IIT-JEE 2010 Paper 1 Offline

In the reaction

the products are :

In the reaction

The intermediate(s) is(are)

In the scheme given below, the total number of intra molecular aldol condensation products formed from Y is ____________.

Amongst the following, the total number of compounds soluble in aqueous NaOH is _________.

In the Newman projection for 2,2-dimethylbutane, X and Y can, respectively, be

The total number of cyclic isomers possible for a hydrocarbon with the molecular formula C4H6 is

The correct statement about the following disaccharide is :

The total number of basic groups in the following form of lysine is

Based on VSEPR theory, the number of 90 degree F-Br-F angles in BrF5 is

Plots showing the variation of the rate constant (\(k\)) with temperature (\(T\)) are given below. The point that follows Arrhenius equation is

The concentration of R in the reaction R \(\to\) P was measured as a function of time and the following data is obtained


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The number of neutrons emitted when \({}_{92}^{235}U\) undergoes controlled nuclear fission to \({}_{54}^{142}Xe\) and \({}_{38}^{90}Sr\) is

The correct structure of ethylenediaminetetraacetic acid (EDTA) is

The ionisation isomer of \(\mathrm{[Cr(H_2O)_4Cl(NO_2)]Cl}\) is

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of
nerve impulses and m...

The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of
nerve impulses and m...

The synthesis of 3-octyne is achieved by adding a bromoalkane into a mixture of sodium amide and and alkyne

The reagent(s) used for softening the temporary hardness of water is (are)

Aqueous solution of HNO3, KOH and CH3COOH and CH3COONa of identical concentrations are provided. The pairs of solutions which form a buffer upon mixing is(are)

Amongst the following the total number of compounds whose aqueous solution turns red litmus paper blue is
KCN, K2SO4, (NH4)2C2O4, NaCl, Zn(NO3)2, FeCl3, K2CO3, NH4NO3 and LiCN

Partial roasting of chalcopyrite produces

Iron is removed from chalcopyrite as

In self-reduction, the reducing species is

The value of \(n\) in the molecular formula \(\mathrm{Be_n Al_2Si_6O_{18}}\) is ___________.

A student performs a titration with different burettes and finds titre values of 25.2 mL, 25.25 mL, and 25.0 mL. The number of significant figures in the average titre value is

The bond energy (in kcal mol-1) of a C-C single bond is approximately

Among the following, the intensive property is (properties are)

The species which by definition has ZERO standard molar enthalpy of formation at 298 K is

If the distance between the plane \(Ax-2y+z=d\) and the plane containing the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\,\) is \(\sqrt 6 \,\,,\) then...

Equation of the plane containing the straight line \({x \over 2} = {y \over 3} = {z \over 4}\) and perpendicular to the plane containing the straight lines \({x \over 3} = {y \over 4} = {z \over 2}\) and $${x \over 4} = {y \over 2} = {z \ov...

Let \(f\) be a real-valued differentiable function on \(R\) (the set of all real numbers) such that \(f(1)=1\). If the \(y\)-intercept of the tangent at any point \(P(x,y)\) on the curve \(y=f(x)\) is equal to the cube of the abscissa of $$...

Let \(f\) be a real-valued function defined on the interval \(\left( {0,\infty } \right)\)
by \(\,f\left( x \right) = \ln x + \int\limits_0^x {\sqrt {1 + \sin t\,} dt.}\) then which of the following
statement(s) is (are) true?

Let \({{z_1}}\) and \({{z_2}}\) be two distinct complex number and let z =( 1 - t)\({{z_1}}\) + t\({{z_2}}\) for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then

Let $z_1$ and $z_2$ be two distinct complex numbers let $z=(1-t) z_1+t z_2$ for some real number t with $0 < t < 1$.
If $\operatorname{Arg}(w)$ denotes the principal argument of a nonzero complex number $w$, then :

For any real number \(x,\) let \(\left[ x \right]\) denote the largest integer less than or equal to \(x.\) Let \(f\) be a real valued function defined on the interval \(\left[ { - 10,10} \right]\) by
$$$f\left( x \right) = \left\{ {\matrix...

The value of \(\int\limits_0^1 {{{{x^4}{{\left( {1 - x} \right)}^4}} \over {1 + {x^2}}}dx}\) is (are)

The value of \(\mathop {\lim }\limits_{x \to 0} {1 \over {{x^3}}}\int\limits_0^x {{{t\ln \left( {1 + t} \right)} \over {{t^4} + 4}}} dt\) is

Let $f, g$ and $h$ be real valued functions defined on the interval $[0,1]$ by
$f(x)=e^{x^2}+e^{-x^2}$,
$g(x)=x e^{x^2}+e^{-x^2}$
and $h(x)=x^2 e^{x^2}+e^{-x^2}$.
If $a, b$ and $c$ denote, respectively, the absolute maximum of $f, g$ an...

The circle \({x^2} + {y^2} - 8x = 0\) and hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) intersect at the points \(A\) and \(B\).
Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

The line \(2x + y = 1\) is tangent to the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). If this line passes through the point of intersection of the nearest directrix and the \(x\)-axis, then the eccentricity of the h...

The circle \({x^2} + {y^2} - 8x = 0\) and hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) intersect at the points \(A\) and \(B\).
Equation of the circle with \(AB\) as its diameter is

The number of $3 \times 3$ matrices A whose entries are either 0 or 1 and for which the system $\mathrm{A}\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solu...

The number of $A$ in $T_p$ such that $A$ is either symmetric or skew-symmetric or both, and $\operatorname{det}(\mathrm{A}) \operatorname{divisible}$ by $p$ is :

The number of A in $\mathrm{T}_p$ such that the trace of A is not divisible by $p$ but $\operatorname{det}(\mathrm{A})$ is divisible by $p$ is
[Note : The trace of a matrix is the sum of its diagonal entries.]

The number of A in $\mathrm{T}_p$ such that $\operatorname{det}(\mathrm{A})$ is not divisible by $p$ is :

Let \(A\) and \(B\) be two distinct points on the parabola \({y^2} = 4x\). If the axis of the parabola touches a circle of radius \(r\) having \(AB\) as its diameter, then the slope of the line joining \(A\) and \(B\) can be

Let \(\omega\) be a complex cube root of unity with \(\omega \ne 1.\) A fair die is thrown three times. If \({r_1},\) \({r_2}\) and \({r_3}\) are the numbers obtained on the die, then the probability that $${\omega ^{{r_1}}} + {\omega ^{{...

If the angles \(A, B\) and \(C\) of a triangle are in an arithmetic progression and if \(a, b\) and \(c\) denote the lengths of the sides opposite to \(A, B\) and \(C\) respectively, then the value of the expression $${a \over c}\sin 2C + ...

Let \(ABC\) be a triangle such that \(\angle ACB = {\pi \over 6}\) and let \(a, b\) and \(c\) denote the lengths of the sides opposite to \(A\), \(B\) and \(C\) respectively. The value(s) of \(x\) for which $$a = {x^2} + x + 1,\,\,\,b = {x...

Let \(p\) and \(q\) be real numbers such that \(p \ne 0,\,{p^3} \ne q\) and \({p^3} \ne - q.\) If \({p^3} \ne - q.\) and \(\,\beta\) are nonzero complex numbers satisfying \(\alpha \, + \beta = - p\,\) and $${\alpha ^3} + {\beta ^3} =...