What is Exam Sprinter?

Exam Sprinter is an AI-powered platform designed for competitive exam preparation like UPSC, JEE, NEET, and SSC. It offers personalized study plans, unlimited practice questions, and real-time AI tutoring.

How does Exam Sprinter help with preparation?

Exam Sprinter uses AI to create personalized study plans based on your strengths and weaknesses. You get access to unlimited AI-generated mocks, deep analytics, and 24/7 AI tutor support for instant doubt resolution.

Is Exam Sprinter free to use?

Yes, Exam Sprinter offers free access (₹0) to start your preparation for exams like JEE, NEET, SSC, and UPSC. Download the app to drop in and start learning.

🚀 COMPLETE PREPARATION LOOP: LEARN → PRACTICE → ANALYZE

Algebra and Matrices Preparation Hub

Master Algebra and Matrices with coaching-grade theory notes, verified video lectures, and 10 interactive MCQs with instant mistake analysis. Continue with 500+ adaptive questions inside the Exam Sprinter app.

📘 Theory Notes ✍️ Interactive Practice ⏱️ CBT Simulator

What is Algebra and Matrices?

Algebra and Matrices covers the essential principles and concepts required for NDA.

💡 Why Study Algebra and Matrices?

Highly important, frequently tested in NDA.

Parameter	Details / Relevance
Target Exam	NDA
Subject Category	Mathematics
Estimated Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Medium
Interactive Solved MCQs	10 Questions with AI Diagnostics
Adaptive App Practice	500+ Questions & Real-Time AI Tutor

⚠️ Common Pitfalls to Avoid

Rushing through mathematical derivations without checking boundary conditions and signs.
Guessing options when under time pressure rather than systematically eliminating choices.
Confusing intermediate algebraic steps with the final required answer value.

✓ COACHING-GRADE CLASSROOM NOTES

Algebra and Matrices Theory & Derivations

Browse All Notes Library ›

Access comprehensive classroom-grade derivations and NCERT micro-extracts for Algebra and Matrices. Features step-by-step proofs and standard assumptions.

Important Formulas & Cheat Sheet

✍️ STEP 3: PRACTICE & ANALYZE

Algebra and Matrices Interactive Practice

⏱️ Take Chapter CBT Test

Solve these 10 standard exam-level questions. The system tracks your response time, detects rapid guessing via Cognitive Reading Thresholds, and outputs your post-session diagnosis.

Interactive Practice Progress:0 / 10 Answered

⏱️ Launch Chapter CBT Simulator

Q1Algebra Fundamentals

Expected: 90sMedium

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$ , then the locus of z is a pair of:

Q2Matrix Algebra

Expected: 90sMedium

What is the modulus of $\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?$

Q3Determinants & Linear Systems

Expected: 90sMedium

What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end{array}\right|=0$ ?

Q4Algebra Fundamentals

Expected: 90sMedium

If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω2)100 + (1 - ω + ω2)100 equal to?

Q5Matrix Algebra

Expected: 90sMedium

If log10 2 log2 10 + log10(10x) = 2, then what is the value of x?

Q6Determinants & Linear Systems

Expected: 90sMedium

What is the number of distinct solutions of the equation ${z^2} + |z|\, = \,0$ (where, z is the complex number)?

Q7Algebra Fundamentals

Expected: 90sMedium

What is the value of ${\left[ {{{i + \sqrt 3 } \over 2}} \right]^{2019}} + {\left[ {{{i - \sqrt 3 } \over 2}} \right]^{2019}}$ ?

Q8Matrix Algebra

Expected: 90sMedium

The equations $x + 2y + 3z = 1$ , $2x + y + 3z = 2$ , $5x + 5y + 9z = 4$

Q9Determinants & Linear Systems

Expected: 90sMedium

If m = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right] and n = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right], then what is the value of the determinant of $m\cos \theta$ $-$ $n\sin \theta$ ?

Q10Algebra Fundamentals

Expected: 90sMedium

It is given that the roots of the equation ${x^2} - 4x - {\log _3}P = 0$ are real. For this the minimum value of P is

🗺️ Recommended Learning Sequence

Algebra and Matrices (Current)➔Trigonometry

Ready to achieve complete mastery in Algebra and Matrices?

Get 500+ chapter-wise questions, real-time AI mistake diagnosis, and personalized daily revision schedules inside the Exam Sprinter Android app.

Practice 500+ Algebra and Matrices Questions in App

Algebra and Matrices Preparation Hub

What is Algebra and Matrices?

💡 Why Study Algebra and Matrices?

⚠️ Common Pitfalls to Avoid

Algebra and Matrices Theory & Derivations

Important Formulas & Cheat Sheet

Algebra and Matrices Interactive Practice

If z z̅ = |z + z̅ |, where z = x + iy, i = −1\sqrt{-1}−1​, then the locus of z is a pair of:

What is the modulus of (−32−12)200?\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?(2−3​​−21​)200?

What is the sum of the roots of the equation ∣0x−ax−b00x−cx+bx+c1∣=0\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end{array}\right|=0 ​00x+b​x−a0x+c​x−bx−c1​​=0 ?

If ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω2)100 + (1 - ω + ω2)100 equal to?

If log10 2 log2 10 + log10(10x) = 2, then what is the value of x?

What is the number of distinct solutions of the equation z2+∣z∣ = 0{z^2} + |z|\, = \,0z2+∣z∣=0 (where, z is the complex number)?

What is the value of [i+32]2019+[i−32]2019{\left[ {{{i + \sqrt 3 } \over 2}} \right]^{2019}} + {\left[ {{{i - \sqrt 3 } \over 2}} \right]^{2019}}[2i+3​​]2019+[2i−3​​]2019?

The equations x+2y+3z=1x + 2y + 3z = 1x+2y+3z=1, 2x+y+3z=22x + y + 3z = 22x+y+3z=2, 5x+5y+9z=45x + 5y + 9z = 45x+5y+9z=4

If m = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right] and n = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right], then what is the value of the determinant of mcos⁡θm\cos \theta mcosθ −-− nsin⁡θn\sin \theta nsinθ ?

It is given that the roots of the equation x2−4x−log⁡3P=0{x^2} - 4x - {\log _3}P = 0x2−4x−log3​P=0 are real. For this the minimum value of P is

🗺️ Recommended Learning Sequence

Ready to achieve complete mastery in Algebra and Matrices?

If z z̅ = |z + z̅ |, where z = x + iy, i = $\sqrt{-1}$ , then the locus of z is a pair of:

What is the modulus of $\left(\frac{\sqrt{-3}}{2}-\frac{1}{2}\right)^{200}?$

What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end{array}\right|=0$ ?

What is the number of distinct solutions of the equation ${z^2} + |z|\, = \,0$ (where, z is the complex number)?

What is the value of ${\left[ {{{i + \sqrt 3 } \over 2}} \right]^{2019}} + {\left[ {{{i - \sqrt 3 } \over 2}} \right]^{2019}}$ ?

The equations $x + 2y + 3z = 1$ , $2x + y + 3z = 2$ , $5x + 5y + 9z = 4$

If m = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right] and n = \left[ {\matrix{ 0 & 1 \cr { - 1} & 0 \cr } } \right], then what is the value of the determinant of $m\cos \theta$ $-$ $n\sin \theta$ ?

It is given that the roots of the equation ${x^2} - 4x - {\log _3}P = 0$ are real. For this the minimum value of P is