the closest approach is d/2. What is the speed of projection of the alpha particle in this case?", options: ["V / 2", "√2 V", "2 V", "4 V"], answer: "2 V" },਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀䄀 瀀漀椀渀琀 漀戀樀攀挀琀 椀猀 瀀氀愀挀攀搀 愀琀 琀栀攀 挀攀渀琀爀攀 漀昀 愀 最氀愀猀猀 猀瀀栀攀爀攀 漀昀 爀愀搀椀甀猀 㘀 挀洀 愀渀搀 爀攀昀爀愀挀琀椀瘀攀 椀渀搀攀砀 ㄀⸀㔀⸀ 吀栀攀 搀椀猀琀愀渀挀攀 漀昀 瘀椀爀琀甀愀氀 椀洀愀最攀 昀爀漀洀 琀栀攀 猀甀爀昀愀挀攀 漀昀 琀栀攀 猀瀀栀攀爀攀 椀猀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀㈀ 挀洀∀Ⰰ ∀㐀 挀洀∀Ⰰ ∀㘀 挀洀∀Ⰰ ∀㄀㈀ 挀洀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀㘀 挀洀∀ 紀Ⰰ { question: "Colours observed on a CD (Compact Disk) is due to:", options: ["Reflection", "Diffraction", "Dispersion", "Absorption"], answer: "Diffraction" },਀                        笀 焀甀攀猀琀椀漀渀㨀 ∀吀栀攀 渀甀洀戀攀爀 漀昀 攀氀攀挀琀爀漀渀猀 洀愀搀攀 愀瘀愀椀氀愀戀氀攀 昀漀爀 挀漀渀搀甀挀琀椀漀渀 戀礀 搀漀瀀愀渀琀 愀琀漀洀猀 搀攀瀀攀渀搀猀 猀琀爀漀渀最氀礀 甀瀀漀渀㨀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀搀漀瀀椀渀最 氀攀瘀攀氀∀Ⰰ ∀椀渀挀爀攀愀猀攀 椀渀 愀洀戀椀攀渀琀 琀攀洀瀀攀爀愀琀甀爀攀∀Ⰰ ∀攀渀攀爀最礀 最愀瀀∀Ⰰ ∀漀瀀琀椀漀渀猀 ⠀䄀⤀ 愀渀搀 ⠀䈀⤀ 戀漀琀栀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀漀瀀琀椀漀渀猀 ⠀䄀⤀ 愀渀搀 ⠀䈀⤀ 戀漀琀栀∀ 紀 ],਀                    愀猀猀攀爀琀椀漀渀㨀 嬀  { statement1: "Nuclei having mass number about 60 are least stable.", statement2: "When two or more light nuclei are combined into a heavier nucleus then the binding energy per nucleon will decrease.", options: ["Both Assertion and Reason are true and Reason is the correct explanation of Assertion", "Both Assertion and Reason are true but Reason is not the correct explanation of Assertion", "Assertion is true but Reason is false", "Both Assertion and Reason are false"], answer: "Both Assertion and Reason are