Exam Details
IIT JEE 2002
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Questions
16
Duration
180 mins
Package
IIT-JEE Advance - Previous Year Papers
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Topic distribution
Subtopic distribution
Difficulty distribution
16questions
Medium
9
56.3%
Hard
5
31.3%
Easy
2
12.5%
Question type distribution
16questions
Subjective
11
68.8%
Multiple Choices
5
31.3%
Syllabus
Full Syllabus
Sample questions from this paper
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2002 · Mathematics · Algebra · Mathematical Induction And Binomial Theorem
IIT JEE 2002
Use mathematical induction to show that
\({\left( {25} \right)^{n + 1}} - 24n + 5735\) is divisible by \({\left( {24} \right)^2}\) for all \(= n = 1,2,...\)
\({\left( {25} \right)^{n + 1}} - 24n + 5735\) is divisible by \({\left( {24} \right)^2}\) for all \(= n = 1,2,...\)
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2002 · Mathematics · Coordinate Geometry · Straight Lines And Pair Of Straight Lines
IIT JEE 2002
A straight line \(L\) with negative slope passes through the point \((8, 2)\) and cuts the positive coordinate axes at points \(P\) and \(Q\). Find the absolute minimum value of \(OP + OQ,\) as \(L\) varies, where \(O\) is the origin.
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2002 · Mathematics · Trigonometry · Inverse Trigonometric Functions
IIT JEE 2002
Prove that \(\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}}\).
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2002 · Mathematics · Algebra · Probability
IIT JEE 2002
A box contains \(N\) coins, \(m\) of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is \(1/2\), while it is \(2/3\) when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. what is the probability that the coin drawn is fair?
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2002 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2002
For any natural number \(m\), evaluate
$$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} + 6} \right)}^{l/m}}dx,x > 0.}$$
$$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} + 6} \right)}^{l/m}}dx,x > 0.}$$
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2002 · Mathematics · Algebra · Vector Algebra
IIT JEE 2002
Let \(V\) be the volume of the parallelopiped formed by the vectors \(\overrightarrow a = {a_1}\widehat i + {a_2}\widehat j + {a_3}\widehat k,\) \(\,\,\,\,\overrightarrow b = {b_1}\widehat i + {b_2}\widehat j + {b_3}\widehat k,\) \(\,\,\,\,\,\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k.\) where \(r=1, 2, 3,\) are non-negative real numbers and \(\sum\limits_{r = 1}^3 {\left( {{a_r} + {b_r} + {c_r}} \right) = 3L,}\) show that \(V \le {L^3}\,\,.\)
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