1
JEE Advanced 2017 Paper 1 Offline
+3
-1
The wave function, $${\psi _{n,1,{m_1}}}$$ is a mathematical function whose value depends upon spherical polar coordinates $$\left( {r,\theta ,\phi } \right)$$ of the electron and characterized by the quantum numbers $$n,1$$ and $${m_1}$$. Here $$r$$ is distance from nucleus, $$\theta$$ is colatitude and $$\phi$$ is azimuth. In the mathematical functions given in the table, $$Z$$ is atomic number and $${a_0}$$ is Bohr radius.

For the given orbital in Column 1, the only CORRECT combination for any hydrogen-like species is :
A
(I) (ii) (S)
B
(IV) (iv) (R)
C
(II) (ii) (P)
D
(III) (iii) (P)
2
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let X and Y be two events such that $$P(X) = {1 \over 3}$$, $$P(X|Y) = {1 \over 2}$$ and $$P(Y|X) = {2 \over 5}$$. Then
A
$$P(Y) = {4 \over {15}}$$
B
$$P(X'|Y) = {1 \over 2}$$
C
$$P(X \cup Y) = {2 \over 5}$$
D
$$P(X \cap Y) = {1 \over 5}$$
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let f : R $$\to$$ (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) ?
A
$${e^x} - \int_0^x {f(t)\sin t\,dt}$$
B
$$f(x) + \int_0^{{\pi \over 2}} {f(t)\sin t\,dt}$$
C
$$f(x) - \int_0^{{\pi \over 2} - x} {f(t)\cos t\,dt}$$
D
x9 $$-$$ f(x)
4
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let a, b, x and y be real numbers such that a $$-$$ b = 1 and y $$\ne$$ 0. If the complex number z = x + iy satisfies $${\mathop{\rm Im}\nolimits} \left( {{{az + b} \over {z + 1}}} \right) = y$$, then which of the following is(are) possible value(s) of x?
A
$$1 - \sqrt {1 + {y^2}}$$
B
$$- 1 - \sqrt {1 - {y^2}}$$
C
$$1 + \sqrt {1 + {y^2}}$$
D
$$- 1 + \sqrt {1 - {y^2}}$$
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