IIT-JEE 2005 Screening
Paper was held on Sun, May 22, 2005 9:00 AM
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Chemistry

The number of radial nodes of 3s and 2p orbitals are respectively
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Which species has the maximum number of lone pair of electrons on the central atom?
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The elevation in boiling point of a solution of 13.44 g of CuCl2 in 1kg of water using the following information will be
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Mathematics

$$a,\,b,\,c$$ are integers, not all simultaneously equal and $$\omega $$ is cube root of unity $$\left( {\omega \ne 1}
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$$\cos \left( {\alpha - \beta } \right) = 1$$ and $$\,\cos \left( {\alpha + \beta } \right) = 1/e$$ where $$\alpha ,\,
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The value of $$$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr }
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A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel
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If the LCM of p, q is $${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then n
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In the quadratic equation $$\,\,a{x^2} + bx + c = 0,$$ $$\Delta $$ $$ = {b^2} - 4ac$$ and $$\alpha + \beta ,\,{\alpha ^
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A circle is given by $${x^2}\, + \,{(y\, - \,1\,)^2}\, = \,1$$, another circle C touches it externally and also the x-a
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The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and
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Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at
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If $$f(x)$$ is a twice differentiable function and given that $$f\left( 1 \right) = 1;f\left( 2 \right) = 4,f\left( 3 \r
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In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The corr
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If $$P(x)$$ is a polynomial of degree less than or equal to $$2$$ and $$S$$ is the set of all such polynomials so that
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If $$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,} $$ then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$
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The area bounded by the parabola $$y = {\left( {x + 1} \right)^2}$$ and $$y = {\left( {x - 1} \right)^2}$$ and the line
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$$\int\limits_{ - 2}^0 {\left\{ {{x^3} + 3{x^2} + 3x + 3 + \left( {x + 1} \right)\cos \left( {x + 1} \right)} \right\}\,
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For the primitive integral equation $$ydx + {y^2}dy = x\,dy;$$ $$x \in R,\,\,y > 0,y = y\left( x \right),\,y\left( 1
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The solution of primitive integral equation $$\left( {{x^2} + {y^2}} \right)dy = xy$$ $$dx$$ is $$y=y(x),$$ If $$y(1)=1$
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If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi $$ then $$y''(0)=$$
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The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with
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A six faced fair dice is thrown until $$1$$ comes, then the probability that $$1$$ comes in even no. of trials is
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A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If t
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If $$\overrightarrow a \,,\,\overrightarrow b ,\overrightarrow c $$ are three non-zero, non-coplanar vectors and $$\ov
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Physics

Which of the following set have different dimensions?
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A simple pendulum has time period T1. The point of suspension is now moved upward according to the relation y = Kt2, (K
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