JEE (Advanced) 2017 Paper-1

Instructions

Answer the Questions by appropriately matching the information given in the three columns of the following table.

The wave function, $$\psi_{n, l, m_1}$$ is a mathematical function whose value depends upon spherical polar coordinates $$(r, \theta, \phi)$$ of the electron and characterized by the quantum numbers n, l and $$m_1$$. Here r is distance from nucleus, $$\theta$$ is colatitude and $$\phi$$ is azimuth. In the mathematical function given in the Table, Z is atomic number and $$a_0$$ is bohr radius.

Question 31

For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is

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Question 32

For hydrogen atom, the only CORRECT combination is

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Question 33

For $$He^+$$ ion, the only INCORRECT combination is

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Instructions

Answer the Questions by appropriately matching the information given in the three columns of the following table.

Columns 1, 2 and 3 contain starting materials, reaction conditions, and type of reactions, respectively.

Question 34

For the synthesis of benzoic acid, the only CORRECT combination is

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Question 35

The only CORRECT combination that gives two different carboxylic acids is

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Question 36

The only CORRECT combination in which the reaction proceeds through radical mechanism is

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Instructions

For the following questions answer them individually

Question 37

If $$2x - y + 1 = 0$$ is a tangent to the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{16} = 1$$, then which of the following CANNOT be sides of a right angled triangle?

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Question 38

If a chord, which is not a tangent, of the parabola $$y^2 = 16 x$$ has the equation $$2x + y = p$$, and midpoint (h, k), then which of the following is(are) possible value(s) of p, h and k?

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Question 39

Let [x] be the greatest integer less than or equals to x. Then, at which of the following point(s) the function $$f(x) = x \cos (\pi(x + [x]))$$ is discontinuous?

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Question 40

Let $$f:R \rightarrow (0, 1)$$ be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval (0, 1)?

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