JEE Main 2005 Question Paper with Solutions

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate ${f \over 2}$ to come to rest. If the total distance traversed is 15 S, then

A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate ${f \over 2}$ to come to rest. If the total distance traversed is 15 S, then

The exothermic formation of ClF 3 is represented by the equation: Cl 2 (g) + 3F 2 (g) ⇋ 2ClF 3 (g); Δ H = -329 kJ Which of the following will increase the quantity of ClF 3 in an equilibrium mixture of Cl 2 , F 2 and ClF 3 ?

Pick out the isoelectronic structure from the following : ( i ) C H 3 + ( i i ) H 3 O + ( i i i ) N H 3 ( i v ) C H 3 −

If the bond dissociation energies of XY, X 2 and Y 2 (all diatomic molecules) are in the ratio of 1:1:0.5 and Δ H f for the formation of XY is -200 kJ mole -1 . The bond dissociation energy of X 2 will be :

Consider the reaction: N 2 + 3H 2 $\to$ 2NH 3 carried out at constant temperature and pressure. If $\Delta H$ and $\Delta U$ are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

Based on lattice energy and other considerations which one of the following alkali metal chlorides is expected to have the highest melting point :

If the coefficients of r th , (r+1) th , and (r + 2) th terms in the binomial expansion of ${{\rm{(1 + y )}}^m}$ are in A.P., then m and r satisfy the equation

If non zero numbers a , b , c are in H . P . , then the straight line x a + y b + 1 c = 0 always passes through a fixed point. That point is :

If $\,\omega = {z \over {z - {1 \over 3}i}}\,$ and $\left| \omega \right| = 1$ , then $z$ lies on :

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $\,\left| {{z_1} + {z_2}} \right| = \left| {{z_1}} \right| + \left| {{z_2}} \right|$ , then arg ${z_1}$ - arg ${z_2}$ is equal to :

Let $f:( - 1,1) \to B$ , be a function defined by $f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$ , then $f$ is both one-one and onto when B is the interval

Let $f:R \to R$ be a differentiable function having $f\left( 2 \right) = 6$ , $f'\left( 2 \right) = \left( {{1 \over {48}}} \right)$ . Then $\mathop {\lim }\limits_{x \to 2} \int\limits_6^{f\left( x \right)} {{{4{t^3}} \over {x - 2}}dt}$ equals :

A lizard, at an initial distance of 21 cm behind an insect moves from rest with an acceleration of $2 \mathrm{~cm} / \mathrm{s}^2$ and pursues the insect which is crawling uniformly along a straight line at a speed of $20 \mathrm{~cm} / \mathrm{s}$ . Then the lizard will catch the insect after :

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

Let $\alpha$ and $\beta$ be the distinct roots of $a{x^2} + bx + c = 0$ , then $\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}$ is equal to

The value of $\int\limits_{ - \pi }^\pi {{{{{\cos }^2}} \over {1 + {a^x}}}dx,\,\,a > 0,}$ is

If α is the degree of dissociation of Na 2 SO 4 , the vant Hoff’s factor (i) used for calculating the molecular mass is :

Acid catalyzed hydration of alkenes except ethene leads to the formation of

Tertiary alkyl halides are practically inert to substitution by S N 2 mechanism because of

t 1/4 can be taken as the time taken for the concentration of a reactant to drop to 3 4 of its initial value. If the rate constant for a first order reaction is K, the t 1/4 can be written as

In both DNA and RNA, heterocyclic base and phosphate ester linkages are at-