JEE Main 2009 Question Paper with Solutions

Arrange the carbanions, ( C H 3 ) 3 C ― , C ― C l 3 , ( C H 3 ) 2 C ― H , C 6 H 5 C ― H 2 in order of their decreasing stability :

In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is (h = 6.6 × 10 -34 kg m 2 s -1 , mass of electron, e m = 9.1 × 10 -31 kg)

The set representing the correct order of ionic radius is :

The number of stereoisomers possible for a compound of the molecular formula CH 3 - CH = CH - CH(OH) - Me is :

In which of the following arrangements, the sequence is not strictly according to the property written against it

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangement is :

If the mean deviation of number 1, 1 + d, 1 + 2d,........, 1 + 100d from their mean is 255, then the d is equal to

Statement - 1 : The variance of first n even natural numbers is ${{{n^2} - 1} \over 4}$ Statement - 2 : The sum of first n natural numbers is ${{n\left( {n + 1} \right)} \over 2}$ and the sum of squares of first n natural numbers is ${{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 6}$

Let A and B denote the statements A : cos ⁡ α + cos ⁡ β + cos ⁡ γ = 0 B : sin ⁡ α + sin ⁡ β + sin ⁡ γ = 0 If cos ⁡ ( β − γ ) + cos ⁡ ( γ − α ) + cos ⁡ ( α − β ) = − 3 2 , then:

The lines p ( p 2 + 1 ) x − y + q = 0 and ( p 2 + 1 ) 2 x + ( p 2 + 1 ) y + 2 q = 0 are perpendicular to a common line for :

The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are :

Given $P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d$ such that $x=0$ is the only real root of $P'\,\left( x \right) = 0.$ If $P\left( { - 1} \right) < P\left( 1 \right),$ then in the interval $\left[ { - 1,1} \right]:$

$\int\limits_0^\pi {\left[ {\cot x} \right]dx,}$ where $\left[ . \right]$ denotes the greatest integer function, is equal to:

Let $y$ be an implicit function of $x$ defined by ${x^{2x}} - 2{x^x}\cot \,y - 1 = 0$ . Then $y'(1)$ equals

The area of the region bounded by the parabola ${\left( {y - 2} \right)^2} = x - 1,$ the tangent of the parabola at the point $(2, 3)$ and the $x$ -axis is :

A binary liquid solution is prepared by mixing n-heptane and ethanol. Which one of the following statements is correct regarding the behaviour of the solution ?

The two functional groups present in a typical carbohydrate are

Which of the following statements is incorrect regarding physisorptions ?

Which of the following pairs represents linkage isomers ?

The half life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2=0.301) :