JEE Main 2007 Question Paper with Solutions

If $\widehat u$ and $\widehat v$ are unit vectors and $\theta$ is the acute angle between them, then $2\widehat u \times 3\widehat v$ is a unit vector for :

A $2$ $kg$ block slides on a horizontal floor with a speed of $4m/s.$ It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is $15N$ and spring constant is $10, 000$ $N/m.$ The spring compresses by

A point mass oscillates along the $x$ -axis according to the law $x = {x_0}\,\cos \left( {\omega t - \pi /4} \right).$ If the acceleration of the particle is written as $a = A\,\cos \left( {\omega t + \delta } \right),$ then

When a system is taken from state $i$ to state $f$ along the path iaf, it is found that $Q=50$ cal and $W=20$ $cal$ . Along the path $ibf$ $Q=36$ $cal.$ $W$ along the path $ibf$ is

If g E and g M are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio e l e c t r o c h arg ⁡ e o n t h e m o o n e l e c t r o n i c c h arg ⁡ e o n t h e e a r t h t o b e

Equal masses of methane and oxygen are mixed in an empty container at 25 o C. The fraction of the total pressure exerted by oxygen is

Which of the following reactions will yield 2, 2-dibromopropane?

Click below to view the full question statement and verified step-by-step solution.

The pK a of a weak acid (HA) is 4.5. The pOH of an aqueous buffered solution of HA in which 50% of the acid is ionized is :

In a sautrated solution of the sparingly soluble strong electrolyte AgIO 3 (Molecular mass = 283) the equilibrium which sets in is AgIO 3(s) $\leftrightharpoons$ Ag + (aq) + $IO_3^-$ If the solubility product constant K sp of AgIO 3 at a given temperature is 1.0 $\times$ 10 −8 , what is the mass of AgIO 3 contained in 100 ml of its saturated solution?

In a geometric progression consisting of positive terms, each term equals the sum of the next two terns. Then the common ratio of its progression is equals

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

If the difference between the roots of the equation ${x^2} + ax + 1 = 0$ is less than $\sqrt 5 ,$ then the set of possible values of $a$ is

The set S = {1, 2, 3, ........., 12} is to be partitioned into three sets A, B, C of equal size. Thus $A \cup B \cup C = S,\,A \cap B = B \cap C = A \cap C = \phi$ . The number of ways to partition S is

Let A $\left( {h,k} \right)$ , B $\left( {1,1} \right)$ and C $(2, 1)$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is $1$ square unit, then the set of values which $'k'$ can take is given by :

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate ?

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields E → and B → with a velocity v → perpendicular to both E → and B → , and comes out without any change in magnitude or direction of v → . Then

In an a . c . circuit the voltage applied is E = E 0 sin ω t . The resulting current in the circuit is I = I 0 sin ⁡ ( ω t − π 2 ) . The power consumption in the circuit is given by

Photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is

Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

If $p$ and $q$ are positive real numbers such that ${p^2} + {q^2} = 1$ , then the maximum value of $(p+q)$ is

The area enclosed between the curves ${y^2} = x$ and $y = \left| x \right|$ is :

If sin -1 $\left( {{x \over 5}} \right)$ + cosec -1 $\left( {{5 \over 4}} \right)$ = ${\pi \over 2}$ , then the value of x is :

A tower stands at the centre of a circular park. $A$ and $B$ are two points on the boundary of the park such that $AB(=a)$ subtends an angle of ${60^ \circ }$ at the foot of the tower, and the angle of elevation of the top of the tower from $A$ or $B$ is ${30^ \circ }$ . The height of the tower is :

Two aeroplanes I and I I bomb a target in succession. The probabilities of I and I I scoring a hit correctly are 0.3 and 0.2 , respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is :

The stability of dihalides of S i , G e , S n and P b increases steadily in the sequence :

The equivalent conductances of two strong electrolytes at infinite dilution in H 2 O (where ions move freely through a solution) at 25 o C are given below: ∧ C H 3 C O O N a o = 91.0 S cm 2 /equiv ∧ H C l o = 426.2 S cm 2 /equiv What additional information/quantity one needs to calculate ∧ o of an aqueous solution of acetic acid?

The energies of activation for forward and reverse reactions for A 2 + B 2 ⇋ 2AB are 180 kJ mol −1 and 200 kJ mol −1 respectively. The presence of catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol −1 . The enthalpy change of the reaction ( A 2 + B 2 → 2AB) in the presence of catalyst will be (in kJ mol −1 )

Which of the following is the correct order of decreasing S N 2 reactivity?

Which one of the following is the strongest base in aqueous solution?