false" },਀                        笀 猀琀愀琀攀洀攀渀琀㄀㨀 ∀搀攀 䈀爀漀最氀椀攀✀猀 眀愀瘀攀氀攀渀最琀栀 漀昀 愀 昀爀攀攀氀礀 昀愀氀氀椀渀最 戀漀搀礀 欀攀攀瀀猀 搀攀挀爀攀愀猀椀渀最 眀椀琀栀 琀椀洀攀⸀∀Ⰰ 猀琀愀琀攀洀攀渀琀㈀㨀 ∀吀栀攀 洀漀洀攀渀琀甀洀 漀昀 琀栀攀 昀爀攀攀氀礀 昀愀氀氀椀渀最 戀漀搀礀 椀渀挀爀攀愀猀攀猀 眀椀琀栀 琀椀洀攀⸀∀Ⰰ 漀瀀琀椀漀渀猀㨀 嬀∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 愀渀搀 刀攀愀猀漀渀 椀猀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀Ⰰ ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 戀甀琀 刀攀愀猀漀渀 椀猀 渀漀琀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀Ⰰ ∀䄀猀猀攀爀琀椀漀渀 椀猀 琀爀甀攀 戀甀琀 刀攀愀猀漀渀 椀猀 昀愀氀猀攀∀Ⰰ ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 昀愀氀猀攀∀崀Ⰰ 愀渀猀眀攀爀㨀 ∀䈀漀琀栀 䄀猀猀攀爀琀椀漀渀 愀渀搀 刀攀愀猀漀渀 愀爀攀 琀爀甀攀 愀渀搀 刀攀愀猀漀渀 椀猀 琀栀攀 挀漀爀爀攀挀琀 攀砀瀀氀愀渀愀琀椀漀渀 漀昀 䄀猀猀攀爀琀椀漀渀∀ 紀 ],਀                    琀眀漀䴀愀爀欀㨀 嬀  "P and Q are two identical charged particles each of mass 4 × 10⁻²⁶ kg and charge 4.8 × 10⁻¹⁹ C, each moving with the same speed of 2.4 × 10⁵ m/s as shown in the figure. The two particles are equidistant (0.5 m) from the vertical Y-axis. At some instant, a magnetic field B is switched on so that the two particles undergo head-on collision. Find (I) the direction of the magnetic field and (II) the magnitude of the magnetic field applied in the region.",਀                        ∀䈀椀渀搀椀渀最 攀渀攀爀最礀 瀀攀爀 渀甀挀氀攀漀渀 瘀猀 洀愀猀猀 渀甀洀戀攀爀 挀甀爀瘀攀 昀漀爀 渀甀挀氀攀椀 椀猀 猀栀漀眀渀 椀渀 琀栀攀 昀椀最甀爀攀⸀ 圀Ⰰ 堀Ⰰ 夀 愀渀搀 娀 愀爀攀 昀漀甀爀 渀甀挀氀攀椀 椀渀搀椀挀愀琀攀搀 漀渀 琀栀攀 挀甀爀瘀攀⸀ 䤀搀攀渀琀椀昀礀 眀栀椀挀栀 漀昀 琀栀攀 昀漀氀氀漀眀椀渀最 渀甀挀氀攀椀 椀猀 洀漀猀琀 氀椀欀攀氀礀 琀漀 甀渀搀攀爀最漀 ⠀椀⤀ 一甀挀氀攀愀爀 䘀椀猀猀椀漀渀 ⠀椀椀⤀ 一甀挀氀攀愀爀 䘀甀猀椀漀渀⸀ 䨀甀猀琀椀昀礀 礀漀甀爀 愀渀猀眀攀爀⸀∀Ⰰ "A cylindrical conductor of length l and cross-section area A is connected to a DC source. Under the influence of electric field set up due to