JEE Main 2010 Question Paper with Solutions

If the vectors a → = i ^ − j ^ + 2 k ^ , b → = 2 i ^ + 4 j ^ + k ^ and c → = λ i ^ + j ^ + μ k ^ are mutually orthogonal, then ( λ , μ ) is equal to :

Ionisation energy of He + is 19.6 x 10 –18 J atom –1 . The energy of the first stationary state (n = 1) of Li 2+ is

Three reactions involving $H_2PO_4^−$ are given below : (i) H 3 PO 4 + H 2 O $\to$ H 3 O + + $H_2PO_4^−$ (ii) $H_2PO_4^−$ + H 2 O $\to$ $HPO_4^{2−}$ + H 3 O + (iii) $H_2PO_4^−$ + OH - $\to$ H 3 PO 4 + O 2- In which of the above does $H_2PO_4^−$ act as an acid?

For a particular reversible reaction at temperature T, ∆H and ∆S were found to be both +ve. If T e is the temperature at equilibrium, the reaction would be spontaneous when :

If 10 –4 dm 3 of water is introduced into a 1.0 dm 3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established ? (Given : Vapour pressure of H 2 O at 300 K is 3170 Pa ; R = 8.314 J K –1 mol –1 )

Out of the following, the alkene that exhibits optical isomerism is

If two tangents drawn from a point $P$ to the parabola ${y^2} = 4x$ are at right angles, then the locus of $P$ is

Let cos ⁡ ( α + β ) = 4 5 and sin ( α − β ) = 5 13 , where 0 ≤ α , β ≤ π 4 . Then t a n 2 α =

Consider the following relations $R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$ ; $S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.$ and $q$ are integers such that $n, q \neq 0$ and $q m=p m\}$ . Then

A person is to count 4500 currency notes. Let a n denote the number of notes he counts in the n t h minute. If a 1 = a 2 = ....= a 10 = 150 and a 10 , a 11 ,.... are in an AP with common difference - 2, then the time taken by him to count all notes is

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

The area bounded by the curves y = cos ⁡ x and y = sin ⁡ x between the ordinates x = 0 and x = 3 π 2 is

A line $AB$ in three-dimensional space makes angles ${45^ \circ }$ and ${120^ \circ }$ with the positive $x$ -axis and the positive $y$ -axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $z$ -axis, then $\theta$ equals :

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :

Let f : R → R be defined by $ f ( x ) = { k − 2 x , i f x ≤ − 1 2 x + 3 , i f x > − 1 $ If f has a local minimum at x = − 1 , then a possible value of k is

Let $f:R \to R$ be a positive increasing function with $\mathop {\lim }\limits_{x \to \infty } {{f(3x)} \over {f(x)}} = 1$ . Then $\mathop {\lim }\limits_{x \to \infty } {{f(2x)} \over {f(x)}} =$

The correct order of E M 2 + / M o values with negative sign for the four successive elements Cr, Mn, Fe and Co is :

If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water (∆T f ), when 0.01 mol of sodium sulphate is dissolved in 1 kg of water, is (K f = 1.86 K kg mol –1 )

Biuret test is not given by

A solution containing 2.675g of CoCl 3 . 6NH 3 (molar mass = 267.5 g mol –1 ) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO 3 to give 4.78 g of AgCl (molar mass = 143.5 g mol –1 ). The formula of the complex is : (At. Mass of Ag = 108 u)

One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is