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

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

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

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

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

View Question The electronegativity of the following elements increases in the order

View Question sp2 hybrid orbitals have equal s and p character.

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

View Question Hydrogen bond is maximum in

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

View Question 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

View Question Sodium when burnt in excess of oxygen gives sodium oxide.

View Question The metallic lustre exhibited by sodium is explained by

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

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

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

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

View Question ## 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

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

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

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

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

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

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

View Question 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(

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

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

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

View Question 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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

View Question ## Physics

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

View Question