IIT-JEE 2002 Screening

Paper was held on
Thu, Apr 11, 2002 9:00 AM

## Chemistry

How many moles of electron weigh one kilogram?

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Rutherford's experiment, which established the nuclear model of the atom, used a beam of

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If the nitrogen atom has electronic configuration 1s7, it would have energy lower than that of the normal ground state c

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Identify the correct order of acidic strengths of CO2, CuO, CaO, H2O

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Specify the coordination geometry around and hybridisation of N and B atoms in a 1 : 1 complex of BF3 and NH3

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Identify the least stable ion amongst the following

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Which of the following molecular species has unpaired electrons(s)?

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## Mathematics

For all complex numbers $${z_1},\,{z_2}$$ satisfying $$\left| {{z_1}} \right| = 12$$ and $$\left| {{z_2} - 3 - 4i} \righ

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The number of integral values of $$k$$ for which the equation $$7\cos x + 5\sin x = 2k + 1$$ has a solution is

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If $${a_1},{a_2}.......,{a_n}$$ are positive real numbers whose product is a fixed number c, then the minimum value of $

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The set of all real numbers x for which $${x^2} - \left| {x + 2} \right| + x > 0$$, is

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The sum $$\sum\limits_{i = 0}^m {\left( {\matrix{
{10} \cr
i \cr
} } \right)\left( {\matrix{
{20} \cr

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The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

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Suppose $$a, b, c$$ are in A.P. and $${a^2},{b^2},{c^2}$$ are in G.P. If $$a < b < c$$ and $$a + b + c = {3 \over

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Let $$0 < \alpha < {\pi \over 2}$$ be fixed angle. If $$P = \left( {\cos \theta ,\,\sin \theta } \right)$$ and $

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Let $$P = \left( { - 1,\,0} \right),\,Q = \left( {0,\,0} \right)$$ and $$R = \left( {3,\,3\sqrt 3 } \right)$$ be three p

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A straight line through the origin $$O$$ meets the parallel lines $$4x+2y=9$$ and $$2x+y+6=0$$ at points $$P$$ and $$Q$$

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If the tangent at the point P on the circle $${x^2} + {y^2} + 6x + 6y = 2$$ meets a straight line 5x - 2y + 6 = 0 at a

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If $$a > 2b > 0$$ then the positive value of $$m$$ for which $$y = mx - b\sqrt {1 + {m^2}} $$ is a common tangent

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The equation of the common tangent to the curves $${y^2} = 8x$$ and $$xy = - 1$$ is

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The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is an

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Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radi

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The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is

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The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)

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The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is

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The integral $$\int\limits_{ - 1/2}^{1/2} {\left( {\left[ x \right] + \ell n\left( {{{1 + x} \over {1 - x}}} \right)} \r

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Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.} $$ Then the real roots of the equation
$${x^2} - f

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Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous
function such that for all $$x \in R$$, $$f\left

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Let $$T>0$$ be a fixed real number . Suppose $$f$$ is a continuous
function such that for all $$x \in R$$, $$f\left

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If $${\overrightarrow a }$$ and $${\overrightarrow b }$$ are two unit vectors such that $${\overrightarrow a + 2\overri

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Let $$\overrightarrow V = 2\overrightarrow i + \overrightarrow j - \overrightarrow k $$ and $$\overrightarrow W = \o

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## Physics

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The

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