MHTCET 2026 Maths TOP 100 Questions! Dont - MHT-CET Maths

Mathematics: Key Concepts, Formulas, and Problem-Solving for Competitive Exams

Vectors: Core Formulas and Applications Vectors are a high-weightage topic, often contributing 5–6 questions (10–12 marks). Mastery of vector formulas and their application is essential for maximizing scores. Key vector operations, properties, and problem-solving techniques are frequently tested. -...

Consider the function $f\left(x\right)=2x^2+3,\text{if}x\≤33x+B,\text{if}x\>3$ find a value of B such that f(x) is continuous at x = 3

12

If $y=\log \left(\tan x\right)$, then $\frac{dy}{dx}$ is:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>sec</mi><mn>2</mn></msup><mi>x</mi></mrow><mrow><mi>tan</mi><mi>x</mi></mrow></mfrac></math>

Consider the function $f\left(x\right)=2x^2+3,\text{if}x\&le;33x+B,\text{if}x\&gt;3$ find a value of B such that f(x) is continuous at x = 3

12

If $y=\log \left(\tan x\right)$, then $\frac{dy}{dx}$ is:

<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><msup><mi>sec</mi><mn>2</mn></msup><mi>x</mi></mrow><mrow><mi>tan</mi><mi>x</mi></mrow></mfrac></math>

What is the formula for the magnitude of a vector $\vec{a} = ai + bj + ck$?

The magnitude of a vector $\vec{a} = ai + bj + ck$ is given by the formula $|\vec{a}| = \sqrt{a^2 + b^2 + c^2}$. This calculates the length of the vector in 3D space.

Define a Unit Vector.

A unit vector is a vector with a magnitude of 1, pointing in the same direction as the given vector. It is calculated by dividing the vector by its magnitude: $\hat{a} = \frac{\vec{a}}{|\vec{a}|}$.