JEE (Advanced) 2019 Paper-2

Instructions

For the following questions answer them individually

Question 31

Total number of hydroxyl groups present in a molecule of the major product P is ______ .

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Question 32

Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular formula $$C_4H_8O$$ is

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Instructions

Answer by appropriately matching the lists based on the information given in the paragraph
Consider the Bohr’s model of a one-electron atom where the electron moves around the nucleus. In the following, List-I contains some quantities for the $$n^{th}$$ orbit of the atom and List-II contains options showing how they depend on n.

Question 33

Which of the following options has the correct combination considering List-I and List-II?

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Question 34

Which of the following options has the correct combination considering List-I and List-II?

Video Solution


Instructions

Answer by appropriately matching the lists based on the information given in the paragraph
List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List-I.

Question 35

Which of the following options has correct combination considering List-I and List-II?

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Question 36

Which of the following options has correct combination considering List-I and List-II?

Video Solution


Instructions

For the following questions answer them individually

Question 37

Let
$$P_1 = I = \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}, P_2 = \begin{bmatrix}1 & 0 & 0 \\0 & 0 & 1\\0 & 1 & 0\end{bmatrix}, P_3 = \begin{bmatrix}0 & 1 & 0 \\1 & 0 & 0\\0 & 0 & 1\end{bmatrix},$$
$$P_4 = \begin{bmatrix}0 & 1 & 0 \\0 & 0 & 1\\1 & 0 & 0\end{bmatrix}, P_5 = \begin{bmatrix}0 & 0 & 1 \\1 & 0 & 0\\0 & 1 & 0\end{bmatrix}, P_6 = \begin{bmatrix}0 & 0 & 1 \\0 & 1 & 0\\1 & 0 & 0\end{bmatrix},$$
and $$X = \sum_{k = 1}^6 P_k \begin{bmatrix}2 & 1 & 3 \\1 & 0 & 2\\3 & 2 & 1\end{bmatrix} P_k^T$$
where $$P_k^T$$ denotes the transpose of the matrix $$P_k$$. Then which of the following options is/are correct?

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Question 38

Let $$x \in R$$ and let
$$P = \begin{bmatrix}1 & 1 & 1 \\0 & 2 & 2\\0 & 0 & 3\end{bmatrix}, Q = \begin{bmatrix}2 & x & x \\0 & 4 & 0\\x & x & 6\end{bmatrix}$$ and $$R = PQP^{-1}$$
Then which of the following options is/are correct?

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Question 39

For non-negative integers n,let
$$f(n) = \frac{{\sum_{k = 0}^n}\sin \left(\frac{k + 1}{n + 2}\pi\right) \sin \left(\frac{k + 2}{n + 2}\pi\right)}{\sum_{k = 0}^n \sin^2 \left(\frac{k + 1}{n + 2}\pi\right)} $$
Assuming $$\cos^{-1}x$$ takes values in $$[0,\pi],$$ which of the following options is/are correct?

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Question 40

Let $$f: R \rightarrow R$$ bea function. We say that f has
PROPERTY 1 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{\sqrt{|h|}}$$ exists and is finite, and
PROPERTY 2 if $$\lim_{h \rightarrow 0} \frac{f(h) - f(0)}{h^2}$$ exists and is finite.
Then which of the following options is/are correct?

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