IIT-JEE 1985

Paper was held on
Thu, Apr 11, 1985 9:00 AM

## Chemistry

Five ml of 8N nitric acid, 4.8ml of 5N hydrochloric acid and a certain volume of 17M sulphuric acid are mixed together a

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Bohr Model can explain

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The radius of an atomic nucleus is of the order of

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Electromangnetic radiation with maximum wavelength is:

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Give reasons why the ground state outermost electronic configuration of silicon is:

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What is the maximum number of electrons that may be present in all atomic orbitals with principal quantum number 3 and a

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On Mulliken scale, the average of ionization potential and electron affinity is known as _____.

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Arrange the following in:
Decreasing ionic size:
Mg2+, O2-, Na+, F-

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Arrange the following in:
Increasing first ionisation potential :
Mg, Al, Si, Na

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Arrange the following in:
Increasing acidic property:
ZnO, Na2O3, P2O5, MgO

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All molecules with polar bonds have dipole moment.

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SnCl2 is a non-linear molecule

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The molecule having one unpaired electron is

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How many sigma bonds and how many pi-bonds are present in a benzene molecule?

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Kinetic Energy of a Molecule is zero at 0oC.

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A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.

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Rate of diffusion of a gas is

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Calculate the root mean square velocity of ozone kept in a closes vessel at 20oC and 82 cm mercury pressure.

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Sodium dissolved in liquid ammonia conducts electricity because ________.

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Hydrogen gas will not reduce

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Molecular formula of Glauber's salt is:

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The oxide that gives hydrogen peroxide on treatment with a dilute acid is

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Write down the balanced equations for the reaction when:
Calcium phosphate is heated with a mixture of sand and carbon;

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## Mathematics

If three complex numbers are in A.P. then they lie on a circle in the complex plane.

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If $$a,\,b,\,c$$ and $$u,\,v,\,w$$ are complex numbers representing the vertics of two triangles such that $$c = \left(

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If $${z_1}$$ = a + ib and $${z_2}$$ = c + id are complex numbers such that $$\left| {{z_1}} \right| = \left| {{z_2}} \ri

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Solve for $$x$$ ; $${\left( {5 + 2\sqrt 6 } \right)^{{x^2} - 3}} + {\left( {5 - 2\sqrt 6 } \right)^{{x^2} - 3}} = 10$$

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If $${n_1}$$, $${n_2}$$,.......$${n_p}$$ are p positive integers, whose sum is an even number, then the number of odd in

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If $$P(x) = a{x^2} + bx + c\,\,and\,\,Q(x) = - a{x^2} + dx + c$$, where $$ac \ne \,0$$, then P(x) Q(x) = 0 has at least

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If $${\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval-

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The product of any r consecutive natural numbers is always divisible by r!

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Use method of mathematical induction $${2.7^n} + {3.5^n} - 5$$ is divisible by $$24$$ for all $$n > 0$$

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7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gen

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If $$a,\,b,\,c$$ are in GP., then the equations $$\,\,\alpha {x^2} + 2bx + c = 0$$ and $$d{x^2} + 2ex + f = 0$$ have a c

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Find the sum of the series :
$$$\sum\limits_{r = 0}^n {{{\left( { - 1} \right)}^r}\,{}^n{C_r}\left[ {{1 \over {{2^r}}} +

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The orthocentre of the triangle formed by the lines $$x + y = 1,\,2x + 3y = 6$$ and $$4x - y + 4 = 0$$ lies in quadrant

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Three lines $$px + qy + r = 0$$, $$qx + ry + p = 0$$ and $$rx + py + q = 0$$ are concurrent if

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One of the diameters of the circle circumscribing the rectangle $$ABCD$$ is $$4y = x + 7$$. If $$A$$ and $$B$$ are the p

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Two sides of rhombus $$ABCD$$ are parallel to the lines $$y = x + 2$$ and $$y = 7x + 3$$. If the diagonals of the rhombu

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Let $${x^2} + {y^2} - 4x - 2y - 11 = 0$$ be a circle. A pair of tangentas from the point (4, 5) with a pair of radi from

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From the origin chords are drawn to the circle $${(x - 1)^2} + {y^2} = 1$$. The equation of the locus of the mid-points

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No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices $$\left( {1,\sqrt 3 }

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If $${f_r}\left( x \right),{g_r}\left( x \right),{h_r}\left( x \right),r = 1,2,3$$ are polynomials in $$x$$ such that $$

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If $$f\left( x \right) = {\log _x}\left( {In\,x} \right),$$ then $$f'\left( x \right)$$ at $$x=e$$ is ................

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The set of all real numbers $$a$$ such that $${a^2} + 2a,2a + 3$$ and $${a^2} + 3a + 8$$ are the sides of a triangle is

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In a triangle $$ABC$$, if cot $$A$$, cot $$B$$, cot $$C$$ are in A.P., then $${a^2},{b^2},{c^2}$$, are in ..............

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A ladder rests against a wall at an angle $$\alpha $$ to the horizintal. Its foot is pulled away from the wall through a

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In a triangle $$ABC$$, the median to the side $$BC$$ is of length
$$${1 \over {\sqrt {11 - 6\sqrt 3 } }}$$$ and it divi

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Find all the tangents to the curve
$$y = \cos \left( {x + y} \right),\,\, - 2\pi \le x \le 2\pi ,$$ that are parallel

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Let $$f\left( x \right) = {\sin ^3}x + \lambda {\sin ^2}x, - {\pi \over 2} < x < {\pi \over 2}.$$ Find the inter

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Evaluate the following $$\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} } $$

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For any integer $$n$$ the integral ...........
$$\int\limits_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^3}\left( {2n + 1} \right

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Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.

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Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$

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A box contains $$100$$ tickets numbered $$1, 2, ....., 100.$$ Two tickets are chosen at random. It is given that the max

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$$P\left( {A \cup B} \right) = P\left( {A \cap B} \right)$$ if and only if the relation between $$P(A)$$ and $$P(B)$$ is

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In a multiple-choice question there are four alternative answers, of which one or more are correct. A candidate will get

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If $$\left| {\matrix{
a & {{a^2}} & {1 + {a^3}} \cr
b & {{b^2}} & {1 + {b^3}} \cr
c & {

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If $$\overrightarrow A \overrightarrow {\,B} \overrightarrow {\,C} $$ are three non-coplannar vectors, then -
$${{\over

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If $$\overrightarrow A = \left( {1,1,1} \right),\,\,\overrightarrow C = \left( {0,1, - 1} \right)$$ are given vectors,

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## Physics

Plank' constant has dimension __________.

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Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. They

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A uniform chain of length L and mass M is lying on a smooth table and one third of its length is hanging vertically down

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