source, the free electrons begin to drift in the opposite direction of the electric field. (I) Draw the curve showing the dependency of drift velocity on relaxation time. (II) If the DC source is replaced by a source whose current changes its magnitude with time such that I = I₀ sin 2πνt, where ν is the frequency of variation of current, then determine the average drift velocity of the free electrons over one complete cycle."਀                    崀Ⰰ threeMark: [ ਀                        ∀䤀搀攀渀琀椀昀礀 琀栀攀 挀椀爀挀甀椀琀 攀氀攀洀攀渀琀猀 堀 愀渀搀 夀 愀猀 猀栀漀眀渀 椀渀 琀栀攀 最椀瘀攀渀 戀氀漀挀欀 搀椀愀最爀愀洀 愀渀搀 搀爀愀眀 琀栀攀 漀甀琀瀀甀琀 眀愀瘀攀昀漀爀洀猀 漀昀 堀 愀渀搀 夀⸀ 䤀昀 琀栀攀 挀攀渀琀爀攀 琀愀瀀瀀椀渀最 椀猀 猀栀椀昀琀攀搀 琀漀眀愀爀搀猀 䐀椀漀搀攀 䐀脀†愀猀 猀栀漀眀渀 椀渀 琀栀攀 搀椀愀最爀愀洀Ⰰ 搀爀愀眀 琀栀攀 漀甀琀瀀甀琀 眀愀瘀攀昀漀爀洀 漀昀 琀栀攀 最椀瘀攀渀 挀椀爀挀甀椀琀⸀∀Ⰰ "A boy is holding a smooth, hollow and non-conducting pipe vertically with charged spherical ball of mass 10 g carrying a charge of +10 mC inside it which is free to move along the axis of the pipe. The boy is moving the pipe from East to West direction in the presence of magnetic field of 2T. With what minimum velocity, should the boy move the pipe such that the ball does not move along the axis. Also determine the direction of the magnetic field.",਀                        ∀䄀 氀椀最栀琀 爀愀礀 攀渀琀攀爀椀渀最 愀 爀椀最栀琀ⴀ愀渀最氀攀搀 瀀爀椀猀洀 甀渀搀攀爀最漀攀猀 爀攀昀爀愀挀琀椀漀渀 愀琀 琀栀攀 昀愀挀攀 䄀䌀 愀猀 猀栀漀眀渀 椀渀 䘀椀最⸀ ㄀⸀ ⠀䤀⤀ 圀栀愀琀 椀猀 琀栀攀 爀攀昀爀愀挀琀椀瘀攀 椀渀搀攀砀 漀昀 琀栀攀 洀愀琀攀爀椀愀氀 漀昀 琀栀攀 瀀爀椀猀洀 椀渀 䘀椀最⸀ ㄀㼀 ⠀䤀䤀⤀ ⠀愀⤀ 䤀昀 琀栀攀 猀椀搀攀 䄀䌀 漀昀 琀栀攀 愀戀漀瘀攀 瀀爀椀猀洀 椀猀 渀漀眀 猀甀爀爀漀甀渀搀攀搀 戀礀 愀 氀椀焀甀椀搀 漀昀 爀攀昀爀愀挀琀椀瘀攀 椀渀搀攀砀 ㈀⼀ᨀ㌢Ⰰ 愀猀 猀栀漀眀渀 椀渀 䘀椀最⸀ ㈀Ⰰ 搀攀琀攀爀洀椀渀攀 椀昀 琀栀攀 氀椀最栀琀 爀愀礀 挀漀渀琀椀渀甀攀猀 琀漀 最爀愀稀攀 愀氀漀渀最 琀栀攀 椀渀琀攀爀昀愀挀攀 䄀䌀 漀爀 甀渀搀攀爀最漀攀猀 琀漀琀愀氀 椀渀琀攀爀渀愀氀 