JEE Advanced 2018 Question Paper

The correct option(s) to distinguish nitrate salts of Mn2+ and Cu2+ taken separately is (are) :-

Aniline reacts with mixed acid (conc. HNO3 and conc. H2SO4) at 288 K to give P (51%), Q (47%) and R (2%). The major product(s) the following reaction sequence is (are) :- R→             3) H O+              4) NaNO2 , HCl/273-278K            5) EtOH, ∆ 1)Ac2 O, pyridin 2) Br2 , CH 3CO2 HS→3) NaNO2 , HCl/273-278K 4) H3PO21) Sn/HCl 2) Br2 /H2O (excess) ,  major product(s)

For a first order reaction A(g) → 2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are P0 and Pt, respectively. Initially, only A is present with concentration [A]0, and t1/3 is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) :- (Assume that all these gases behave as ideal gases)

In the following reaction sequence, the correct structure(s) of X is (are) X→2)Nal ,Me2CO3)NaN3 , HCONMe21)PBr3,Et2O

The Fischer presentation of D-glucose is given below The correct structure(s) of β-glucopyranose is (are) :-

Let ƒ : [0, ∞)→ℝ) be a continuous function such thatƒ(x) =1- 2x + ∫0xex-t ƒ(t)dt for all x ∈ [0, ∞). Then, which of the following statement(s) is (are) TRUE ?

In a triangle PQR, let ∠PQR = 30° and the sides PQ and QR have lengths 10 3 and 10, respectively. Then, which of the following statement(s) is (are) TRUE ?

Let T be the line passing through the points P(–2, 7) and Q(2, –5). Let F1 be the set of all pairs of circles (S1, S2) such that T is tangents to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1, S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2. Let E2 be the set of the mid-points of the line segments in the set F2. Then, which of the following tatement(s) is (are) TRUE ?

For a non-zero complex number z, let arg(z) denotes the principal argument with-π< arg(z) ≤π. Then, which of the following statement(s) is (are) FALSE ?

For any positive integer n, define ƒn : 0,∞ →ℝas fx(x)=∑j=1ntan-111+(x+j)(x+j-1)  for all  x ∈(0,∞) (Here, the inverse trigonometric function tan–1x assume values in-π2,π2.)Then, which of the following statement(s) is (are) TRUE ?

One mole of a monatomic ideal gas undergoes a cyclic process as shown in the figure (whre V is the volume and T is the temperature). Which of the statements below is (are) true ?

The electric field E is measured at a point P(0,0,d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II List–I List–II P. E is indpendent of d 1. A point charge Q at the origin Q. E∝1d 2. A small dipole with point charges Q at (0,0,ι) and – Q at (0,0, – ι). Take 2ι << d R. E∝1d2 3. An infinite line charge coincident with the x-axis, with uniform linear charge density λ S. E∝1d3 4. Two infinite wires carrying uniform linear Charge density parallel to the x - axis. The one along (y = 0, z = ι) has a charge density + λ and the one along (y = 0, z = –ι ) has a charge density – λ. Take 2 ι<< d 5. Infinite plane charge coincident with the xy-plane with uniform surface charge density

A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height h in the capillary tube above the water surface in the beaker. The surface tension of water isσ. The angle of contact between water and the wall of the capillary tube is θ Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

Two infinitely long straight wires lie in the xy-plane along the lines x = ±R. The wire located at x = +R carries a constant current I1 and the wire located at x = –R carries a constant current I2. A circular loop of radius R is suspended with its centre at (0, 0, 3R ) and in a plane parallel to the xy-plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the + j^direction. Which of the following statements regarding the magnetic field B→ is (are) true ?

In an experment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hzis used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true ?