IIT-JEE 2007 Paper 1 Offline

Statement 1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.
Statement 2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

The number of structural isomers for C\(_6\)H\(_{14}\) is :

The species having bond order different from that in CO is :

Among the following the paramagnetic compound is:

Statement 1 : Boron always forms covalent bond.
Statement 2 : The small size of B\(^{3+}\) favours formation of covalent bond.

Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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The total number of moles of chlorine gas evolved is :

If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is:

The total charge (coulombs) required for complete electrolysis is:

Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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In the following reaction,

The structure of the major 'X' is

The reagent(s) for the following conversion,

Extraction of zinc from zinc blende is achieved by

The percentage of p-character in the orbitals forming P-P bonds in P\(_4\) is

Statement 1 : In water, orthoboric acid behaves as a weak monobasic acid.

Statement 2 : In water, orthoboric acid acts as a proton donor.

Argon is used in arc welding because of its

The structure of XeO\(_3\)

XeF\(_4\) and XeF\(_6\) are expected to be

Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

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When 20 g of naphthoic acid (C\(_{11}\)H\(_{8}\)O\(_{2}\)) is dissolved in 50 g of benzene in 50 g of benzene (K\(_f\) = 1.72 K kg mol\(^{-1}\)), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is :

Statement 1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).

Statement 2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

The value of log\(_{10}\) K for a reaction $A \rightleftharpoons B$ is
(Given : \({\Delta _r}H{^\circ _{298\,K}} = - 54.07\) kJ mol\(^{-1}\), \({\Delta _r}S{^\circ _{298\,K}} = 10\) J K\(^{-1}\) mol\(^{-1}\) and R = 8.314 J K\(^{-1}\) mol$...

Let \(f(x)\) be differentiable on the interval (0, \(\infty\)) such that \(f(1)=1\), and \(\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1\) for each \(x > 0\). Then \(f(x)\) is

Tangents are drawn from the point (17, 7) to the circle \(x^2+y^2=169\).
Statement 1 : The tangents are mutually perpendicular.
Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circl...

A man walks a distance of 3 units from the origin towards the north-east (N 45\(^\circ\)E) direction. From there, he walks a distance of 4 units towards the north-west (N 45\(^\circ\)W) direction to reach a point P. Then the position of P i...

\(\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\int\limits_2^{{{\sec }^2}x} {f(t)\,dt} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}\) equal

Match the integrals in Column I with the values in Column II.

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A hyperbola, having the transverse axis of the length \(2\sin \theta\), is confocal with the ellipse \(3{x^2} + 4{y^2} = 12\). Then its equation is

Let F(x) be an indefinite integral of \(\sin^2x\).
Statement 1 : The function F(x) satisfies F(\(x+\pi\)) = F(\(x\)) for all real x.
Statement 2 : \({\sin ^2}(x + \pi ) = {\sin ^2}x\) for all real x.

In the following [x] denotes the greatest integer less than or equal to x.
Match the functions in Column I with the properties Column II.

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The tangent to the curve \(y=e^x\) drawn at the point (\(c,e^c\)) intersects the line joining the points (\(c-1,e^{c-1}\)) and (\(c+1,e^{c+1}\))

The ratio of the areas of the triangles PQS and PQR is

The radius of the circumcircle of the triangle PRS is

The radius of the incircle of the triangle PQR is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his w...

Let H\(_1\), H\(_2\), ..., H\(_n\) be mutually exclusive and exhaustive events with P(H\(_i\)) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1.
Statement 1 : P(H\(_i\) | E) > P(E | H\(_i\)). P(H\(_i\)) for \(i=1,2,...,n\)....

Let \(\alpha,\beta\) be the roots of the equation \(x^2-px+r=0\) and \(\frac{\alpha}{2},2\beta\) be the roots of the equation \(x^2-qx+r=0\). Then the value of r is

The sum V\(_1\) + V\(_2\) + ... + V\(_n\) is

T\(_r\) is always

Which one of the following is a correct statement?

Consider the following linear equations
\(ax + by + cz = 0\)
\(bx + cy + az = 0\)
\(cx + ay + bz = 0\)
Match the conditions/expressions in Column I with statements in Column II.

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The number of solutions of the pair of equations
\(2{\sin ^2}\theta - \cos 2\theta = 0\)
\(2{\cos ^2}\theta - 3\sin \theta = 0\)
in the interval \([0,2\pi]\) is

The number of distinct real values of \(\lambda\), for which the vectors \(- {\lambda ^2}\widehat i + \widehat j + \widehat k,\widehat i - {\lambda ^2}\widehat j + \widehat k\) and \(\widehat i + \widehat j - {\lambda ^2}\widehat k\) are c...

Let the vector \(\overrightarrow {PQ} ,\overrightarrow {QR} ,\overrightarrow {RS} ,\overrightarrow {ST} ,\overrightarrow {TU}\) and \(\overrightarrow {UP}\), represent the sides of a regular hexagon.
Statement 1 : $$\overrightarrow {PQ} ...

In the option given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening ...

A resistance of 2 \(\Omega\) is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 \(\Omega\), is connected across the other gap. When these resistance are interchanged, t...

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 \(\times\) 4 matrix given in the ORS.

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