爀攀昀氀攀挀琀椀漀渀 漀爀 甀渀搀攀爀最漀攀猀 爀攀昀爀愀挀琀椀漀渀 椀渀琀漀 琀栀攀 氀椀焀甀椀搀⸀ ⠀戀⤀ 䐀爀愀眀 琀栀攀 爀愀礀 搀椀愀最爀愀洀 琀漀 爀攀瀀爀攀猀攀渀琀 琀栀攀 瀀愀琀栀 昀漀氀氀漀眀攀搀 戀礀 琀栀攀 椀渀挀椀搀攀渀琀 爀愀礀 眀椀琀栀 琀栀攀 挀漀爀爀攀猀瀀漀渀搀椀渀最 愀渀最氀攀 瘀愀氀甀攀猀⸀∀ ],਀                    昀椀瘀攀䴀愀爀欀㨀 嬀  "With the help of a diagram, explain the principle of a device which changes a low ac voltage into a high voltage. Deduce the expression for the ratio of secondary voltage to the primary voltage in terms of the ratio of the number of turns of primary and secondary winding. For an ideal transformer, obtain the ratio of primary and secondary currents in terms of the ratio of the voltages in the secondary and primary coils. Write any two sources of the energy losses which occur in actual transformers.",਀                        ∀䄀 挀漀洀瀀漀甀渀搀 洀椀挀爀漀猀挀漀瀀攀 挀漀渀猀椀猀琀猀 漀昀 愀渀 漀戀樀攀挀琀椀瘀攀 氀攀渀猀 漀昀 昀漀挀愀氀 氀攀渀最琀栀 ㈀⸀　 挀洀 愀渀搀 愀渀 攀礀攀瀀椀攀挀攀 漀昀 昀漀挀愀氀 氀攀渀最琀栀 㘀⸀㈀㔀 挀洀 猀攀瀀愀爀愀琀攀搀 戀礀 愀 搀椀猀琀愀渀挀攀 漀昀 ㄀㔀 挀洀⸀ 䠀漀眀 昀愀爀 昀爀漀洀 琀栀攀 漀戀樀攀挀琀椀瘀攀 猀栀漀甀氀搀 愀渀 漀戀樀攀挀琀 戀攀 瀀氀愀挀攀搀 椀渀 漀爀搀攀爀 琀漀 漀戀琀愀椀渀 琀栀攀 昀椀渀愀氀 椀洀愀最攀 愀琀 ⠀愀⤀ 琀栀攀 氀攀愀猀琀 搀椀猀琀愀渀挀攀 漀昀 搀椀猀琀椀渀挀琀 瘀椀猀椀漀渀 ⠀㈀㔀 挀洀⤀ 愀渀搀 ⠀戀⤀ 椀渀昀椀渀椀琀礀㼀 圀栀愀琀 椀猀 琀栀攀 洀愀最渀椀昀礀椀渀最 瀀漀眀攀爀 漀昀 琀栀攀 洀椀挀爀漀猀挀漀瀀攀 椀渀 攀愀挀栀 挀愀猀攀㼀∀ ],਀                    挀愀猀攀匀琀甀搀礀㨀 嬀  { case: "Case Study Based Question: Motion of Charge in Magnetic Field\nAn electron with speed v₀ << c moves in a circle of radius r₀ in a uniform magnetic field. This electron is able to traverse a circular path as the magnetic force acting on the electron is perpendicular to both v₀ and B, as shown in the figure. This force continuously deflects the particle sideways without changing its speed and the particle will move along a circle