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IIT-JEE 2009

Exam Held on Sat Apr 11 2009 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

The compound(s) formed upon combustion of sodium metal in excess air is (are)

Mathematics

Let z = x + iy be a complex number where x and y are integers. Then the area of ...
Let $$z = \,\cos \,\theta \, + i\,\sin \,\theta $$ . Then the value of $$\sum\li...
For $$0 < \theta < {\pi \over 2},$$ the solution (s) of $$$\sum\limits_...
If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then
The smallest value of $$k$$, for which both the roots of the equation $$${x^2} ...
Let $$\left( {x,\,y,\,z} \right)$$ be points with integer coordinates satisfying...
the number of seven digit integers, with sum of the digits equal to 10 and forme...
In the sum of first $$n$$ terms of an A.P. is $$c{n^\angle }$$, then the sum of ...
Tangents drawn from the point P (1, 8) to the circle <br> $${x^2}\, + \,{y^2}\,...
The centres of two circles $${C_1}$$ and $${C_2}$$ each of unit radius are at a ...
The line passing through the extremity $$A$$ of the major axis and extremity $$B...
The normal at a point $$P$$ on the ellipse $${x^2} + 4{y^2} = 16$$ meets the $$x...
The locus of the orthocentre of the triangle formed by the lines $$$\left( {1 +...
In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that ...
The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a po...
An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The ec...
Match the conics in <b>Column $$I$$</b> with the statements/expressions in <b>C...
If the function $$f\left( x \right) = {x^3} + {e^{{x \over 2}}}$$ and $$g\left( ...
Let $$ABC$$ and $$ABC'$$ be two non-congruent triangles with sides $$AB=4$$, $$A...
For the function $$$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$$
Let $$p(x)$$ be a polynomial of degree $$4$$ having extremum at <br>$$x = 1,2$$...
The maximum value of the function <br>$$f\left( x \right) = 2{x^3} - 15{x^2} + 3...
The maximum value of the function <br>$$f\left( x \right) = 2{x^3} - 15{x^2} + 3...
let $$f$$be a non-negative function defined on the interval <br>$$\left[ {0,1} ...
Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=...
If $${I_n} = \int\limits_{ - \pi }^\pi {{{\sin nx} \over {\left( {1 + {\pi ^x}}...
Match the statements/expressions in <b>Column $$I$$</b> with the open intervals ...
Let $$f:R \to R$$ be a continuous function which satisfies $$$f\left( x \right)...
A fair die is tossed repeatedly until a six is obtained. Let $$X$$ denote the nu...
A fair die is tossed repeatedly until a six is obtained. Let $$X$$ denote the nu...
A fair die is tossed repeatedly until a six is obtained. Let $$X$$ denote the nu...
If $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ and $$\overr...
Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line $$$\wideh...
A line with positive direction cosines passes through the point $$P(2, -1, 2)$$ ...
Match the statements / expressions given in <b>Column-$$I$$</b> with the values ...
Match the statements/expressions given in <b>Column-$$I$$</b> with the values gi...

Physics

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The...
A piece of wire is bent in the shape of a parabola y = kx<sup>2</sup> (y-axis ve...

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