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 $$\left( {\omega \ne 1} View Question$$\cos \left( {\alpha - \beta } \right) = 1$$and$$\,\cos \left( {\alpha + \beta } \right) = 1/e$$where$$\alpha ,\,
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The value of $$\left( {\matrix{ {30} \cr 0 \cr } } \right)\left( {\matrix{ {30} \cr {10} \cr } View Question A rectangle with sides of lenght (2m - 1) and (2n - 1) units is divided into squares of unit lenght by drawing parallel View Question If the LCM of p, q is$${r^2}\,{r^4}\,{s^2}$$, where r, s, t are prime numbers and p, q are the positive integers then n View Question In the quadratic equation$$\,\,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 $$f\left( 1 \right) = 1;f\left( 2 \right) = 4,f\left( 3 \r View Question In a triangle$$ABC$$,$$a,b,c$$are the lengths of its sides and$$A,B,C$$are the angles of triangle$$ABC$$. The corr View Question If$$P(x)$$is a polynomial of degree less than or equal to$$2$$and$$S$$is the set of all such polynomials so that View Question If$$\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,} $$then f$$\left( {{1 \over {\sqrt 3 }}} \right)$$View Question The area bounded by the parabola$$y = {\left( {x + 1} \right)^2}$$and$$y = {\left( {x - 1} \right)^2}$$and the line View Question$$\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 $$ydx + {y^2}dy = x\,dy;$$ $$x \in R,\,\,y &gt; 0,y = y\left( x \right),\,y\left( 1 View Question The solution of primitive integral equation$$\left( {{x^2} + {y^2}} \right)dy = xydx$$is$$y=y(x),$$If$$y(1)=1$View Question If $$y=y(x)$$ and it follows the relation $$x\cos \,y + y\,cos\,x = \pi$$ then $$y''(0)=$$ View Question The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with View Question A six faced fair dice is thrown until $$1$$ comes, then the probability that $$1$$ comes in even no. of trials is View Question A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If t View Question 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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