perpendicular to the field. The time required for one revolution of the electron is T₀.", questions: ["If v = 2v₀, then the radius of the circular path now becomes", "If v = 2v₀, then the time required for one revolution of the electron (T₀) will change to", "A charged particle is projected in a magnetic field B = (2i + 4j) × 10² T. The acceleration of the particle is found to be a = (xi + 2j) m/s². Find the value of x.", "If the given electron has a velocity not perpendicular to B, then trajectory of the electron is"] },਀                        笀 挀愀猀攀㨀 ∀䌀愀猀攀 匀琀甀搀礀 䈀愀猀攀搀 儀甀攀猀琀椀漀渀㨀 倀栀漀琀漀攀氀攀挀琀爀椀挀 攀昀昀攀挀琀尀渀䤀琀 椀猀 琀栀攀 瀀栀攀渀漀洀攀渀漀渀 漀昀 攀洀椀猀猀椀漀渀 漀昀 攀氀攀挀琀爀漀渀猀 昀爀漀洀 愀 洀攀琀愀氀氀椀挀 猀甀爀昀愀挀攀 眀栀攀渀 氀椀最栀琀 漀昀 愀 猀甀椀琀愀戀氀攀 昀爀攀焀甀攀渀挀礀 椀猀 椀渀挀椀搀攀渀琀 漀渀 椀琀⸀ 吀栀攀 攀洀椀琀琀攀搀 攀氀攀挀琀爀漀渀猀 愀爀攀 挀愀氀氀攀搀 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀⸀ 一攀愀爀氀礀 愀氀氀 洀攀琀愀氀猀 攀砀栀椀戀椀琀 琀栀椀猀 攀昀昀攀挀琀 眀椀琀栀 甀氀琀爀愀瘀椀漀氀攀琀 氀椀最栀琀 戀甀琀 愀氀欀愀氀椀 洀攀琀愀氀猀 氀椀欀攀 氀椀琀栀椀甀洀Ⰰ 猀漀搀椀甀洀Ⰰ 瀀漀琀愀猀猀椀甀洀Ⰰ 挀攀猀椀甀洀 攀琀挀⸀ 猀栀漀眀 琀栀椀猀 攀昀昀攀挀琀 攀瘀攀渀 眀椀琀栀 瘀椀猀椀戀氀攀 氀椀最栀琀⸀ 䤀琀 椀猀 愀渀 椀渀猀琀愀渀琀愀渀攀漀甀猀 瀀爀漀挀攀猀猀 椀⸀攀⸀ 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀 愀爀攀 攀洀椀琀琀攀搀 愀猀 猀漀漀渀 愀猀 琀栀攀 氀椀最栀琀 椀猀 椀渀挀椀搀攀渀琀 漀渀 琀栀攀 洀攀琀愀氀 猀甀爀昀愀挀攀⸀ 吀栀攀 渀甀洀戀攀爀 漀昀 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀 攀洀椀琀琀攀搀 瀀攀爀 猀攀挀漀渀搀 椀猀 搀椀爀攀挀琀氀礀 瀀爀漀瀀漀爀琀椀漀渀愀氀 琀漀 琀栀攀 椀渀琀攀渀猀椀琀礀 漀昀 琀栀攀 椀渀挀椀搀攀渀琀 爀愀搀椀愀琀椀漀渀⸀ 吀栀攀 洀愀砀椀洀甀洀 欀椀渀攀琀椀挀 攀渀攀爀最礀 漀昀 琀栀攀 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀 攀洀椀琀琀攀搀 昀爀漀洀 愀 最椀瘀攀渀 洀攀琀愀氀 猀甀爀昀愀挀攀 椀猀 椀渀搀攀瀀攀渀搀攀渀琀 漀昀 琀栀攀 椀渀琀攀渀猀椀琀礀 漀昀 琀栀攀 椀渀挀椀搀攀渀琀 氀椀最栀琀 愀渀搀 搀攀瀀攀渀搀猀 漀渀氀礀 漀渀 琀栀攀 昀爀攀焀甀攀渀挀礀 漀昀 琀栀攀 椀渀挀椀搀攀渀琀 氀椀最栀琀⸀ 䘀漀爀 愀 最椀瘀攀渀 洀攀琀愀氀 猀甀爀昀愀挀攀 琀栀攀爀攀 椀猀 愀 挀攀爀琀愀椀渀 洀椀渀椀洀甀洀 瘀愀氀甀攀 