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## IIT-JEE 1992

Exam Held on Sat Apr 11 1992 09:00:00 GMT+0000 (Coordinated Universal Time)
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For the redox reaction:<br> $$MnO_4^ - + {C_2}O_4^{ - 2} + {H^ + }$$ $$\to M{n... A 2.0 g sample of a mixture containing sodium carbonate, sodium bicarbonate and ... One gram of commercial AgNO<sub>3</sub> is dissolved in 50 ml. of water. It is t... Which of the following relates to photons both as wave motion and as a stream of... Which of the following does not characterise X-rays? The statement that is not correct for the periodic classification of element is The maximum number of hydrogen bonds a water molecule can form is The cyanide ion, CN<sup>-</sup> and N<sub>2</sub> are isoelectronic, But in cont... The type of hybrid orbitals used by the chlorine atom in$$ClO_2^-$$is Which of the following have identical bond order? The molecules that will have dipole moment are At 27<sup>o</sup>C, hydrogen is leaked through a tiny hole into a vessel for 20 ... At room temperature the following reacton is procedd nearly to completion:<br><b... The species that do not contain peroxide ions are Give reasons of the following:<br> Hydrogen peroxide acts as an oxidising as wel... For the galvanic cell<br> Ag | AgCl(s), KCl (0.2M) || KBr (0.001M), AgBr(s) | Ag... An aqueous solution of NaCl on electrolysis gives H<sub>2</sub>(g), Cl<sub>2</su... ## Mathematics In this questions there are entries in columns 1 and 2. Each entry in column 1 i...$${\rm{z }} \ne {\rm{0}}$$is a complex number <p> <b> Column I </b></p><b> </b>... Show that the value of$${{\tan x} \over {\tan 3x}},$$wherever defined never li... Let$$\alpha \,,\,\beta $$be the roots of the equation (x - a) (x - b) = c,$$c...
The expansion $${\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \righ... If$$\sum\limits_{r = 0}^{2n} {{a_r}{{\left( {x - 2} \right)}^r}\,\, = \sum\limi...
Let $$p \ge 3$$ be an integer and $$\alpha$$, $$\beta$$ be the roots of $${x^2... Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 ... If the sum of the distances of a point from two perpendicular lines in a plane i... Determine all values of$$\alpha $$for which the point$$\left( {\alpha ,\,{\al...
The centre of a circle passing through the points (0, 0), (1, 0) and touching th...
Let a circle be given by 2x (x - a) + y (2y - b) = 0, $$(a\, \ne \,0,\,\,b\, \ne... Three circles touch the one another externally. The tangent at their point of co... A cubic$$f(x)$$vanishes at$$x=2$$and has relative minimum / maximum at$$x=-...
What normal to the curve $$y = {x^2}$$ forms the shortest chord?
In this questions there are entries in columns $$I$$ and $$II$$. Each entry in c...
Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 ... Sketch the region bounded by the curves$$y = {x^2}$$and <br>$$y = {2 \over {1...
Determine a positive integer $$n \le 5,$$ such that $$\int\limits_0^1 {{e^x}{{... Three faces of a fair die are yellow, two faces red and one blue. The die is to... India plays two matches each with West Indies and Australia. In any match the pr... A lot contains$$50$$defective and$$50$$non defective bulbs. Two bulbs are dr... A unit vector coplanar with$$\overrightarrow i + \overrightarrow j + 2\overri...

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