IIT-JEE 1998

Paper was held on
Sat, Apr 11, 1998 9:00 AM

## Chemistry

An aqueous solution containing 0.10 g KIO3 (formula weight = 214.0) was treated with an excess of KI solution. The solut

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The orbital diagram in which the Aufbau principle is violated is

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Decrease in atomic number is observed during

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Which of the following statement(s) is (are) correct?

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The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The possible energy value(s) of the excited sta

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ASSERTION:
Nuclide $${}_{13}^{30}Al$$ is less stable than $${}_{20}^{40}Ca$$
REASON:
Nuclides having odd number of proto

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The geometry and the type of hybrid orbital present about the central atom in BF3 is

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Interpret the non-linear shape of H2S molecule and non-planar shape of PCl3 using valence shell electron pair repulsion

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Read the following Assertion and Reason and answer as per the options given below
Assetion: LiCl is predominantly a cov

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Highly pure dilute solution of sodium in liquid ammonia

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Work out the following using chemical equation :
Chlorination of calcium hydroxide produces bleaching powder.

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Hydrogen peroxide acts both as an oxidising and as a reducing agent in alkaline solution towards certain first row trans

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A solution of a nonvolatile solute in water freezes at -0.30oC. The vapour pressure of pure water at 298 K s 23.51 mm Hg

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Calculate the equilibrium constant for the reaction:
2Fe3+ + 3I- $$\leftrightharpoons$$ 2Fe2+ + $$I_3^-$$. The standard

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Find the solubility product of a saturated solution of Ag2CrO4 in water at 298 K if the emf of the cell Ag|Ag+ (satd. Ag

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The rate constant of a reaction is 1.5 $$\times$$ 107 s-1 at 50oC and 4.5 $$\times$$ 107 s-1 at 100oC. Evaluate the Arrh

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## Mathematics

If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals

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If $$\,\left| {\matrix{
{6i} & { - 3i} & 1 \cr
4 & {3i} & { - 1} \cr
{20} & 3 & i

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The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals

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Which of the following number(s) is /are rational?

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The number of values of $$x\,\,$$ in the interval $$\left[ {0,\,5\pi } \right]$$ satisfying the equation $$3\,{\sin ^2}x

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Prove that $$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha = \cot \alpha $$

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Number of divisor of the form 4$$n$$$$ + 2\left( {n \ge 0} \right)$$ of the integer 240 is

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If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}}}

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An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using

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Let $$p$$ be a prime and $$m$$ a positive integer. By mathematical induction on $$m$$, or otherwise, prove that whenever

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Let $$n$$ be an odd integer. If $$\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta ,} $$ for every value of

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Let $${T_r}$$ be the $${r^{th}}$$ term of an A.P., for $$r=1, 2, 3, ....$$ If for some positive integers $$m$$, $$n$$ we

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If $$x > 1,y > 1,z > 1$$ are in G.P., then $${1 \over {1 + In\,x}},{1 \over {1 + In\,y}},{1 \over {1 + In\,z}}$

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The diagonals of a parralleogram $$PQRS$$ are along the lines $$x + 3y = 4$$ and $$6x - 2y = 7$$. Then $$PQRS$$ must be

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If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right

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If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of the following points of the triangle $$P

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Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.

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The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is

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If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}

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$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C

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The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches the curve $$\left( {{x^2}/4} \right) + {

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If $$P=(x, y)$$, $${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)$$ and $$16{x^2} + 25{y^2} = 400,$$ the

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The angle between a pair of tangents drawn from a point $$P$$ to the parabola $${y^2} = 4ax$$ is $${45^ \circ }$$. Show

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If$$\,\,\,$$ $$y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)\left( {x - c} \right)}} + {{bx} \over {

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If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then

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Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of th

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A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose $${60^ \circ }$$ an

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Prove that a triangle $$ABC$$ is equilateral if and only if $$\tan A + \tan B + \tan C = 3\sqrt 3 $$.

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The number of values of $$x$$ where the function
$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attai

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Let $$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right)^2} + {\left( {f\left( x \right)} \righ

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If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real number $$x$$, then the minimum value of $$f$$

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A curve $$C$$ has the property that if the tangent drawn at any point $$P$$ on $$C$$ meets the co-ordinate axes at $$A$$

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Suppose $$f(x)$$ is a function satisfying the following conditions
(a) $$f(0)=2,f(1)=1$$,
(b) $$f$$has a minimum value

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If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is

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Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, where $$\left[ x \right]$$ is the integra

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Prove that $$\int_0^1 {{{\tan }^{ - 1}}} \,\left( {{1 \over {1 - x + {x^2}}}} \right)dx = 2\int_0^1 {{{\tan }^{ - 1}}} \

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The order of the differential equation whose general solution is given by
$$y = \left( {{C_1} + {C_2}} \right)\cos \left

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If from each of the three boxes containing $$3$$ white and $$1$$ black, $$2$$ white and $$2$$ black, $$1$$ white and $$3

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If $$\overline E $$ and $$\overline F $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0

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There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random or

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If $$E$$ and $$F$$ are events with $$P\left( E \right) \le P\left( F \right)$$ and $$P\left( {E \cap F} \right) > 0,$

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Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed

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A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing o

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Three players, $$A,B$$ and $$C,$$ toss a coin cyclically in that order (that is $$A, B, C, A, B, C, A, B,...$$) till a h

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Let $${C_1}$$ and $${C_2}$$ be the graphs of the functions $$y = {x^2}$$ and $$y = 2x,$$ $$0 \le x \le 1$$ respectively.

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If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vector

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For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?

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Which of the following expressions are meaningful?

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Prove, by vector methods or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line p

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For any two vectors $$u$$ and $$v,$$ prove that
(a) $${\left( {u\,.\,v} \right)^2} + {\left| {u \times v} \right|^2} =

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## Physics

The SI unit of inductance, the henry can be written as

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Let [$${\mathrm\varepsilon}_\mathrm o$$] denote the dimentional formula of the permittivity of the vacuum, and [$$\mu_o$

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