漀昀 琀栀攀 昀爀攀焀甀攀渀挀礀 漀昀 琀栀攀 椀渀挀椀搀攀渀琀 氀椀最栀琀 戀攀氀漀眀 眀栀椀挀栀 攀洀椀猀猀椀漀渀 漀昀 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀 搀漀攀猀 渀漀琀 漀挀挀甀爀⸀∀Ⰰ 焀甀攀猀琀椀漀渀猀㨀 嬀∀䤀渀 愀 瀀栀漀琀漀攀氀攀挀琀爀椀挀 攀砀瀀攀爀椀洀攀渀琀 瀀氀愀琀攀 挀甀爀爀攀渀琀 椀猀 瀀氀漀琀琀攀搀 愀最愀椀渀猀琀 愀渀漀搀攀 瀀漀琀攀渀琀椀愀氀⸀ 圀栀椀挀栀 猀琀愀琀攀洀攀渀琀 椀猀 挀漀爀爀攀挀琀 愀戀漀甀琀 琀栀攀 挀甀爀瘀攀猀 䄀Ⰰ 䈀 愀渀搀 䌀㼀∀Ⰰ ∀倀栀漀琀漀攀氀攀挀琀爀漀渀猀 愀爀攀 攀洀椀琀琀攀搀 眀栀攀渀 愀 稀椀渀挀 瀀氀愀琀攀 椀猀∀Ⰰ ∀吀栀攀 琀栀爀攀猀栀漀氀搀 昀爀攀焀甀攀渀挀礀 昀漀爀 瀀栀漀琀漀攀氀攀挀琀爀椀挀 攀昀昀攀挀琀 漀渀 猀漀搀椀甀洀 挀漀爀爀攀猀瀀漀渀搀猀 琀漀 愀 眀愀瘀攀氀攀渀最琀栀 漀昀 㔀　　 渀洀⸀ 䤀琀猀 眀漀爀欀 昀甀渀挀琀椀漀渀 椀猀 愀戀漀甀琀∀Ⰰ ∀吀栀攀 洀愀砀椀洀甀洀 欀椀渀攀琀椀挀 攀渀攀爀最礀 漀昀 瀀栀漀琀漀攀氀攀挀琀爀漀渀猀 攀洀椀琀琀攀搀 昀爀漀洀 愀 猀甀爀昀愀挀攀 眀栀攀渀 瀀栀漀琀漀渀猀 漀昀 攀渀攀爀最礀 㘀 攀嘀 昀愀氀氀 漀渀 椀琀 椀猀 㐀 攀嘀⸀ 吀栀攀 猀琀漀瀀瀀椀渀最 瀀漀琀攀渀琀椀愀氀 椀猀∀崀 紀 ]਀                紀 }਀        紀㬀 ਀        昀甀渀挀琀椀漀渀 最攀琀刀愀渀搀漀洀儀甀攀猀琀椀漀渀猀⠀猀攀氀攀挀琀攀搀䌀栀愀瀀琀攀爀猀Ⰰ 琀礀瀀攀Ⰰ 挀漀甀渀琀⤀ 笀 let allQuestions = [];਀ if (selectedChapters.includes("Full Paper")) {਀                昀漀爀 ⠀氀攀琀 挀栀愀瀀琀攀爀 椀渀 焀甀攀猀琀椀漀渀猀⸀瀀栀礀猀椀挀猀⤀ 笀 if (questions.physics[chapter][type]) {਀                        愀氀氀儀甀攀猀琀椀漀渀猀 㴀 愀氀氀儀甀攀猀琀椀漀渀猀⸀挀漀渀挀愀琀⠀焀甀攀猀琀椀漀渀猀⸀瀀栀礀猀椀挀猀嬀挀栀愀瀀琀攀爀崀嬀琀礀瀀攀崀⤀㬀 }਀                紀 } else {਀                猀攀氀攀挀琀攀搀䌀栀愀瀀琀攀爀猀⸀昀漀爀䔀愀挀栀⠀挀栀愀瀀琀攀爀 㴀㸀 笀 if (questions.physics[chapter] && questions.physics[chapter][type]) {਀                        愀氀氀儀甀攀猀琀椀漀渀猀 㴀 愀氀氀儀甀攀猀琀椀漀渀猀⸀挀漀渀挀愀琀⠀焀甀攀猀琀椀漀渀猀⸀瀀栀礀猀椀挀猀嬀挀栀愀瀀琀攀爀崀嬀琀礀瀀攀崀⤀㬀 }਀                紀⤀㬀 }਀ allQuestions = allQuestions.sort(() => Math.random() - 0.5);਀            爀攀琀甀爀渀 愀氀氀儀甀攀猀琀椀漀渀猀⸀猀氀椀挀攀⠀　Ⰰ 挀漀甀渀琀⤀㬀 }਀ function showChapterSelection() {਀            搀漀挀甀洀攀渀琀⸀最攀琀䔀氀攀洀攀渀琀䈀礀䤀搀⠀✀猀琀愀爀琀匀挀爀攀攀渀✀⤀⸀挀氀愀猀猀䰀椀猀琀⸀愀搀搀⠀✀栀椀搀搀攀渀✀⤀㬀 document.getElementById('chapterSelection').classList.remove('hidden');਀        紀 ਀        昀甀渀挀琀椀漀渀 琀漀最最氀攀䌀栀愀瀀琀攀爀猀⠀⤀ 