Manzil 2026: BASIC MATHS in One Shot: All Concepts & PYQs Covered | JEE Main & Advanced

Manzil 2026: BASIC MATHS in One Shot: Notes

1. Summary

This video by JEE Wallah covers fundamental concepts of basic maths, including units, dimensions, and errors, focusing on key topics for JEE Main & Advanced preparation. Saleem Ahmad Sir emphasizes the importance of these topics and presents various question types, offering strategies for solving them effectively.

2. Key Takeaways

* **Units, Dimensions, and Errors:** Essential concepts for JEE Main & Advanced.

* **Focus on Practice:** The lecture emphasizes problem-solving and application of concepts.

* **Clear Definitions:** Provides fundamental definitions of key terms.

* **Problem-Solving Strategies:** Explains how to tackle different question types.

3. Detailed Notes

* **Introduction:**

* The lecture covers Basic Maths, Unit, Dimension, and Error.

* Manzil Series.

* The aim is to help students score well in JEE Main & Advanced.

* Focus on previous year's questions.

* **Physical Quantities:**

* Physical quantities are those that can be measured.

* Based on direction:

* **Scalar:** Magnitude only (e.g., length, time)

* **Vector:** Both magnitude and direction (e.g., force, velocity)

* Based on dependency:

* **Fundamental:** Independent (e.g., length, mass, time). There are 7 fundamental physical quantities.

* **Derived:** Dependent (e.g., velocity, acceleration, force, etc.)

* **Classification of Units:**

* **FPS (Foot, Pound, Second):**

* **MKS (Meter, Kilogram, Second):**

* **CGS (Centimeter, Gram, Second):**

* **SI (International System of Units):** Includes the base units for 7 fundamental physical quantities:

* Length (meter - m)

* Mass (kilogram - kg)

* Time (second - s)

* Temperature (kelvin - K)

* Electric current (ampere - A)

* Luminous intensity (candela - cd)

* Amount of substance (mole - mol)

* **Dimensions:**

* A way to represent a physical quantity using fundamental quantities.

* **Example:**

* Density = Mass / Volume

* Dimension of Density = [M¹ L⁻³ T⁰]

* Dimension of length = [L]

* Dimension of time = [T]

* **Questions:**

* * **Conversion of Units:**

* Density = 6 g/cc to MKS

* Density = [M L⁻³]

* 6 g/cc = 6 x 10⁻³ kg / (10⁻² m)³

* 6 * 10⁻³ / 10⁻⁶ = 6000 kg/m³

* * **Conversion of units**

* Momentum = 20 kg m/s to CGS

* Momentum = M * V

* Momentum = 20 kg m/s = 20 * 10³ g * 100 cm/s = 2 x 10⁶ g.cm/s

* **Types of Questions:**

* * **Conversion of Units**

* Conversion of units: density, converting kg/m³ to g/cm³

* Conversion of units: momentum, converting kg m/s to g cm/s

* * **Direct Formula Questions:**

* * X = at² + bt

* Find dimensional formulas of a and b.

* X = Length

* At² = Length

* [a] [T]²= [L]

* A = [L T⁻²]

* BT = [L]

* [B] [T] = [L]

* B = [L T⁻¹]

* * F= aV + bT²

* * F= ax² + bt

* **Error:**

* * **Types of Errors:**

* * **Systematic Error:** Can be corrected by calibration.

* * **Random Error:** Unpredictable and can be minimized by taking multiple measurements.

* * **Mean Value:**

* Mean of value = (a1 + a2 + a3 + a4 + a5)/n

* * delta a1 = a1 - mean value

* Delta A mean = average of delta A

* **Rules (Significant figures)**

* All non-zero digits are significant.

* All zeros between non-zero digits are significant.

* Zeros to the left of the first non-zero digit are not significant.

* Zeros at the end of a number with a decimal point are significant.

* **How do I know how many Significant Figures?**

* * * In Addition/ Subtraction:

* The final answer should have the same number of decimal places as the number in the calculation with the *least* number of decimal places.

* * In Multiplication/Division:

* * The final answer should have the same number of significant figures as the number in the calculation with the *least* number of significant figures.

* Examples:

* 2.30 + 2.345

* = 4.6

* 4. 875 - 3.20

* **Round Off:**

* * If the digit to be dropped is less than 5, then the preceding digit is left unchanged.

* If the digit to be dropped is greater than 5, then the preceding digit is increased by 1.

* If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is increased by 1.

* If the digit to be dropped is 5, followed by no digits, or followed only by zeros, then the preceding digit is left unchanged if it is even and increased by 1 if it is odd.

* **Multiplication and Division:**

* In multiplication and division, the final answer should have the same number of significant figures as the number in the calculation with the *least* number of significant figures.

* Examples

* 1. * Volume of cube

* 3 sides, so 1

* V = 1 X 1 X 1 = 1 cc

* 1. * Volume of the cube -

* - If 3 sides: 0.63 * 0.8 * 0.6 = 0.30 cc.

* **Propagation of Error:**

* * y = a + b

* * Delta Y/y

* = (Delta a / a + delta b/b)

* * **Relative Error:**

* * y = a + b

* | Delta Y = Delta a + Delta B |

* Δy/y= Δa/a + Δb/b

* **Propagation of Error Continued:**

* y = a²b/c⁴

* * ΔY/y = 2Δa/a + Δb/b + 4Δc/c

* * Example of the same

* 2

* * x = a sin (bt)

* d = 2 x²

* **Small Angle approximation:**

* * * sin(θ) ≈ θ, where θ is small

* **Summary of formulas:**

* * 1 (d = vt)

* * 2 (v = s/t)

* * 3 (a = change in velocity/ time)

* * 4 (F = ma)

* * 5 (T = F/l)

* * 6 (Force = 6 π r * n * v)

* * 7 (MKS)

* * 8 (CGS)

* * 9 (SI Units)

* * 10 (F = mg)

* * 11 ( E = mv² / 2)

* * 12 (T = 4π² l / g)

* * 13 (g = F / m)

* * 14 (v = displacement / time

* * v = v₀ + at

* * x = x₀ + v₀t + 1/2at²

* * v² = v₀² + 2a(x - x₀)

* * 15 (Density = mass / volume)

* * 16 (U = 3/2 * k * T)

* * 17 (F = K * q1 * q2 / r²

* * 18 (P = energy / time)

* * 19 (V= IR)

* * 20 (E= force / q)

* * 21( ɸ = BA)

* * 22 (F = qvb)

* * 23 (C = q / v)

* * 24 (1 / c eq = 1/c1 + 1 / c2)

* * 25 (p = 1 / R + -1 / R)²

* **Important Question Types:**

* * Direct formula based.

* * Equation-based: (e.g., `X = at² + bt`, `F = aV + bT²`)

* * Using the values of a, b, and c to determine the error.

* * Determine the dimensions using force, length, velocity as fundamental physical quantities.

* **Error Related Questions:**

* * Types of error

* * Finding Mean Value, True Value

* * **If y = a²b/c⁴**

* * Delta Y/y = 2 * Delta A/ a + Delta B/ B + 4* Delta C/ C

* **In the Last:**

* * Most questions are based on direct formulas.