1
JEE Advanced 2018 Paper 1 Offline
+3
-0.75
Treatment of benzene with $$CO/HCl$$ in the presence of anhydrous $$AlC{l_3}/CuCl$$ followed by reaction with $$A{c_2}O/NaOAc$$ gives compound $$X$$ as the major product. Compound $$X$$ upon reaction with $$B{r_2}/N{a_2}C{O_3},$$ followed by heating at $$473$$ $$K$$ with moist $$KOH$$ furnishes $$Y$$ as the, major product. Reaction of $$X$$ with $${H_2}/Pd$$-$$C,$$ followed by $${H_3}P{O_4}$$ treatment gives $$Z$$ as the major product.
The compound $$Z$$ is
A
B
C
D
2
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
For a non-zero complex number z, let arg(z) denote the principal argument with $$-$$ $$\pi$$ < arg(z) $$\le$$ $$\pi$$. Then, which of the following statement(s) is (are) FALSE?
A
arg($$-$$1$$-$$i) = $${\pi \over 4}$$, where i = $$\sqrt { - 1}$$
B
The function f : R $$\to$$ ($$-$$$$\pi$$, $$\pi$$), defined by f(t) = arg ($$-$$1 + it) for all t $$\in$$ R, is continuous at all points of R, where i = $$\sqrt { - 1}$$.
C
For any two non-zero complex numbers z1 and z2, arg $$\left( {{{{z_1}} \over {{z_2}}}} \right)$$$$-$$ arg (z1) + arg(z2) is an integer multiple of 2$$\pi$$.
D
For any three given distinct complex numbers z1, z2 and z3, the locus of the point z satisfying the condition arg$$\left( {{{(z - {z_1})({z_2} - {z_3})} \over {(z - {z_3})({z_2} - {z_1})}}} \right) = \pi$$, lies on a straight line.
3
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
In a $$\Delta$$PQR = 30$$^\circ$$ and the sides PQ and QR have lengths 10$$\sqrt 3$$ and 10, respectively. Then, which of the following statement(s) is(are) TRUE?
A
$$\angle QPR = 45^\circ$$
B
The area of the $$\Delta PQR$$ is $$25\sqrt 3$$ and $$\angle QRP = 120^\circ$$
C
The radius of the incircle of the $$\Delta PQR$$ is $$10\sqrt 3$$ $$-$$ 15
D
The area of the circumcircle of the $$\Delta PQR$$ is 100$$\pi$$
4
JEE Advanced 2018 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let P1 : 2x + y $$-$$ z = 3 and P2 : x + 2y + z = 2 be two planes. Then, which of the following statement(s) is(are) TRUE?
A
The line of intersection of P1 and P2 has direction ratios 1, 2, $$-$$1
B
The line $${{3x - 4} \over 9} = {{1 - 3y} \over 9} = {z \over 3}$$ is perpendicular to the line of intersection of P1 and P2
C
The acute angle between P1 and P2 is 60$$^\circ$$
D
If P3 is the plane passing through the point (4, 2, $$-$$2) and perpendicular to the line of intersection of P1 and P2, then the distance of the point (2, 1, 1) from the plane P3 is $${2 \over {\sqrt 3 }}$$
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