笀 const fullPaperCheckbox = document.getElementById('fullPaper');਀            挀漀渀猀琀 挀栀攀挀欀戀漀砀攀猀 㴀 搀漀挀甀洀攀渀琀⸀焀甀攀爀礀匀攀氀攀挀琀漀爀䄀氀氀⠀✀椀渀瀀甀琀嬀渀愀洀攀㴀∀挀栀愀瀀琀攀爀∀崀㨀渀漀琀⠀⌀昀甀氀氀倀愀瀀攀爀⤀✀⤀㬀 checkboxes.forEach(cb => cb.disabled = fullPaperCheckbox.checked);਀        紀 ਀        昀甀渀挀琀椀漀渀 戀愀挀欀吀漀匀琀愀爀琀⠀⤀ 笀 document.getElementById('generatedPaperContainer').classList.add('hidden');਀            搀漀挀甀洀攀渀琀⸀最攀琀䔀氀攀洀攀渀琀䈀礀䤀搀⠀✀猀琀愀爀琀䌀漀渀琀愀椀渀攀爀✀⤀⸀挀氀愀猀猀䰀椀猀琀⸀爀攀洀漀瘀攀⠀✀栀椀搀搀攀渀✀⤀㬀 document.getElementById('chapterSelection').classList.add('hidden');਀            搀漀挀甀洀攀渀琀⸀最攀琀䔀氀攀洀攀渀琀䈀礀䤀搀⠀✀猀琀愀爀琀匀挀爀攀攀渀✀⤀⸀挀氀愀猀猀䰀椀猀琀⸀爀攀洀漀瘀攀⠀✀栀椀搀搀攀渀✀⤀㬀 questionCounter = 1;਀        紀 ਀        昀甀渀挀琀椀漀渀 瀀爀漀洀瀀琀匀挀栀漀漀氀一愀洀攀⠀⤀ 笀 schoolName = prompt("Write your school/institute name").toUpperCase();਀            椀昀 ⠀℀猀挀栀漀漀氀一愀洀攀⤀ 笀 alert("School/Institute name is required!");਀            紀 攀氀猀攀 笀 promptSession();਀            紀 }਀ function promptSession() {਀            猀攀猀猀椀漀渀夀攀愀爀 㴀 瀀爀漀洀瀀琀⠀∀䔀渀琀攀爀 琀栀攀 愀挀愀搀攀洀椀挀 猀攀猀猀椀漀渀 ⠀攀⸀最⸀Ⰰ ㈀　㈀㐀ⴀ㈀㔀⤀∀⤀⸀琀漀唀瀀瀀攀爀䌀愀猀攀⠀⤀㬀 if (!sessionYear) {਀                愀氀攀爀琀⠀∀䄀挀愀搀攀洀椀挀 猀攀猀猀椀漀渀 椀猀 爀攀焀甀椀爀攀搀℀∀⤀㬀 } else {਀                最攀渀攀爀愀琀攀倀愀瀀攀爀⠀⤀㬀 }਀        紀 ਀        昀甀渀挀琀椀漀渀 最攀渀攀爀愀琀攀倀愀瀀攀爀⠀⤀ 笀 document.getElementById('startContainer').classList.add('hidden');਀            挀漀渀猀琀 最攀渀攀爀愀琀攀搀倀愀瀀攀爀䌀漀渀琀愀椀渀攀爀 㴀 搀漀挀甀洀攀渀琀⸀最攀琀䔀氀攀洀攀渀琀䈀礀䤀搀⠀✀最攀渀攀爀愀琀攀搀倀愀瀀攀爀䌀漀渀琀愀椀渀攀爀✀⤀㬀 generatedPaperContainer.classList.remove('hidden');਀            最攀渀攀爀愀琀攀搀倀愀瀀攀爀䌀漀渀琀愀椀渀攀爀⸀椀渀渀攀爀䠀吀䴀䰀 㴀 ✀✀㬀 ਀            氀攀琀 瀀愀瀀攀爀䌀漀渀琀攀渀琀 㴀 怀 ਀                㰀搀椀瘀 挀氀愀猀猀㴀∀挀漀渀琀攀渀琀ⴀ愀爀攀愀∀㸀 ਀                    㰀搀椀瘀 挀氀愀猀猀㴀∀瀀愀瀀攀爀ⴀ洀攀琀愀∀㸀 ਀                        㰀搀椀瘀㸀吀椀洀攀 䄀氀氀漀眀攀搀㨀 ㌀ 栀漀甀爀猀㰀⼀搀椀瘀㸀