IIT-JEE 1987

Paper was held on
Sat, Apr 11, 1987 9:00 AM

## Chemistry

The brown ring complex compound is formulated as [Fe(H2O)5(NO)+]SO4. The oxidation state of iron is

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(i) What is the weight of sodium bromate and molarity pf solution necessary to prepare 85.5 ml of 0.672 B solution when

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In group IA, of alkali metals, the ionisation potential decreases on moving down the group. Therefore, lithium is a stro

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The first ionisation potential in electron volts of nitrogen and oxygen atoms are respectively given by

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Atomic radii of fluorine and neon in Angstrom units are respectively given by

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The electronegativity of the following elements increases in the order

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sp2 hybrid orbitals have equal s and p character.

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In benzene, carbon uses all the three p-orbitals for hybridisation.

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Hydrogen bond is maximum in

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The value of PV for 5.6 litres of an ideal gas is ________ RT, at NTP.

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A spherical balloon of 21 cm diameter is to be filled up with hydrogen at N.T.P from a cylinder containing the gas at 20

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Sodium when burnt in excess of oxygen gives sodium oxide.

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The metallic lustre exhibited by sodium is explained by

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Give reasons of the following:
Magnesium oxide is used for the lining of steel making furnace.

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Give reasons of the following:
Why is sodium chloride added during electrolysis of fused anhydrous magnesium chloride?

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The IUPAC name of the compound
CH2 = CH $$-$$ CH(CH3)2

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An unknown compound of carbon, hydrogen and oxygen
contains 69.77% carbon and 11.63% hydrogen and has
a molecular weight

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## Mathematics

The solution set of the system of equations $$X + Y = {{2\pi } \over 3},$$ $$cox\,x + cos\,y = {3 \over 2},$$ where x an

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The sides of a triangle inscribed in a given circle subtend angles $$\alpha $$, $$\beta $$ and $$\gamma $$ at the centre

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The set of all $$x$$ in the interval $$\left[ {0,\,\pi } \right]$$ for which $$2\,{\sin ^2}x - 3$$ $$\sin x + 1 \ge 0,$

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If the expression
$$${{\left[ {\sin \left( {{x \over 2}} \right) + \cos {x \over 2} + i\,\tan \left( x \right)} \right]}

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If $${{{z_1}}}$$ and $${{{z_2}}}$$ are two nonzero complex numbers such that $$\left| {{z_1}\, + {z_2}} \right| = \left|

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The value of $$\sum\limits_{k = 1}^6 {(\sin {{2\pi k} \over 7}} - i\,\cos \,{{2\pi k} \over 7})$$ is

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The number of all possible triplets $$\left( {{a_1},\,{a_2},\,{a_3}} \right)$$ such that $${a_1} + {a_2}\,\,\cos \left(

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If $$a,\,b,\,c,\,d$$ and p are distinct real numbers such that
$$$\left( {{a^2} + {b^2} + {c^2}} \right){p^2} - 2\left(

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Find the set of all $$x$$ for which $${{2x} \over {\left( {2{x^2} + 5x + 2} \right)}}\, > \,{1 \over {\left( {x + 1}

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Prove by mathematical induction that $$ - 5 - {{\left( {2n} \right)!} \over {{2^{2n}}{{\left( {n!} \right)}^2}}} \le {1

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Solve for x the following equation:
$${\log _{(2x + 3)}}(6{x^2} + 23x + 21) = 4 - {\log _{(3x + 7)}}(4{x^2} + 12x + 9)\

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The area of the triangle formed by the tangents from the point (4, 3) to the circle $${x^2} + {y^2} = 9$$ and the line

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Let a given line $$L_1$$ intersects the x and y axes at P and Q, respectively. Let another line $$L_2$$, perpendicular t

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The circle $${x^2}\, + \,{y^2} - \,4x\, - 4y + \,4 = 0$$ is inscribed in a triangle which has two of its sides along the

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A polygon of nine sides, each of length $$2$$, is inscribed in a circle. The radius of the circle is .................

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In a triangle, the lengths of the two larger sides are $$10$$ and $$9$$, respectively. If the angles are in $$AP$$. Then

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The set of all $$x$$ for which $$in\left( {1 + x} \right) \le x$$ is equal to ..........

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The smallest positive root of the equation, $$\tan x - x = 0$$ lies in

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Let $$f$$ and $$g$$ be increasing and decreasing functions, respectively from $$\left[ {0,\infty } \right)$$ to $$\left[

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Find the point on the curve $$\,\,\,4{x^2} + {a^2}{y^2} = 4{a^2},\,\,\,4 < {a^2} < 8$$
that is farthest from the

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Evaluate :$$\,\,\int {\left[ {{{{{\left( {\cos 2x} \right)}^{1/2}}} \over {\sin x}}} \right]dx} $$

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$$f\left( x \right) = \left| {\matrix{
{\sec x} & {\cos x} & {{{\sec }^2}x + \cot x\cos ec\,x} \cr
{{{\c

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Find the area bounded by the curves, $${x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|$$ and $$x=0$$ above the $$x$

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A man takes a step forward with probability $$0.4$$ and backwards with probability $$0.6$$ Find the probability that at

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If the vectors $$a\widehat i + \widehat j + \widehat k,\,\,\widehat i + b\widehat j + \widehat k$$ and $$\widehat i + \

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Let $$b = 4\widehat i + 3\widehat j$$ and $$\overrightarrow c $$ be two vectors perpendicular to each other in the $$xy$

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The number of vectors of unit length perpendicular to vectors $$\overrightarrow a = \left( {1,1,0} \right)$$ and $$\ove

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If $$A, B, C, D$$ are any four points in space, prove that -
$$\left| {\overrightarrow {AB} \times \overrightarrow {CD

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## Physics

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle

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