IIT-JEE 2004

Draw the structure of XeF4 and OSF4 according to VSEPR theory clearly indicating the state of hybridisation of the central atom and lone pair of electrons (if any) on the central atom.

Arrange the following :
In the decreasing order of the O - O bond length present in them
O2, KO2 and O2[AsF4]

For the given reactions, A + B \(\to\) Products, following data were obtained


.tg {border-collapse:collapse;border-spacing:0;margin: 0 auto}
.tg td{font-family:Arial, sans-serif;font-size:14px;padding:10px 5px;border-style:solid;border-w...

Find the equilibrium constant for the reaction,
In2+ + Cu2+ \(\to\) In3+ + Cu+ at 298 K given
\(E_{C{u^{2 + }}/C{u^ + }}^o\) = 0.15 V; \(E_{l{n^{2 + }}/l{n^ + }}^o\) = -0.40 V; \(E_{l{n^{3 + }}/l{n^ + }}^o\) = -0.42 V;

A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest A - B distance is Y1/3 nm, where Y is an arbitrary number
(a) Find the density of the lattice
(b) If the density of lattice is found to be ...

1.22 g of benzoic acid is dissolved in 100 g of acetone and 100 g of benzene separately. Boiling point of the solution in acetone increases by 0.17 oC, while that in the benzene increases by 0.13oC; Kb for acetone and benzene is 1.7 K kg m...

(a) The Schrodinger wave equation for hydrogen atom is
\($\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}} \right)^{3/2}}\left( {2 - {{{r_0}} \over {{a_0}}}} \right){e^{ - {r_0}/{a_0}}}\)$
Where a0 is Bohr's radius. If the rad...

A ball of mass 100 g is moving with 100 ms-1. Find it's wavelength.

\({P_1}\) and \({P_2}\) are planes passing through origin. \({L_1}\) and \({L_2}\) are two line on \({P_1}\) and \({P_2}\) respectively such that their intersection is origin. Show that there exists points \(A, B, C,\) whose permutation $$A...

A parallelopiped \('S'\) has base points \(A, B, C\) and \(D\) and upper face points \(A',\) \(B',\) \(C'\) and \(D'.\) This parallelopiped is compressed by upper face \(A'B'C'D'\) to form a new parallelopiped \('T'\) having upper face poin...

Find the equation of plane passing through \((1, 1, 1)\) & parallel to the lines \({L_1},{L_2}\) having direction ratios \((1,0,-1),(1,-1,0).\) Find the volume of tetrahedron formed by origin and the points where these planes intersect the ...

Using Rolle's theorem, prove that there is at least one root
in \(\left( {{{45}^{1/100}},46} \right)\) of the polynomial
\(P\left( x \right) = 51{x^{101}} - 2323{\left( x \right)^{100}} - 45x + 1035\).

Prove that for \(x \in \left[ {0,{\pi \over 2}} \right],\) \(\sin x + 2x \ge {{3x\left( {x + 1} \right)} \over \pi }\). Explain
the identity if any used in the proof.

Find the equation of circle touching the line 2x + 3y + 1 = 0 at (1, -1) and cutting orthogonally the circle having line segment joining (0, 3) and (- 2, -1) as diameter.

Find the centre and radius of circle given by \(\,\left| {{{z - \alpha } \over {z - \beta }}} \right| = k,k \ne 1\,\)
where, $${\rm{z = x + iy, }}\alpha {\rm{ = }}\,{\alpha _1}{\rm{ + i}}{\alpha _2}{\rm{,}}\,\beta = {\beta _1}{\rm{ ...

Find the value of \(\int\limits_{ - \pi /3}^{\pi /3} {{{\pi + 4{x^3}} \over {2 - \cos \left( {\left| x \right| + {\pi \over 3}} \right)}}dx}\)

If \(y\left( x \right) = \int\limits_{{x^2}/16}^{{x^2}} {{{\cos x\cos \sqrt \theta } \over {1 + {{\sin }^2}\sqrt \theta }}d\theta ,}\) then find \({{dy} \over {dx}}\) at \(x = \pi\)

A curve \('C''\) passes through \((2,0)\) and the slope at \((x,y|)\) as \(\,{{{{\left( {x + 1} \right)}^2} + \left( {y - 3} \right)} \over {x + 3}}\). Find the equation of the curve. Find the area bounded by curve and \(x\)-axis in fourth ...

Tangent is drawn to parabola \({y^2} - 2y - 4x + 5 = 0\) at a point \(P\) which cuts the directrix at the point \(Q\). \(A\) point \(R\) is such that it divides \(QP\) externally in the ratio \(1/2:1\). Find the locus of point \(R\)

Prove by permulation or otherwise \({{({n^2})!} \over {{{(n!)}^n}}}\) is an integer \((n \in {1^ + })\).

A box contains \(12\) red and \(6\) white balls. Balls are drawn from the box one at a time without replacement. If in \(6\) draws there are at least \(4\) white balls, find the probability that exactly one white is drawn in the next two dr...

\(A\) and \(B\) are two independent events. \(C\) is even in which exactly one of \(A\) or \(B\) occurs. Prove that \(P\left( C \right) \ge P\left( {A \cup B} \right)P\left( {\overline A \cap \overline B } \right)\)

If \(a,\,b,c\) are positive real numbers. Then prove that
\(${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left( {c + 1} \right)^7} > {7^7}\,{a^4}{b^4}{c^4}\)$

If \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) and \(\overrightarrow d\) are distinct vectors such that
\(\,\overrightarrow a \times \overrightarrow c = \overrightarrow b \times \overrightarrow d\) and $$\overrightarr...

In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.05 cm ( measured by a scale of least count 0.001 cm ) and length is L = 110 cm ( measured by a scale of least count 0.1 ...

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length 5.6 cm. The main scale reading is 1mm and 47th circular division coincides
with the main scale. Find the curved surface ...