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📐 Mathematics PYQ: Vectors & 3D Geometry JEE Main 2025 | Intersection of Line and Plane Question 1: Shortest Distance to a Plane The equation of a plane $P$ passing through the line $\frac{x-1}{2} = \frac{y-2}{1} = \frac{z+1}{-2}$ and perpendicular to the plane $x - 2y + 4z = 3$ is given by $Ax + By + Cz = D$. Find the shortest distance of the point $(0, 0, 0)$ from this plane $P$. 1) $\frac{2}{\sqrt{29}}$ 2) $\frac{5}{\sqrt{29}}$ 3) $\frac{2}{\sqrt{58}}$ 4) $\frac{5}{\sqrt{58}}$ Check Answer Solution: 3D Geometry The normal vector $\mathbf{n} = \langle a, b, c \rangle$ of Plane $P$ must be perpendicular to the direction vector of the line $\mathbf{v}_1 = \langle 2, 1, -2 \rangle$ and the normal of the given plane $\mathbf{n}_2 = \langle 1, -2, 4 \rangle$. The normal $\mat...

Physics JEE main pyQ (JEE/NEET PYQs) Practice fundamental concepts and calculations across core subjects. Question 1: Maximum Fractional Error A quantity $Q$ is formulated as $Q = X^{-2}Y^{\frac{3}{2}}Z^{-\frac{2}{5}}$. $X$, $Y$, and $Z$ are independent parameters which have fractional errors of $0.1$, $0.2$, and $0.5$, respectively in measurement. The maximum fractional error of $Q$ ($\frac{\Delta Q}{Q}$) is: A) 0.6 B) 0.8 C) 0.7 D) 0.1 Check Answer 1 Solution 1: Error Propagation The maximum fractional error is calculated by summing the absolute value of the powers multiplied by their respective fractional errors. All exponents are treated as positive to maximize the error. $$Q = X^...

 Chemistry Quiz: 8 Key Concepts (JEE/NEET PYQs) Master topics from $S_N2$ reactions to bond order calculations. Question 1: Salt Solution Nature (Ionic Equilibrium) Given below are two statements: Statement (I): Aqueous solution of ammonium carbonate is basic. Statement (II): Acidic/basic nature of salt solution of a weak acid and weak base depends on $K_a$ and $K_b$ value of acid and the base forming it. (1) Both Statement I and Statement II are correct (2) Statement I is correct but Statement II is incorrect (3) Both Statement I and Statement II are incorrect (4) Statement I is incorrect but Statement II is correct Check Answer Solution 1: Salt Hydrolysis Ammonium carbonate ($\mathbf{(NH_...

Chemistry Marathon: From Polarity to p-Block (JEE/NEET PYQs) Test your knowledge on five diverse and crucial chemistry concepts. Question 1: Polarity of Molecules Choose the polar molecule from the following: (1) $CCl_4$ (2) $CO_2$ (3) $CH_2=CH_2$ (4) $CHCl_3$ Check Answer  Solution 1: Polarity Key Concept: A molecule is non-polar if its net **dipole moment ($\mu$) is zero**. This usually occurs when the molecule is highly symmetrical, canceling out all bond dipoles. $CCl_4$ (Tetrahedral), $CO_2$ (Linear), and $CH_2=CH_2$ (Planar) are highly symmetrical, so $\mu = 0$. $CHCl_3$ (Trichloromethane) has a **tetrahedral geometry**, but the central carbon is bo...

Dimensional Analysis Marathon (JEE/NEET PYQs) Master the dimensions of key physical quantities with these three challenging questions. Question 1: Dipole Moment Ratio In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $[M^P L^Q T^R A^S]$. The value of P and Q are: A) -1, 0 B) 0, -1 C) -1, 1 D) 1, -1 Check Answer 1 Solution 1 **Electric Dipole Moment ($\vec{p}$):** $p = \text{charge} \times \text{distance}$. Dimensions: $[A T] \times [L] = [M^0 L^1 T^1 A^1]$. **Magnetic Dipole Moment ($\vec{m}$):** $m = \text{Current} \times \text{Area}$. Dimensions: $[A] \times [L^2] = [M^0 L^2 T^0 ...

English हिन्दी Physics MCQs Explained: Travelling Microscope & Dipole Moments Let’s solve two conceptual physics questions — one from experimental optics (Least Count) and another from electromagnetic dimensions (Dipole Moments). Both test your analytical approach and formula application. Question 1: Least Count of a Travelling Microscope Problem: For the determination of the refractive index of a glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equal to 15 cm. The vernier scale attached to the microscope has 25 divisions equal to 24 divisions of the main scale. Find the least count (LC) of the travelling microscope in cm. Solution: \( 300\ \text{MSD} = 15\ \text{cm} \Rightarrow 1\ \text{MSD} = 0.05\ \text{cm} \) \( 25\ \text{VSD} = 24\ \text{MSD} \Rightarrow 1\ \text{VSD} = \frac{24}{25}\ \text{MSD} \) \( \text{LC} = 1\ \text{MSD} - 1\ \text{VSD} = \frac{1}{25}\ \te...

Q1. The ascending order of relative rate of solvolysis of the following compounds is: (choose)   A.  (C) < (D) < (B) < (A) B.(D) < (A) < (B) < (C) C.(D) < (B) < (A) < (C) D.(C) < (B) < (A) < (D) Check Answer Explanation: Solvolysis (SN1) depends on carbocation stability. Resonance-stabilized benzylic cations are fastest; tertiary or bridged rings next; simple secondary/primary are slower. The correct ascending order (slow → fast) matches the highlighted choice above. Q2. Assertion (A): SN2 reaction of C₆H₅CH₂Br occurs more readily than SN2 reaction of CH₃CH₂Br. Reason (R): The partially bonded unhybridized p-orbital that develops in the trigonal bipyramidal transition state is s...