What sets Tata McGraw Hill apart from other publishers is its structured approach to problem-solving:
Hint: Vector triple product is always coplanar. Box product $[\veca \vecb \vecc] = \veca \cdot (\vecb \times \vecc)$. Angle $\vecb, \vecc = \pi/3$. Let $\vecb=\hatj, \vecc=\frac12\hatj+\frac\sqrt32\hatk$. $\vecb\times\vecc = \frac\sqrt32\hati$. $\veca \cdot (\vecb\times\vecc) = \frac\sqrt32 (\veca \cdot \hati)$. $\veca \cdot \vecb = a_y = 0$. $\veca \cdot \vecc = \frac12a_y + \frac\sqrt32a_k = \frac12$. If $a_y=0 \implies \frac\sqrt32a_k = 1/2 \implies a_k = 1/\sqrt3$. Since $\veca$ is unit vector, $a_x^2 + a_y^2 + a_z^2 = 1 \implies a_x^2 + 1/3 = 1 \implies a_x = \pm \sqrt2/3$. Box product = $\frac\sqrt32 a_x = \frac\sqrt32 (\pm \sqrt\frac23) = \pm \frac1\sqrt2$. Wait, check Option B. It says $\sqrt3/2$. Let me re-read $\veca \cdot \vecc = 1/2$. Check option C. Formula identity: $[\veca \vecb \vecc]^2 = \dots$ Lagrange Identity. Check D: $|\veca+\vecb+\vecc|^2 = 1+1+1+0+1+1 = 5 \implies \sqrt5$. Incorrect. Answer: (A, C) . (Verify B calculation again). tata mcgraw hill mathematics for iit jee
The line $\fracx-23 = \fracy-34 = \fracz-45$ and the plane $2x - 3y + z = 0$: (A) Are parallel to each other. (B) Intersect at a point. (C) The line lies in the plane. (D) The angle between the line and plane is $\sin^-1(\frac1\sqrt29)$. What sets Tata McGraw Hill apart from other
Hint: $f(x) = \int_0^x |t-1|dt$. If $x > 1$: $\int_0^1 (1-t)dt + \int_1^x (t-1)dt$. $f(x) = [\frac(t-1)^22]_1^x$ (after simplification) or geometric area. Function is $x|x-1|/2$ type shape shifted. It is continuous. At $x=1$: Left derivative is 1, Right derivative is -1? $t < 1 \implies f'(t) = -(t-1) = 1-t$. $f'(1^-) = 0$. $t > 1 \implies f'(t) = t-1$. $f'(1^+) = 0$. It IS differentiable at 1. So (A), (B). Check local min/max. $f'(x)$ changes sign? For $x < 1$, $f'(x) > 0$. For $x > 1$, $f'(x) > 0$. No change of sign. Monotonically increasing. Wait, let's re-evaluate. Integral of $ Let $\vecb=\hatj, \vecc=\frac12\hatj+\frac\sqrt32\hatk$
Unlike many western texts that focus on proofs, the Tata McGraw Hill volume excels in operational mathematics . A typical chapter on Indefinite Integration may have over 150 solved examples, methodically categorized (e.g., integration by substitution, by parts, partial fractions, special integrals). This exhaustive collection allows a self-studying student to recognize patterns—a critical skill for JEE.
Hint: Differentiate twice to eliminate constants.