Exam Details
IIT JEE 2003
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Questions
24
Duration
180 mins
Package
IIT-JEE Advance - Previous Year Papers
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24questions
Medium
16
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Hard
4
16.7%
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4
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24questions
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Sample questions from this paper
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2003 · Mathematics · Algebra · Sequences And Series
IIT JEE 2003
If a, b, c are in A.P., \({a^2}\), \({b^2}\), \({c^2}\) are in H.P., then prove that either a = b = c or a, b, \({ - {c \over 2}}\) form a G.P.
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2003 · Chemistry · Physical Chemistry · Some Basic Concepts Of Chemistry
IIT JEE 2003
Calculate the molarity of water if it's density is 1000 kg/m3
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2003 · Physics · Mechanics · Units And Measurements
IIT JEE 2003
If nth divisions of the main scale coincide with (n+1)th divisions
of vernier scale. Given one main scale division is equal to 'a' units. Find the
least count of the vernier.
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2003 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 2003
Prove that
$${2^k}\left( {\matrix{ n \cr 0 \cr } } \right)\left( {\matrix{ n \cr k \cr } } \right) - {2^{^{k - 1}\left( {\matrix{ n \cr 2 \cr } } \right)}}\left( {\matrix{ n \cr 1 \cr } } \right)\left( {\matrix{ {n - 1} \cr {k - 1} \cr } } \right)$$
$$+ {2^{k - 2}}\left( {\matrix{ {n - 2} \cr {k - 2} \cr } } \right) - .....{\left( { - 1} \right)^k}\left( {\matrix{ n \cr k \cr } } \right)\left( {\matrix{ {n - k} \cr 0 \cr } } \right) = {\left( {\matrix{ n \cr k \cr } } \right)^ \cdot }$$
$${2^k}\left( {\matrix{ n \cr 0 \cr } } \right)\left( {\matrix{ n \cr k \cr } } \right) - {2^{^{k - 1}\left( {\matrix{ n \cr 2 \cr } } \right)}}\left( {\matrix{ n \cr 1 \cr } } \right)\left( {\matrix{ {n - 1} \cr {k - 1} \cr } } \right)$$
$$+ {2^{k - 2}}\left( {\matrix{ {n - 2} \cr {k - 2} \cr } } \right) - .....{\left( { - 1} \right)^k}\left( {\matrix{ n \cr k \cr } } \right)\left( {\matrix{ {n - k} \cr 0 \cr } } \right) = {\left( {\matrix{ n \cr k \cr } } \right)^ \cdot }$$
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2003 · Chemistry · Physical Chemistry · Electrochemistry
IIT JEE 2003
Two students use the same stock solution of ZnSO4 and solution of CuSO4. The emf of one cell is 0.03 V higher than other. The conc. of CuSO4 in the cell with higher emf value is 0.5 M. Find out the conc. of CuSO4 in the other cell (2.203 RT/F = 0.06)
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2003 · Mathematics · Algebra · Quadratic Equation And Inequalities
IIT JEE 2003
If \({x^2} + \left( {a - b} \right)x + \left( {1 - a - b} \right) = 0\) where \(a,\,b\, \in \,R\) then find the values of a for which equation has unequal real roots for all values of \(b\).
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