IIT-JEE 1988

Paper was held on
Tue, Apr 11, 1989 9:00 AM

## Chemistry

The equivalent weight of MnSO4 is half of its molecular weight, when it converts to

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In which mode of expression, the concentration of a solution remains independent of temperature?

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A sugar syrup of weight 214.2 g contains 34.2 g of sugar (C12H22O11). Calculate (i) molal concentration and (ii) mole fr

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A sample of hydrazine sulphate (N2H6SO4) was dissolved in 100 ml. of water, 10 ml of this solution was reacted with exce

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The uncertainty principle and the concept of wave nature of matter were proposed by ______ and ______ respectively. (Hei

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The triad of nuclei that is isotonic is

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The wavelength of a spectral line for an electronic transition is inversely related to :

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The outermost electronic configuration of the most electronegative element is

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The first ionisation potential of Na, Mg, Al and Si are in the order

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The statements that are true for the long form of the periodic table are:

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The molecule that has linear structure is

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The species in which the central atom uses sp2 hybrid orbitals in its bonding is

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Arrange the following :
N2, O2, F2, Cl2 in increasing order of bond dissociation energy

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Write down the balanced equation for the reaction when:
Carbon dioxide is passed through a concentrated aqueous solution

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## Mathematics

The value of the expression $$\sqrt 3 \,\cos \,ec\,{20^0} - \sec \,{20^0}$$ is equal to

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For any two complex numbers $${z_1},{z_2}$$ and any real number a and b.
$$\,{\left| {a{z_1} - b{z_2}} \right|^2} + {\le

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The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle.

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The values of $$\theta $$ lying between $$\theta = \theta $$ and $$\theta = \pi /2$$ and satisfying the equation
$$\l

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Solve $$\left| {{x^2} + 4x + 3} \right| + 2x + 5 = 0$$

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Total number of ways in which six ' + ' and four ' - ' signs can be arranged in a line such that no two ' - ' signs occu

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There are four balls of different colours and four boxes of colours, same as those of the balls. The number of ways in w

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Let $$R$$ $$ = {\left( {5\sqrt 5 + 11} \right)^{2n + 1}}$$ and $$f = R - \left[ R \right],$$ where [ ] denotes the grea

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The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + .........$$ is
$$n\,

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Sum of the first n terms of the series $${1 \over 2} + {3 \over 4} + {7 \over 8} + {{15} \over {16}} + ............$$ is

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If the first and the $$(2n-1)$$st terms of an A.P., a G.P. and an H.P. are equal and their $$n$$-th terms are $$a,b$$

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The lines $$2x + 3y + 19 = 0$$ and $$9x + 6y - 17 = 0$$ cut the coordinates axes in concyclic points.

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If $$P=(1, 0),$$ $$Q=(-1, 0)$$ and $$R=(2, 0)$$ are three given points, then locus of the point $$S$$ satisfying the rel

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Lines$${L_1} = ax + by + c = 0$$ and $${L_2} = lx + my + n = 0$$ intersect at the point $$P$$ and make an angle $$\theta

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If the circle $${C_1}:{x^2} + {y^2} = 16$$ intersects another circle $${C_2}$$ of radius 5 in such a manner that common

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If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2}\, = \,{k^2}$$ orthogonally, then the

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The equations of the tangents drawn from the origin to the circle $${x^2}\, + \,{y^2}\, - \,2rx\,\, - 2hy\, + {h^2} = 0$

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If $${y^2} = P\left( x \right)$$, a polynomial of degree $$3$$, then $$2{d \over {dx}}\left( {{y^3}{{{d^2}y} \over {d{x^

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If the angles of a triangle are $${30^ \circ }$$ and $${45^ \circ }$$ and the included side is $$\left( {\sqrt 3 + 1} \

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A sign -post in the form of an isosceles triangle $$ABC$$ is mounted on a pole of height $$h$$ fixed to the ground. The

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Investigate for maxima and minimum the function
$$$f\left( x \right) = \int\limits_1^x {\left[ {2\left( {t - 1} \right

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The integral $$\int\limits_0^{1.5} {\left[ {{x^2}} \right]dx,} $$
Where [ ] denotes the greatest integer function, equa

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The value of the integral $$\int\limits_0^{2a} {[{{f\left( x \right)} \over {\left\{ {f\left( x \right) + f\left( {2a -

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Find the area of the region bounded by the curve $$C:y=$$
$$\tan x,$$ tangent drawn to $$C$$ at $$x = {\pi \over 4}$$

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Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$

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Urn $$A$$ contains $$6$$ red and $$4$$ black balls and urn $$B$$ contains $$4$$ red and $$6$$ black balls. One ball is d

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One hundred identical coins, each with probability, $$p,$$ of showing up heads are tossed once. If $$0 < p < 1$$ a

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For two given events $$A$$ and $$B,$$ $$P\left( {A \cap B} \right)$$

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A box contains $$2$$ fifty paise coins, $$5$$ twenty five paise coins and a certain fixed number $$N\,\,\left( { \ge 2}

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The components of a vector $$\overrightarrow a $$ along and perpendicular to a non-zero vector $$\overrightarrow b $$ ar

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Let $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c ,$$ be three non-coplanar vectors and $$\overrightarrow p

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Let $$OA$$ $$CB$$ be a parallelogram with $$O$$ at the origin and $$OC$$ a diagonal. Let $$D$$ be the midpoint of $$OA.

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## Physics

In the formula X = 3YZ2, X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y

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A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15

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Two bodies M and N of equal masses are suspended from two separate massless springs of spring constant k1 and k2 respect

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