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

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 36

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

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?

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?

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?

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)?