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## IIT-JEE 1999

Exam Held on Sun Apr 11 1999 09:00:00 GMT+0000 (Coordinated Universal Time)
Click View All Questions to see questions one by one or you can choose a single question from below.

## Chemistry

The normality of 0.3 M phosphorus acid (H<sub>3</sub>PO<sub>3</sub>) is
The oxidation number of sulphur in S<sub>8</sub>,S<sub>2</sub>F<sub>2</sub>,H<su...
How many millilitres of 0.5 M H<sub>2</sub>SO<sub>4</sub> are needed to dissolve...
A plant virus is found to consist of uniform cylindrical particles of 150 Å in d...
The electrons, identified by quantum numbers n and l, (i) n = 4, l = 1, (ii) n =...
Ground state electronic configuration of nitrogen atom can be represented by
The correct order of increasing C - O bond length of CO, $$CO_3^{2-}$$, CO<sub>2...
The geometry of H<sub>2</sub>S and its dipole moment are
One mole of nitrogen gas at 0.8 atm takes 38 s to diffuse through a pinhole. whe...
When 3.06 g of solid NH<sub>4</sub>HS is introduced into a two litre evacuated f...
Give reasons of the following:<br> BeCl<sub>2</sub> can be easily hydrolysed.
Nitrobenzene is formed as the major product along with a minor product in the re...
A cell, Ag | Ag<sup>+</sup> || Cu<sup>2+</sup> | Cu, initially contains 1 M Ag<s...
The rate constant for an isomerisation reaction, A $$\to$$ B is 4.5 $$\times$$ 1...

## Mathematics

In a triangle $$PQR,\angle R = \pi /2$$. If $$\,\,\tan \left( {P/2} \right)$$ a...
$$If\,i = \sqrt { - 1} ,\,\,then\,\,4 + 5{\left( { - {1 \over 2} + {{i\sqrt 3 } ... For a positive integer$$\,n$$, let <br>$${f_n}\left( \theta \right) = \left...
For complex numbers z and w, prove that $${\left| z \right|^2}w - {\left| w \rig... If the roots of the equation$${x^2} - 2ax + {a^2} + a - 3 = 0$$are real and le... If in the expansion of$${\left( {1 + x} \right)^m}{\left( {1 - x} \right)^n},$$... Let$$n$$be any positive integer. Prove that$$\$\sum\limits_{k = 0}^m {{{\left...
The harmonic mean of the roots of the equation $$\left( {5 + \sqrt 2 } \right){x... Let$${a_1},{a_2},......{a_{10}}$$be in$$A,\,P,$$and$${h_1},{h_2},......{h_{...
Let a, b, c, d be real numbers in G.P. If u, v, w, satisfy the system of equatio...
For a positive integer $$n$$, let <br>$$a\left( n \right) = 1 + {1 \over 2} + {... Lt$$PQR$$be a right angled isosceles triangle, right angled at$$P(2, 1)$$. If... If$${x_1},\,{x_2},\,{x_3}$$as well as$${y_1},\,{y_2},\,{y_3}$$, are in G.P. w... Let$${L_1}$$be a straight line passing through the origin and$${L_2}$$be the... If two distinct chords, drawn from the point (p, q) on the circle$${x^2}\, + \,...
Let $${T_1}$$, $${T_2}$$ be two tangents drawn from (- 2, 0) onto the circle $$C... Let$$P\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)$$and$$Q$$... The curve described parametrically by$$x = {t^2} + t + 1,y = {t^2} - t + 1...
If $$x$$ $$=$$ $$9$$ is the chord of contact of the hyperbola $${x^2} - {y^2} = ... On the ellipse$$4{x^2} + 9{y^2} = 1,$$the points at which the tangents are par... Consider the family of circles$${x^2} + {y^2} = {r^2},\,\,2 &lt; r &lt; 5$$. If... Find the co-ordinates of all the points$$P$$on the ellipse$${{{x^2}} \over {{...
Let $$ABC$$ be a triangle having $$O$$ and $$I$$ as its circumcenter and in cent...
The number of real solutions of <br>$${\tan ^{ - 1}}\,\,\sqrt {x\left( {x + 1} ... The function$$f(x)={\sin ^4}x + {\cos ^4}x$$increases if The function$$f\left( x \right) = \int\limits_{ - 1}^x {t\left( {{e^t} - 1} \ri...
Integrate $$\int {{{{x^3} + 3x + 2} \over {{{\left( {{x^2} + 1} \right)}^2}\left... If for a real number$$y$$,$$\left[ y \right]$$is the greatest integer less th...$$\int\limits_{\pi /4}^{3\pi /4} {{{dx} \over {1 + \cos x}}} $$is equal to For which of the following values of$$m$$, is the area of the region bounded by... Integrate$$\int\limits_0^\pi {{{{e^{\cos x}}} \over {{e^{\cos x}} + {e^{ - \co...
Let $$f(x)$$ be a continuous function given by $$f\left( x \right) = \left\{ {... A solution of the differential equation <br>$${\left( {{{dy} \over {dx}}} \righ...
The differential equation representing the family of curves <br>$${y^2} = 2c\le... If the integers$$m$$and$$n$$are chosen at random from$$1$$to$$100$$, then... The probabilities that a student passes in Mathematics, Physics and Chemistry ar... Eight players$${P_1},{P_2},.....{P_8}$$play a knock-out tournament. It is know... Let$$a=2i+j-2k$$and$$b=i+j.$$If$$c$$is a vector such that$$a.c = \l...
Let $$a=2i+j+k, b=i+2j-k$$ and a unit vector $$c$$ be coplanar. If $$c$$ is per...
Let $$a$$ and $$b$$ two non-collinear unit vectors. If $$u = a - \left( {a\,.\,b... Let$$u$$and$$v$$be units vectors. If$$w$$is a vector such that$$w + \left...

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