IIT-JEE 2007 Paper 2 Offline

Which one of the following reagents is used in the above reaction?

The electrophile in this reaction is :

The structure of the intermediate I is

Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is :

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

.tg {border-collapse:collapse;border-spacing:0;}
....

The number of stereoisomers obtained by bromination of \(trans\)-2-butene is :

Among the following the least stable resonance structure is :

Statement-1 : Glucose gives a reddish-brown precipitate with Fehling's solution.
Statement-2 : Reaction of glucose with Fehling's solution gives \(\mathrm{CuO}\) and gluconic acid.

Consider a reaction aG + bH \(\to\) Products. When concentration of both the reactants G and H is doubled, the rate
increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is
doub...

Among the following metal carbonyl, the C-O bond order is lowest in

Among the following, identify the correct statement.

While \(\mathrm{Fe}^{3+}\) is stable, \(\mathrm{Mn}^{3+}\) is not stable in acid solution because

Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of

Statement-1 : Molecules that are not superimposable on their mirror images are chiral.
Statement-2 : All chiral molecules have chiral centres.

STATEMENT-1 : Band gap in germanium is small.
STATEMENT-2 : The energy gap of each germanium atomic energy level is infinitesimally small.

Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

.tg {border-collapse:collapse;border-...

Statement-1 : Alkali metals dissolves in liquid ammonia to give blue solutions
Statement-2 : Alkali metals in liquid ammonia give solvated species of the type \(\left[\mathrm{M}\left(\mathrm{NH}_{3}\right)_{n}\right]^{+} (\mathrm{M}=\) alka...

A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion
treatment with a solution of cobalt (II) thiocyanate gives rise to a de...

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 \(\times\) 4 matrix given in the ORS.

.tg {border-coll...

Consider a titration of potassium dichromate solution with acidified Mohr’s salt solution using diphenylamine as indicator. The number of moles of Mohr’s salt required per mole of dichromate is

A positron is emitted from \(_{11}^{23}\)Na The ratio of the atomic mass and atomic number of the resulting nuclide is :

For the process \(\mathrm{H_2O}(l)\) (1 bar, 373 K) \(\to\) \(\mathrm{H_2O}(g)\) (1 bar, 373 K), the correct set of thermodynamic parameters is:

Consider the planes \(3 x-6 y-2 z=15\) and \(2 x+y-2 z=5\).
STATEMENT - 1 : The parametric equations of the line of intersection of the given planes are \(x=3+14 t, y=1+2 t, z=15 t\)
STATEMENT - 2 : The vectors $$14 \hat{i}+2 \hat{j}+15 \ha...

Let \(\mathrm{ABCD}\) be a quadrilateral with area 18 , with side \(\mathrm{A B}\) parallel to the side \(\mathrm{C D}\) and \(\mathrm{A B}=2 \mathrm{CD}\). Let \(\mathrm{AD}\) be perpendicular to \(\mathrm{AB}\) and \(\mathrm{CD}\). If a c...

Match the statements in Column I with the properties Column II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden...

If \(|z|=1\) and \(z \neq \pm 1\), then all the values of \(\frac{z}{1-z^{2}}\) lie on

The differential equation \(\frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{y}\) determines a family of circles with :

\(\frac{d^{2} x}{d y^{2}}\) equals :

Let \(f(x)=\frac{x}{\left(1+x^{n}\right)^{1 / n}}\) for \(n \geq 2\) and \(g(x)=\underbrace{(f o f o \ldots . o f)}_{f \text { occurs } n \text { times }}(x)\). Then \(\int x^{n-2} g(x) d x\) equals :

Let \((x,y)\) be such that \({\sin ^{ - 1}}(ax) + {\cos ^{ - 1}}(y) + {\cos ^{ - 1}}(bxy) = {\pi \over 2}\).
Match the statements in Column I with the statements in Column II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{borde...

Let \(f(x)=2+\cos x\) for all real \(x\).
STATEMENT - 1 : For each real \(t\), there exists a point \(c\) in \([t, t+\pi]\) such that \(f^{\prime}(C)=0\).
STATEMENT - 2 : \(f(t)=f(t+2 \pi)\) for each real \(t\).

The line \(y=x\) meets \(y=k e^{\mathrm{x}}\) for \(k \leq 0\) at

The positive value of \(k\) for which \(k e^{x}-x=0\) has only one root is

For \(k > 0\), the set of all values of \(k\) for which \(k e^{x}-x=0\) has two distinct roots is

Let \(f(x) = {{{x^2} - 6x + 5} \over {{x^2} - 5x + 6}}\).
Match the conditions/expressions in Column I with statements in Column II.

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-widt...

STATEMENT - 1 : The curve \(y=\frac{-x^{2}}{2}+x+1\) is symmetric with respect to the line \(x=1\).
STATEMENT - 2 : A parabola is symmetric about its axis.

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is :

Let \({E^c}\) denote the complement of an event \(E.\) Let \(E, F, G\) be pairwise independent events with \(P\left( G \right) > 0\) and \(P\left( {E \cap F \cap G} \right) = 0.\) Then \(P\left( {{E^c} \cap {F^c}|G} \right)\) equals

Which one of the following statements is correct?

Which one of the following statements is correct?

Which one of the following statements is correct?

Let \(\mathrm{O(0,0), P(3,4), Q(6,0)}\) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

Lines \(\mathrm{L}_{1}: y-x=0\) and \(\mathrm{L}_{2}: 2 x+y=0\) intersect the line \(\mathrm{L}_{3}: y+2=0\) at \(\mathrm{P}\) and \(\mathrm{Q}\), respectively. The bisector of the acute angle between \(L_{1}\) and \(L_{2}\) intersects $$L_...

Let \(\vec{a}, \vec{b}, \vec{c}\) be unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\). Which one of the following is correct?

STATEMENT 1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the co...

Electrons with de-Broglie wavelength \(\lambda\) fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Positive and negative point charges of equal magnitude are kept at \(\left(0,0, \frac{a}{2}\right)\) and \(\left(0,0, \frac{-a}{2}\right)\), respectively. The work done by the electric field when another positive point charge is moved from ...

Light travels as a

The phases of the light wave at \(c, d, e\) and \(f\) are \(\phi_c, \phi_d, \phi_{e}\) and \(\phi_{f}\) respectively.
It is given that \(\phi_{c} \neq \phi_{f}\).