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## IIT-JEE 1998

Exam Held on Sat Apr 11 1998 09:00:00 GMT+0000 (Coordinated Universal Time)
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## Chemistry

An aqueous solution containing 0.10 g KIO<sub>3</sub> (formula weight = 214.0) w...
The orbital diagram in which the Aufbau principle is violated is
Decrease in atomic number is observed during
Which of the following statement(s) is (are) correct?
The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The pos...
<b>ASSERTION:</b><br> Nuclide $${}_{13}^{30}Al$$ is less stable than $${}_{20}^{... The geometry and the type of hybrid orbital present about the central atom in BF... Interpret the non-linear shape of H<sub>2</sub>S molecule and non-planar shape o... Read the following Assertion and Reason and answer as per the options given belo... Highly pure dilute solution of sodium in liquid ammonia Work out the following using chemical equation :<br> Chlorination of calcium hyd... Hydrogen peroxide acts both as an oxidising and as a reducing agent in alkaline ... A solution of a nonvolatile solute in water freezes at -0.30<sup>o</sup>C. The v... Calculate the equilibrium constant for the reaction:<br> 2Fe<sup>3+</sup> + 3I<s... Find the solubility product of a saturated solution of Ag<sub>2</sub>CrO<sub>4</... The rate constant of a reaction is 1.5$$\times$$10<sup>7</sup> s<sup>-1</sup> ... ## Mathematics If$${\omega}$$is an imaginary cube root of unity, then$${(1\, + \omega \, - {...
If $$\,\left| {\matrix{ {6i} &amp; { - 3i} &amp; 1 \cr 4 &amp; {3i} &amp... The value of the sum$$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$,... Which of the following number(s) is /are rational? The number of values of$$x\,\,$$in the interval$$\left[ {0,\,5\pi } \right]$$... Prove that$$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha =...
Number of divisor of the form 4$$n$$$$+ 2\left( {n \ge 0} \right)$$ of the inte...
If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\l... An n-digit number is a positive number with exactly digits. Nine hundred distinc... Let$$p$$be a prime and$$m$$a positive integer. By mathematical induction on ... Let$$n$$be an odd integer. If$$\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{...
Let $${T_r}$$ be the $${r^{th}}$$ term of an A.P., for $$r=1, 2, 3, ....$$ If fo...
If $$x &gt; 1,y &gt; 1,z &gt; 1$$ are in G.P., then $${1 \over {1 + In\,x}},{1 \... The diagonals of a parralleogram$$PQRS$$are along the lines$$x + 3y = 4$$and... If$$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \righ...
If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of ...
Using co-ordinate geometry, prove that the three altitudes of any triangle are c...
The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^... If the circle$${x^2}\, + \,{y^2} = \,{a^2}$$intersects the hyperbola$$xy = {c...
$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twic...
The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches t...
If $$P=(x, y)$$, $${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right... The angle between a pair of tangents drawn from a point$$P$$to the parabola$$...
If$$\,\,\,$$ $$y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)... If in a triangle$$PQR$$,$$\sin P,\sin Q,\sin R$$are in$$A.P.,$$then Let$${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$be a regular hexagon inscribed in a circl... A bird flies in a circle on a horizontal plane. An observer stands at a point on... Prove that a triangle$$ABC$$is equilateral if and only if$$\tan A + \tan B + ...
The number of values of $$x$$ where the function <br>$$f\left( x \right) = \cos... Let$$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right...
If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real numbe...
A curve $$C$$ has the property that if the tangent drawn at any point $$P$$ on $... Suppose $$f(x)$$ is a function satisfying the following conditions <br>(a) $$f(... If$$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,... Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, w... Prove that $$\int_0^1 {{{\tan }^{ - 1}}} \,\left( {{1 \over {1 - x + {x^2}}}} \r... The order of the differential equation whose general solution is given by <br>$$... If from each of the three boxes containing $$3$$ white and $$1$$ black, $$2$$ wh... If $$\overline E$$ and $$\overline F$$ are the complementary events of events... There are four machines and it is known that exactly two of them are faulty. The... If $$E$$ and $$F$$ are events with $$P\left( E \right) \le P\left( F \right)$$ a... Seven white balls and three black balls are randomly placed in a row. The probab... A fair coin is tossed repeatedly. If the tail appears on first four tosses, then... Three players, $$A,B$$ and $$C,$$ toss a coin cyclically in that order (that is ... Let $${C_1}$$ and $${C_2}$$ be the graphs of the functions $$y = {x^2}$$ and $$y... If$$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$and$$c = i + \alpha j +... For three vectors $$u,v,w$$ which of the following expression is not equal to an... Which of the following expressions are meaningful? Prove, by vector methods or otherwise, that the point of intersection of the dia... For any two vectors $$u$$ and $$v,$$ prove that <br>(a) $${\left( {u\,.\,v} \ri... ## Physics The SI unit of inductance, the henry can be written as Let [$${\mathrm\varepsilon}_\mathrm o$\$] denote the dimentional formula of the p...

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