IIT-JEE 1986

Paper was held on
Fri, Apr 11, 1986 9:00 AM

## Chemistry

A molal solution is one that contains one mole of solute in

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Complete and balance the following equation:
S + OH- $$\to$$ S2- + $$S_2O_3^-$$

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Complete and balance the following equation:
Ag+ + AsH3 $$\to$$ H3AsO3 + H+

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Complete and balance the following equation:
Mn2+ + PbO2 $$\to$$ $$MnO_4^-$$ + H2O

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Complete and balance the following equation:
$$ClO_3^-$$ + I- + H2SO4 $$\to$$ Cl- + $$HSO_4^-$$

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Arrange the following in increasing oxidation number of iodine.
I2, HI, HIO4, ICl

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The electron density in the XY plane in 3dx2 - y2 orbital is zero

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Rutherford's alpha particle scattering experiment eventually led to the conclusion that:

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Which one of the following sets of quantum numbers represents an impossible arrangement?

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The ratio of the energy of a photon of 2000Å wavelength to that 4000Å radiation is

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The sum of the number of neutrons and proton in the isotope of hydrogen is

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Arrange the following in:
Increasing size:
Cl-, S2-, Ca2+, Ar

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The bond between two identical non-metal atoms has a pair of electrons

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The hydrogen bond is strongest in

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The hybridisation of sulphur in sulphur dioxide is

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CO2 is isostructural with

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Write the lewis dot structure of the following:
O3, COCl2

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The rate of diffusion of gas is _______ proportional to both ________ and square root of molecular mass.

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The average velocity of an ideal gas molecule at 27oC is 0.3m/sec. The average velocity at 927oC will be

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The softness of group I-A metals increases down the group with increasing atomic number.

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The pair of compound which cannot exist together in solution is:

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Give reasons of the following:
Hydrogen peroxide is a better oxidising agent than water.

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Write the IUPAC name of :
CH3CH2CH = CHCOOH

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The vapour pressure of ethanol and methanol are 44.5 and 88.7 mm Hg respectively. An ideal solution is formed at the sam

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## Mathematics

Let $${z_1}$$ and $${z_2}$$ be complex numbers such that $${z_1}$$ $$ \ne $$ $${z_2}$$ and $$\left| {{z_1}} \right| =\

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The expression $$2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \ri

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Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is $${1 \over 2}

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If $$S$$ is the set of all real $$x$$ such that $${{2x - 1} \over {2{x^3} + 3{x^2} + x}}$$ is positive, then $$S$$ conta

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If $$a,\,b$$ and $$c$$ are distinct positive numbers, then the expression
$$\left( {b + c - a} \right)\left( {c + a - b

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For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$

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If the quadratic equations $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ $$(a \ne b)$$ have a common root, then the

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The solution of equation $${\log _7}\,{\log _5}\,\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is ...................

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If $${C_r}$$ stands for $${}^n{C_r},$$ then the sum of the series
$${{2\left( {{n \over 2}} \right){\mkern 1mu} !{\mke

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A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the

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The solution of the equation $$lo{g_7}$$ $$lo{g_5}$$ $$\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is .............

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The points $$\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)$$ and $$\left( {82,\,30} \right)$$ are vertices o

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All points lying inside the triangle formed by the points $$\left( {1,\,3} \right),\,\left( {5,\,0} \right)$$ and $$\lef

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A vector $$\overline a $$ has components $$2p$$ and $$1$$ with respect to a rectangular cartesian system. This system is

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From the point A(0, 3) on the circle $${x^2} + 4x + {(y - 3)^2} = 0$$, a chord AB is drawn and extended to a point M suc

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The equation of the line passing through the points of intersection of the circles $$3{x^2} + 3{y^2} - 2x + 12y - 9 = 0$

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Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle $$C_1$$ of diameter 6. If the centre of $$C_1$$ lies in the

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The derivative of $${\sec ^{ - 1}}\left( {{1 \over {2{x^2} - 1}}} \right)$$ with respect to $$\sqrt {1 - {x^2}} $$ at $$

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There exists a triangle $$ABC$$ satisfying the conditions

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If in a triangle $$ABC$$, $$\cos A\cos B + \sin A\sin B\sin C = 1,$$ Show that $$a:b:c = 1:1:\sqrt 2 $$

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The principal value of $${\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)$$ is

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Let $$P\left( x \right) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + ...... + {a_n}{x^{2n}}$$ be a polynomial in a real variable

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If the line $$ax+by+c=0$$ is a normal to the curve $$xy=1$$, then

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Evaluate : $$\int\limits_0^\pi {{{x\,dx} \over {1 + \cos \,\alpha \,\sin x}},0 < \alpha < \pi } $$

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If $${{1 + 3p} \over 3},\,\,\,{{1 - p} \over 4}$$ and $$\,{{1 - 2p} \over 2}$$ are the probabilities of three mutually e

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A student appears for tests, $$I$$, $$II$$ and $$III$$. The student is successful if he passes either in tests $$I$$ and

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The probability that at least one of the events $$A$$ and $$B$$ occurs is $$0.6$$. If $$A$$ and $$B$$ occur simultaneous

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A lot contains $$20$$ articles. The probability that the lot contains exactly $$2$$ defective articles is $$0.4$$ and th

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Let $$\overrightarrow a = {a_1}i + {a_2}j + {a_3}k,\,\,\,\overrightarrow b = {b_1}i + {b_2}j + {b_3}k$$ and $$\overrig

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The position vectors of the points $$A, B, C$$ and $$D$$ are $$3\widehat i - 2\widehat j - \widehat k,\,2\widehat i + 3\

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## Physics

The dimensions of the quantities in one ( or more ) of the following pairs are the same. Identify the pair(s)

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A reference frame attached to the earth

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A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limit $$

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