JEE Main 2011 Question Paper with Solutions

Let a → , b → , c → be three non-zero vectors which are pairwise non-collinear. If $\overrightarrow a+3 \overrightarrow b$ is collinear with $\overrightarrow c$ and $\overrightarrow b+2 \overrightarrow c$ is collinear with $\overrightarrow a$ , then $\overrightarrow a+\overrightarrow b+6 \overrightarrow c$ is :

The vectors $\overrightarrow a$ and $\overrightarrow b$ are not perpendicular and $\overrightarrow c$ and $\overrightarrow d$ are two vectors satisfying $\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d$ and $\overrightarrow a .\overrightarrow d = 0\,\,.$ Then the vector $\overrightarrow d$ is equal to :

Two bodies of masses $m$ and $4$ $m$ are placed at a distance $r.$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ . It is moving with speed v and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperature increases by:

Three perfect gases at absolute temperatures ${T_1},\,{T_2}$ and ${T_3}$ are mixed. The masses of molecules are ${m_1},{m_2}$ and ${m_3}$ and the number of molecules are ${n_1},$ ${n_2}$ and ${n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

Identify the compound that exhibits tautomerism.

A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

A vessel at 1000 K contains CO 2 with a pressure of 0.5 atm. Some of the CO 2 is converted into CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is :

A 5.2 molal aqueous solution of methyl alcohol, CH 3 OH, is supplied. What is the mole fraction of methyl alcohol in the solution ?

The hybridization of orbitals of N atom in N O 3 − , N O 2 + and N H 4 + are respectively :

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:

Let α , β be real and z be a complex number. If z 2 + α z + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that :

If ω ( ≠ 1 ) is a cube root of unity, and ( 1 + ω ) 7 = A + B ω . Then ( A , B ) equals :

Equation of the ellipse whose axes of coordinates and which passes through the point $(-3,1)$ and has eccentricity $\sqrt {{2 \over 5}}$ is :

Let $R$ be the set of real numbers. Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$ . Statement II : $B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$ .

A boat is moving due east in a region where the earth's magnetic fields is 5.0 × 10 − 5 N A − 1 m − 1 due north and horizontal. The best carries a vertical aerial 2 m long. If the speed of the boat is 1.50 m s − 1 , the magnitude of the induced e m f in the wire of aerial is :

A resistor ′ R ′ and 2 μ F capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V . Calculate the value of R to make the bulb light up 5 s after the switch has been closed. ( log 10 2.5 = 0.4 )

A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R . The magnitude of the magnetic induction along its axis is:

If a wire is stretched to make it 0.1 % longer, its resistance will:

This question has a paragraph followed by two statements, Statement $-1$ and Statement $-2$ . Of the given four alternatives after the statements, choose the one that describes the statements. A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plane. With monochromatic light, this film gives an interference pattern due to light, reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement - $1$ : When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of $\pi .$ Statement - $2$ : The center of the interference pattern is dark.

The value of $\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$ is

Statement - 1 : The point A ( 1 , 0 , 7 ) is the mirror image of the point B ( 1 , 6 , 3 ) in the line : x 1 = y − 1 2 = z − 2 3 Statement - 2 : The line x 1 = y − 1 2 = z − 2 3 bisects the line segment joining A ( 1 , 0 , 7 ) and B ( 1 , 6 , 3 )

${{{d^2}x} \over {d{y^2}}}$ equals:

Let I be the purchase value of an equipment and V ( t ) be the value after it has been used for t years. The value V ( t ) depreciates at a rate given by differential equation d v ( t ) d t = − k ( T − t ) , where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V ( T ) of the equipment is

Let $A$ and $B$ be two symmetric matrices of order $3$ . Statement - 1 : $A(BA)$ and $(AB)$ $A$ are symmetric matrices. Statement - 2 : $AB$ is symmetric matrix if matrix multiplication of $A$ with $B$ is commutative.

Trichloroacetaldehyde was subjected to Cannizzaro’s reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :

Which of the following facts about the complex [Cr (NH 3 ) 6 ]Cl 3 is wrong?

The reduction potential of hydrogen half cell will be negative if :

Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6 o C will be : [K f for water = 1.86 K kg mol −1 , and molar mass of ethylene glycol = 62 g mol −1 )

Which of the following statement is wrong?