The National Defence Academy (NDA) exam includes a wide range of topics, including mathematics. Here are some common math formulas that are often used in the NDA exam: **1. Trigonometric Formulas:** – Pythagorean identities: \( \sin^2(x) + \cos^2(x) = 1 \) – Sum and difference formulas: – \( \sin(A \pm B) = \sin(A)\cos(B) \pm \cos(A)\sin(B) \) – \( \cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B) \) **2. Algebraic Formulas:** – Quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \) – Binomial theorem: \( (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \) – Factorization formulas: Difference of squares, perfect square trinomials, etc. **3. Geometry Formulas:** – Area of a triangle: \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \) – Perimeter and area of different polygons: square, rectangle, circle, etc. – Volume and surface area of basic 3D shapes: cube, cylinder, sphere, etc. **4. Arithmetic and Number System Formulas:** – LCM (Least Common Multiple) and GCD (Greatest Common Divisor) relationships. – Divisibility rules for numbers. – Arithmetic operations involving fractions, decimals, and percentages. **5. Mensuration Formulas:** – Area and perimeter of rectangles, squares, circles, triangles, etc. – Volume and surface area of cubes, spheres, cylinders, cones, etc. **6. Algebraic Identities:** – \( (a + b)^2 = a^2 + 2ab + b^2 \) – \( (a – b)^2 = a^2 – 2ab + b^2 \) – \( a^2 – b^2 = (a + b)(a – b) \) **7. Exponents and Logarithms:** – Laws of exponents: multiplication, division, power of a power, etc. – Logarithm properties: \( \log(ab) = \log a + \log b \), \( \log(a^b) = b \log a \) Remember that understanding the concepts behind these formulas is just as important as memorizing the formulas themselves. Practice using these formulas in different types of problems to enhance your problem-solving skills for the NDA exam. Always refer to the NDA syllabus and previous year’s question papers to get a better idea of the specific topics and types of questions that are commonly asked.
