Algebra and Number Systems

Lakshya NDA

Build foundations in sets, complex numbers, sequences, and binomial theorem.

Level

Foundation

Study Time

24 min

Exam Relevance

High (direct and concept-application questions)

What this chapter covers

This chapter creates the base for many NDA maths questions. If this is strong, later topics become easier.

Core concepts

Sets and operations: union, intersection, complement, Venn-based logic.
Complex numbers: real + imaginary parts, modulus and basic properties.
Progressions: AP, GP and harmonic progression.
Permutation and combination basics.
Binomial theorem and common expansion patterns.

Smart approach

Convert every word problem into symbols first.
For sequence questions, write first 4 terms before formula.
In binomial questions, identify required term index quickly.

Common mistakes

Mixing up nCr and nPr.
Sign mistakes in complex number simplification.
Using AP formula for GP by habit.

NCERT-CBSE bridge

Revise solved examples first, then do objective conversion:

each descriptive question -> create 4 options,
decide why 3 are wrong.

This sharpens elimination skill needed in NDA MCQs.

Chapter-end mini quiz

5 quick questions from the question bank.

Question 1

For what value of the angle between the vectors $\vec{a}$ and $\vec{b}$ is the quantity $|\vec{a} \times \vec{b}| + \sqrt{3}|\vec{a} \cdot \vec{b}|$ maximum?

$0^\circ$$30^\circ$$45^\circ$$60^\circ$

Question 2

What is the angle between $(\vec{a} + \vec{b})$ and $\vec{c}$?

$\dfrac{\pi}{2}$$\dfrac{\pi}{3}$$\dfrac{\pi}{4}$$\dfrac{\pi}{6}$

Question 3

A spacecraft located at $\hat{i}+2\hat{j}+3\hat{k}$ is subjected to a force $\lambda\hat{k}$ by firing a rocket. The spacecraft is subjected to a moment of magnitude

$\lambda$$\sqrt3\,\lambda$$\sqrt5\,\lambda$None of the above

Question 4

If the position vectors of $A$ and $B$ are $(\sqrt{2}-1)\hat{i} - \hat{j}$ and $\hat{i} + (\sqrt{2}+1)\hat{j}$ respectively, then what is the magnitude of $\overrightarrow{AB}$?

$2\sqrt{2}$$3\sqrt{2}$$2\sqrt{3}$$3\sqrt{3}$

Question 5

If $x^3 + y^3 = (100010111)_2$ and $x + y = (11111)_2$, then what is $(x - y)^2 + xy$ equal to?

$(1101)_2$$(1001)_2$$(1011)_2$$(1111)_2$

Source Base

NCERT Class XI Mathematics: Sets and Complex Numbers chapters
CBSE algebra practice pattern for AP/GP and binomial basics

Back to Mathematics Chapters Next: Matrices and Determinants