IIT-JEE 2001
Paper was held on Wed, Apr 11, 2001 9:00 AM
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## Chemistry

Hydrogen peroxide solution (20 ml) reacts quantitatively with a solution of KMnO4 solution is just decolourised by 10 ml
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The standard potential of the following cell is 0.23V at 15oC and 0.21 V at 35oC. Pt | H2 (g) | HCl (aq) | AgCl (s) | Ag
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The rate of a first order reaction is 0.04 mol litre-1 s-1 at 10 minutes and 0.03 mol litre-1 s-1 at 20 minutes after in
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The vapour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 moles o
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## Mathematics

Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta$$ be the roots of the equation $$a{x^2} + View Question Let$${a_1}$$,$${a_2}$$,.....,$${a_n}$$be positive real numbers in geometric progression. For each n, let$${A_n}$$,  View Question Let$$a, b, c$$be real numbers with$${a^2} + {b^2} + {c^2} = 1.$$Show that the equation$$\left| {\matrix{ {ax -
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Let $$C_1$$ and $$C_2$$ be two circles with $$C_2$$ lying inside $$C_1$$. A circle C lying inside $$C_1$$ touches $$C_1 View Question Let$$\,2{x^2}\, + \,{y^2} - \,3xy = 0$$be the equation of a pair of tangents drawn from the origin O to a circle of ra View Question Let$$P$$be a point on the ellipse$${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1,0 &lt; b &lt; a$$. Let the l View Question If$$\Delta $$is the area of a triangle with side lengths$$a, b, c, $$then show that$$\Delta \le {1 \over 4}\sqrt {
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Let $$- 1 \le p \le 1$$. Show that the equation $$4{x^3} - 3x - p = 0$$ has a unique root in the interval $$\left[ {1/ View Question Evaluate$$\int {{{\sin }^{ - 1}}\left( {{{2x + 2} \over {\sqrt {4{x^2} + 8x + 13} }}} \right)} \,dx.$$View Question Let$$b \ne 0$$and for$$j=0, 1, 2, ..., n,$$let$${S_j}$$be the area of the region bounded by the$$y$$-axis and t View Question A hemispherical tank of radius$$2$$metres is initially full of water and has an outlet of$$12$$cm2 cross-sectional a View Question An urn contains$$m$$white and$$n$$black balls. A ball is drawn at random and is put back into the urn along with$$k
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An unbiased die, with faces numbered $$1,2,3,4,5,6,$$ is thrown $$n$$ times and the list of $$n$$ numbers showing up is
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Show, by vector methods, that the angular bisectors of a triangle are concurrent and find an expression for the position
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Find $$3-$$dimensional vectors $${\overrightarrow v _1},{\overrightarrow v _2},{\overrightarrow v _3}$$ satisfying $$\ View Question Let$$\overrightarrow A \left( t \right) = {f_1}\left( t \right)\widehat i + {f_2}\left( t \right)\widehat j$$and$$\$\
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