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Set and relations Question: Consider the relation R on the set {-2,-1,0,1,2} defined by (a,b) ∈ R if and only if 1+ ab > 0 . Then, among the statements : I. The number of elements in R is 17 II. R is an equivalence relation  A) only I is true  B) only II is true  C) Both I and II are true   D) Neither I nor II is true Your Answer: Check Answer Correct Answer: A) only I is true Solution: \(\) Difficulty: Medium Tags: Set and relations , Medium, JEE MATHS  Explore More 🧭

StudyBeacon Quiz – Mole Concept (JEE Main 2026 PYQ) Score: 0 Q1.  In the reaction: $2Al + 6HCl \rightarrow 2Al^{3+} + 6Cl^- + 3H_2$ 6.72 L H₂ at STP per mole Al 33.6 L H₂ regardless of T,P 12 L HCl consumed for 6 L H₂ 11.2 L H₂ at STP per mole HCl Check Answer From equation: $6$ mol HCl → $3$ mol H₂ $1$ mol HCl → $\frac{1}{2}$ mol H₂ At STP: $1$ mol gas = 22.4 L $\frac{1}{2} \times 22.4 = 11.2$ L Q2. Reaction: $CaCO_3 + 2HCl → CaCl_2 + H_2O + CO_2$ Given: 90 g $CaCO_3$, 300 mL HCl (38.55%, density 1.13 g/mL) 32.85 g CaCO₃ remains 97.30 g HCl reacted 64.97 g HCl remains 60.32 g HCl remains Check Answer Mass of solution = $300×1.13=339$ g Mass HCl = $0.3855×339=130.7$ g Moles HCl = $\frac{130.7}{36.5}=3.58$ mol Moles CaCO₃ = $\frac{90}{100}=0.9$ mol Needed HCl = $2×0.9=1.8$ mol Excess HCl remains → 64.97 g Q3. $A + 2B → AB_2$ 36 g A (60 g/mol), 56 g B (80 g/mol) A and B only C and D only B and D only A and C only ...

Modern Physics – JEE Main PYQs (2026) Quiz Important Constants: $h = 6.63 \times 10^{-34}\ \text{J·s}$ $c = 3 \times 10^8\ \text{m/s}$ $e = 1.6 \times 10^{-19}\ \text{C}$ $k = 1.38 \times 10^{-23}\ \text{J/K}$ $1\text{ eV} = 1.6 \times 10^{-19}\ \text{J}$ Score: 0 Q1. Two electrons are moving in orbits of two hydrogen-like atoms with speeds $3 \times 10^5$ m/s and $2.5 \times 10^5$ m/s respectively. If the radii of these orbits are nearly same then the possible order of energy states are respectively: 9 and 8 8 and 10 10 and 12 6 and 5 Check Answer For hydrogen-like atom: $v \propto \frac{1}{n}$ $\frac{v_1}{v_2} = \frac{n_2}{n_1}$ $\frac{3}{2.5} = 1.2$ Closest integer ratio → 9 and 8. Q2. Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is: $1\times10^{16}$ $5\times10^{16}$ $2\times10^{16}$ $5\times10^{15}$ Check Answer $E = \frac{hc}{\lambda}$ $E = \frac{6.63\times10^{-34...

Alternating Current (AC) – Complete Formula Framework (JEE Mains) Phasors | Impedance | Resonance | Power | PYQ Mapping 1️⃣ AC Basics Alternating current: \[ i = I_0 \sin \omega t \] Peak current = \( I_0 \) Angular frequency = \( \omega = 2\pi f \) Time period = \( T = \frac{2\pi}{\omega} \) RMS value: \[ I_{rms} = \frac{I_0}{\sqrt{2}} \] \[ V_{rms} = \frac{V_0}{\sqrt{2}} \] ⚠ Mains Trap: Household voltage is RMS, not peak. 2️⃣ AC through Pure Resistor Voltage & current in phase \[ V = IR \] Power: \[ P = V_{rms} I_{rms} \] Phase angle: \[ \phi = 0 \] 3️⃣ AC through Pure Inductor Inductive reactance: \[ X_L = \omega L \] Current: \[ I = \frac{V}{X_L} \] Phase: \[ \phi = +90^\circ \] Voltage leads current. 4️⃣ AC through Pure Capacitor Capacitive reactance: \[ X_C = \frac{1}{\omega C} \] Current: \[ I = \frac{V}{X_C} \] Phase: \[ \phi = -90^\circ \] Current leads voltage. 5️⃣ RLC Series Circuit Imped...

    Chemistry PYQ  Q. The rate of hydrolysis of alkyl chloride improves because of better Nucleophilicity of I-. Order of Covalent bond;  A. KF > KI; LiF > KF  B. KF < KI; LiF > KF  C. SnCl4 > SnCl2; CuCl > NaCl  D. LiF > KF; CuCl < NaCl  E. KF <KI; CuCl > NaCl                                                         (jee mains 2024) 1. C, E only  2. B, C only 3. B, C, E only 4. A, B only Show Answer According to Fajan's Rule,  A. KF > KI - False; LiF > KF - True  B. KF <KI-True; LiF > KF - True  C. SnCl4 > SnCl2 - True; CuCl > NaCl - True  D. LiF > KF - True; CuCl < NaCl - False  E. KF <KI - True; CuCl > NaCl - True

 Q. All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" IS                                                         (jee mains 2024) Show Answer (553)  Words starting with E = 360  Words starting with GE = 60  Words starting with GN = 60  Words starting with GTE = 24  Words starting with GTN = 24  Words starting with GTT = 24  GTWENTY = 1  Total = 553 Physics                  Chemistry

 Q. A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:                                                                     (JEE 2024) 1. 6 2. 2 3. 3 4. 5 Show Answer Momentum will remain conserve  1000×6=1200 x v  v = 5 m/s   More Questions

 Q. A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, g 10 m/s²):                                                                        (JEE mains 2024) 1. 6.0 cm 2. 5.4 cm 3. 4.8 cm 4. 4.2 cm Show Answer Ans. (2)  Soln.   

 Q.  The acceleration due to gravity on the surface of earth is g. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

 Q. Position of an ant (S in metres) moving in Y-Z plane is given by S=2t²j+5k (where t is in second). The magnitude and direction of velocity of the ant at t = 1 s will be :                                                         (Jee mains- 2024) 1. 16 m/s in y-direction  2. 4 m/s in x- direction  3. 9 m/s in z- direction  4. 4 m/s in y-direction  Show Answer 4 m/s in y-direction. v=ds/dt=4t ĵ At t = 1 sec v = 4ĵ More Questions kinametics PYQ