IIT-JEE 1997

Paper was held on
Fri, Apr 11, 1997 9:00 AM

## Chemistry

For a d-electron the orbital angular momentum is

View Question The critical temperature of water is higher than that of O2 because the H2O molecule has

View Question Which contains both polar and non-polar bonds?

View Question Which one of the following compounds has sp2 hybridization?

View Question A compound of vanadium has a magnetic moment of 1.73 BM. Work out the electronic configuration of the vanadium ion in th

View Question Give reasons of the following:
The crystalline salts of alkaline earth metals contain more water of crystallisation than

View Question To a 25ml H2O2 solution, excess of acidified solution of potassium iodide was added. The iodine liberated required 20 ml

View Question Give reactions for the oxidation of hydrogen peroxide with potassium permanganate in acidic medium.

View Question Element A burns in nitrogen to give an ionic compound B. Compound B reacts with water to give C and D. A solution of C b

View Question Arrange the following sulphates of Alkaline earth metals in order of decreasing thermal stability : BeSO4, MgSO4, CaSO4,

View Question How many grams of silver could be plated out on a serving tray by electrolysis of a solution containing silver in +1 oxi

View Question Calculate the equilibrium constant for the reaction
Fe2+ + Ce4+ $$\leftrightharpoons$$ Fe3+ + Ce3+
(given $$E_{C{e^{4 +

View Question ## Mathematics

The real roots of the equation $$\,{\cos ^7}x + {\sin ^4}x = 1$$ in the interval $$\left( { - \pi ,\pi } \right)$$ are .

View Question Let $${z_1}$$ and $${z_2}$$ be roots of the equation $${z^2} + pz + q = 0\,$$ , where the coefficients p and q may be co

View Question Prove that the values of the function $${{\sin x\cos 3x} \over {\sin 3x\cos x}}$$ do not lie between $${1 \over 3}$$ and

View Question Prove that $$\sum\limits_{k = 1}^{n - 1} {\left( {n - k} \right)\,\cos \,{{2k\pi } \over n} = - {n \over 2},} $$ where

View Question Let $$S$$ be a square of unit area. Consider any quadrilateral which has one vertex on each side of $$S$$. If $$a,\,b,\,

View Question The sum of all the real roots of the equation $${\left| {x - 2} \right|^2} + \left| {x - 2} \right| - 2 = 0$$ is .......

View Question The sum of the rational terms in the expansion of $${\left( {\sqrt 2 + {3^{1/5}}} \right)^{10}}$$ is ...............

View Question Let $$0 < {A_i} < n$$ for $$i = 1,\,2....,\,n.$$ Use mathematical induction to prove that
$$$\sin {A_1} + \sin {A

View Question Let $$p$$ and $$q$$ be roots of the equation $${x^2} - 2x + A = 0$$ and let $$r$$ and $$s$$ be the roots of the equation

View Question For each natural number k, let $${C_k}$$ denote the circle with radius k centimetres and centre at the origin. On the ci

View Question The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to circle $${x^2} + {y^2} = 1

View Question Let C be any circle with centre $$\,\left( {0\, , \sqrt {2} } \right)$$. Prove that at the most two rational points can

View Question A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that the tangents at P and Q of t

View Question If $$f\left( x \right) = {x \over {\sin x}}$$ and $$g\left( x \right) = {x \over {\tan x}}$$, where $$0 < x \le 1$$,

View Question Let $$a+b=4$$, where $$a<2,$$ and let $$g(x)$$ be a differentiable function.
If $${{dg} \over {dx}} > 0$$ for all

View Question The value of $$\int_1^{{e^{37}}} {{{\pi \sin \left( {\pi In\,x} \right)} \over x}\,dx} $$ is ...............

View Question Let $${d \over {dx}}\,F\left( x \right) = {{{e^{\sin x}}} \over x},\,x > 0.$$ If $$\int_1^4 {{{2{e^{\sin {x^2}}}} \ov

View Question If $$g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,} $$ then $$g\left( {x + \pi } \right)$$ equals

View Question Determine the value of $$\int_\pi ^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} \,dx.$$

View Question Let $$f(x)= Maximum $$ $$\,\left\{ {{x^2},{{\left( {1 - x} \right)}^2},2x\left( {1 - x} \right)} \right\},$$ where $$0

View Question Let $$u(x)$$ and $$v(x)$$ satisfy the differential equation $${{du} \over {dx}} + p\left( x \right)u = f\left( x \right)

View Question If $$p$$ and $$q$$ are chosen randomly from the set $$\left\{ {1,2,3,4,5,6,7,8,9,10} \right\},$$ with replacement, deter

View Question Let $$OA=a,$$ $$OB=10a+2b$$ and $$OC=b$$ where $$O,A$$ and $$C$$ are non-collinear points. Let $$p$$ denote the area of

View Question If $$A,B$$ and $$C$$ are vectors such that $$\left| B \right| = \left| C \right|.$$ Prove that
$$\left[ {\left( {A + B}

View Question ## Physics

The equation of state for real gas is given by $$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$. Th

View Question