With the shift to JEE Main being computer-based and numerical-answer focused, the need for speed and accuracy has intensified. The Tata McGraw Hill Mathematics book, despite its age, remains because it trains the two muscles JEE most tests: pattern recognition (through thousands of examples) and procedural fluency (through graded exercises).
If the system of equations $x + ay = 0$, $az + y = 0$, and $ax + z = 0$ has infinitely many solutions, then $a$ can be: (A) $1$ (B) $-1$ (C) $0$ (D) $2$
Hint: $D = \beginvmatrix 1 & a & 0 \ 0 & 1 & a \ a & 0 & 1 \endvmatrix = 1(1) - a(0-a) + 0 = 1 + a^2$. For infinite solutions, $D=0 \implies a^2 = -1$. Real value? Wait. The system is $x+ay=0$, $az+y=0$, $ax+z=0$. From eq 1: $x = -ay$. Eq 2: $y = -az$. Eq 3: $z = -ax$. Substitute: $x = -a(-az) = a^2z = a^2(-ax) = -a^3x$. $x(1+a^3) = 0$. So infinite solutions if $1+a^3 = 0 \implies a=-1$. Is $a=0$ possible? $x=0, y=0, z=0$. Unique solution $(0,0,0)$. So not C. Answer is (B) . Wait , if $a=0$, solution is $x=0, y=0, z=0$. It is unique, not infinite. If $a=-1$, $x=y, y=z, z=x$. $x=y=z$. Infinite solutions (any point on line $x=y=z$). Correct Answer: (B) . tata mcgraw hill mathematics for iit jee
The series for IIT JEE has long been a staple in the arsenal of aspirants aiming for top ranks in the Indian Institutes of Technology (IITs) . Known for its rigorous problem sets and concise conceptual summaries, the series is designed to help students transition from basic school-level math to the highly competitive level required for both JEE Main and JEE Advanced . Core Offerings for JEE Aspirants
Here are some key features of the book:
Sprinkled throughout are sections like “Important Note,” “Caution,” or “Shortcut Method.” For example, in the chapter on Binomial Theorem , the book demonstrates how to find the greatest coefficient without expanding fully. These nuggets are gold for speed in JEE Main.
If $I = \int_0^\pi/2 \frac\sin x\sin x + \cos x dx$, find the value of $2I$. With the shift to JEE Main being computer-based
This textbook is a comprehensive resource for students preparing for the Indian Institutes of Technology Joint Entrance Examination (IIT JEE). The book covers various topics in mathematics, including algebra, calculus, geometry, and trigonometry, which are crucial for success in the IIT JEE.
| Feature | Tata McGraw Hill (RD Sharma) | Cengage (G. Tewani) | Arihant (SK Goyal) | | :--- | :--- | :--- | :--- | | | Enormous solved examples | Concept application & illustrations | Topic-wise past papers | | Theory Depth | Moderate | High (with conceptual notes) | Moderate to Low | | Problem Difficulty Gradient | Gradual, well-graded | Steep, jumps quickly | Mixed, sometimes erratic | | Best for | Building speed & pattern recognition | Deep conceptual clarity | Exam-focused revision | | Price-to-Value | Excellent (highly economical) | Expensive | Moderate | For infinite solutions, $D=0 \implies a^2 = -1$