Tata Mcgraw Hill Mathematics For Iit Jee Jun 2026

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 $\sin^-1(\frac1\sqrt29)$.

This is one of the most pirated books in India. Counterfeit copies have poor print quality, missing pages, and wrong answer keys. Always buy from a trusted seller (Amazon, Flipkart Retail, or a physical bookstore) and check for McGraw Hill’s hologram. tata mcgraw hill mathematics for iit jee

It is crucial to distinguish between the standard school textbooks (for CBSE exams) and the dedicated "Tata McGraw Hill Mathematics for IIT JEE" volume. The latter is an abridged, reorganized, and problem-heavy incarnation designed specifically for the JEE pattern, stripping away some of the repetitive elementary exercises found in the school editions and amplifying the difficulty gradient toward JEE Main and Advanced levels. The line $\fracx-23 = \fracy-34 = \fracz-45$ and

The book is primarily intended for students preparing for the IIT JEE, particularly those who are in their 11th or 12th standard. However, it can also be useful for students who are preparing for other engineering entrance exams, such as the Graduate Aptitude Test in Engineering (GATE). (D) The angle between the line and plane

Phase 3 (Pre-JEE Main, 6 months before): Solve only the “Archives” and “Competitive Edge” sections of relevant chapters. Time yourself.

Hint: Angle between line and plane $\sin \theta = \frac\vecb \cdot \vecn$. Check if point $(2,3,4)$ satisfies plane. It does ($4-9+4 \neq 0$). So line intersects plane. Correction: $(2)(3) + (-3)(4) + (1)(5) = 6 - 12 + 5 = -1 \neq 0$. Line is not parallel. It intersects. Angle calculation: $\sin \theta = \frac-1\sqrt3^2+4^2+5^2\sqrt14 = \frac1\sqrt50\sqrt14$. Wait. Let's check option D: $\sin^-1(1/\sqrt29)$. $\vecb \cdot \vecn = 6-12+5 = -1$. $|\vecb|=\sqrt9+16+25=\sqrt50$. $|\vecn|=\sqrt4+9+1=\sqrt14$. $\sin \theta = \frac1\sqrt700$. Option D is wrong? Review Q13 Options: Let's calculate dot product: $3(2) + 4(-3) + 5(1) = 6 - 12 + 5 = -1$. Dot product is not zero. Line is not parallel. Point $(2,3,4)$ on line: $2(2) - 3(3) + 4 = 4 - 9 + 4 = -1 \neq 0$. Line does not lie in plane. Line intersects plane at some point. Check Option D again. Maybe vector is $(2, -3, 1)$? No, coeff are $A=2, B=-3, C=1$. Let's re-evaluate the question to ensure a clean answer. If the plane was $x+y+z=0$? Let's assume standard TMH trick. Actually, if $\vecb \cdot \vecn \neq 0$, it intersects. Let's assume the intended answer for D was correct in the author's mind or fix the numbers. Correction: Let's mark (B) as correct for Intersection.