JEE Advanced 2021 Paper 1 Online

In the reaction given below, the total number of atoms having sp2 hybridization in the major product P is _________.

Among the following, the conformation that corresponds to the most stable conformation of meso-butane-2,3-diol is

The maximum number of possible isomers (including stereoisomers) which may be formed on mono-bromination of 1-methylcyclohex-1-ene using Br2 and UV light is ___________.

Given : The compound(s), which on reaction with HNO3 will give the product having degree of rotation, [\(\alpha\)]D = \(-\)52.7\(^\circ\) is (are)

The reaction of Q with PhSNa yields an organic compound (major product) that gives positive Carius test on treatment with Na2O2 followed by addition of BaCl2. The correct option(s) for Q is (are)

The calculated spin only magnetic moments of [
Cr(NH3)6]3+ and [CuF6]3\(-\) in BM, respectively, are(Atomic numbers of Cr and Cu are 24 and 29, respectively)

The total number of possible isomers for [Pt(NH3)4Cl2]Br2 is ______.

The major product formed in the following reaction of

For the following reaction scheme, percentage yields are given along the arrow:x g and y g are mass of R and U, respectively.(Use : Molar mass (in g mol\(-\)1) of H, C and O as 1, 12 and 16, respectively)The value of x is ________.

The value of y is ________.

The correct statement(s) related to the metal extraction processes is (are) :

A mixture of two salts is used to prepare a solution S, which gives the following results :The correct option(s) for the salt mixture is (are)

For the given close packed structure of a salt made of cation X and anion Y shown below (ions of only one face are shown for clarity), the packing fraction is approximately (packing fraction = \({{packing\,efficiency} \over {100}}\))

The value of x is ________.

The value of | y | is ________.

The correct statement(s) related to colloids is (are)

The value of standard enthalpy, \(\Delta\)Ho (in kJ mol\(-\)1) for the given reaction is _______.

The value of \(\Delta\)S\(\theta\) (in J K\(-\)1 mol\(-\)1) for the given reaction, at 1000 K is _________.

An ideal gas undergoes a reversible isothermal expansion from state I to state II followed by a reversible adiabatic expansion from state II to state III. The correct plot(s) representing the changes from state I to state III is (are)(p : p...

The area of the region \(\left\{ {\matrix{ {(x,y):0 \le x \le {9 \over 4},} & {0 \le y \le 1,} & {x \ge 3y,} & {x + y \ge 2} \cr } } \right\}\) is

Consider a triangle \(\Delta\) whose two sides lie on the x-axis and the line x + y + 1 = 0. If the orthocenter of \(\Delta\) is (1, 1), then the equation of the circle passing through the vertices of the triangle \(\Delta\) is

Let $\theta_1, \theta_2, \ldots, \theta_{10}$ be positive valued angles (in radian) such that $\theta_1+\theta_2+\cdots+\theta_{10}=2 \pi$. Define the complex numbers $z_1=e^{i \theta_1}, z_k=z_{k-1} e^{i \theta_k}$ for $k=2,3, \ldots, 10$,...

For any complex number w = c + id, let \(\arg (w) \in ( - \pi ,\pi ]\), where \(i = \sqrt { - 1}\). Let \(\alpha\) and \(\beta\) be real numbers such that for all complex numbers z = x + iy satisfying $$\arg \left( {{{z + \alpha } \over {z...

Let f : R \(\to\) R be defined by \(f(x) = {{{x^2} - 3x - 6} \over {{x^2} + 2x + 4}}\)Then which of the following statements is (are) TRUE?

Let \(\alpha\), \(\beta\) and \(\gamma\) be real numbers such that the system of linear equationsx + 2y + 3z = \(\alpha\)4x + 5y + 6z = \(\beta\)7x + 8y + 9z = \(\gamma\) \(-\) 1is consistent. Let | M | represent the determinant of the mat...

Let \(\alpha\), \(\beta\) and \(\gamma\) be real numbers such that the system of linear equationsx + 2y + 3z = \(\alpha\)4x + 5y + 6z = \(\beta\)7x + 8y + 9z = \(\gamma\) \(-\) 1is consistent. Let | M | represent the determinant of the mat...

For any 3 \(\times\) 3 matrix M, let | M | denote the determinant of M. Let\(E = \left[ {\matrix{ 1 & 2 & 3 \cr 2 & 3 & 4 \cr 8 & {13} & {18} \cr } } \right]\), $$P = \left[ {\matrix{
1 & 0 & 0 \cr
0 & 0 & 1 \cr
...

For any 3 \(\times\) 3 matrix M, let |M| denote the determinant of M. Let I be the 3 \(\times\) 3 identity matrix. Let E and F be two 3 \(\times\) 3 matrices such that (I \(-\) EF) is invertible. If G = (I \(-\) EF)\(-\)1, then which of the...

Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 \(-\) S1 and F2 = F1 \(\cup\)...

Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chose...

Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chose...

Let E, F and G be three events having probabilities \(P(E) = {1 \over 8}\), \(P(F) = {1 \over 6}\) and \(P(G) = {1 \over 4}\), and let P (E \(\cap\) F \(\cap\) G) = \({1 \over {10}}\). For any event H, if Hc denotes the complement, then whi...

In a triangle ABC, let AB = \(\sqrt {23}\), BC = 3 and CA = 4. Then the value of \({{\cot A + \cot C} \over {\cot B}}\) is _________.

For x \(\in\) R, the number of real roots of the equation \(3{x^2} - 4\left| {{x^2} - 1} \right| + x - 1 = 0\) is ________.

For any positive integer n, let Sn : (0, \(\infty\)) \(\to\) R be defined by \({S_n}(x) = \sum\nolimits_{k = 1}^n {{{\cot }^{ - 1}}\left( {{{1 + k(k + 1){x^2}} \over x}} \right)}\), where for any x \(\in\) R, $${\cot ^{ - 1}}(x) \in (0,\pi...

Consider the lines L1 and L2 defined by \({L_1}:x\sqrt 2 + y - 1 = 0\) and \({L_2}:x\sqrt 2 - y + 1 = 0\)For a fixed constant \(\lambda\), let C be the locus of a point P such that the product of the distance of P from L1 and the distance...

Consider the lines L1 and L2 defined by \({L_1}:x\sqrt 2 + y - 1 = 0\) and \({L_2}:x\sqrt 2 - y + 1 = 0\)For a fixed constant \(\lambda\), let C be the locus of a point P such that the product of the distance of P from L1 and the distance...

Let \(\overrightarrow u\), \(\overrightarrow v\) and \(\overrightarrow w\) be vectors in three-dimensional space, where \(\overrightarrow u\) and \(\overrightarrow v\) are unit vectors which are not perpendicular to each other and $$\o...

A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60% and beta-decay with probability of 40%. Initially, the number of Q nuclei is 1000. The number of alpha-decays of Q in the first one hour is

Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \(\mu\)C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \(\mu\)C.The...

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 \(\mu\)C. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 \(\mu\)C.The...

Two point charges \(-\)Q and +Q/\(\sqrt 3\) are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane w...

Two point charges \(-\)Q and +Q/\(\sqrt 3\) are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius R and potential V = 0 in the xy-plane w...

An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses ae 20 cm. The refracti...

A wide slab consisting of two media of refractive indices n1 and n2 is placed in air as shown in the figure. A ray of light is incident from medium n1 to n2 at an angle \(\theta\), where sin\(\theta\) is slightly larger than 1/n1. Take refr...

An ideal gas undergoes a four step cycle as shown in the P-V diagram below. During this cycle, heat is absorbed by the gas in

A small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at 0 K. At time t = 0, the temperature of the object is 200 K. The temperature of the object becomes 100 K at t ...

A particle of mass M = 0.2 kg is initially at rest in the xy-plane at a point (x = \(-\)l, y = \(-\)h), where l = 10 m and h = 1 m. The particle is accelerated at time t = 0 with a constant acceleration a = 10 m/s2 along the positive x-dire...

A projectile is thrown from a point O on the ground at an angle 45\(^\circ\) from the vertical and with a speed 5\(\sqrt 2\) m/s. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically ...