IIT-JEE 2004 Screening

According to molecular orbital theory which of the following statement about the magnetic character and bond order is correct regarding \(O_2^+\)

The pair of compounds having metals in their highest oxidation state is

A sodium salt on treatment with MgCl3 gives white precipitate only on heating. The anion of the sodium salt is

The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom?

If the lines \({{x - 1} \over 2} = {{y + 1} \over 3} = {{z - 1} \over 4}\) and \(\,{{x - 3} \over 1} = {{y - k} \over 2} = {z \over 1}\) intersect, then the value of \(k\) is

If \(f\left( x \right) = {x^a}\log x\) and \(f\left( 0 \right) = 0,\) then the value of \(\alpha\) for which Rolle's theorem can be applied in \(\left[ {0,1} \right]\) is

If \(f\left( x \right) = {x^3} + b{x^2} + cx + d\) and \(0 < {b^2} < c,\) then in \(\left( { - \infty ,\infty } \right)\)

The area enclosed between the curves \(y = a{x^2}\) and
\(x = a{y^2}\left( {a > 0} \right)\) is \(1\) sq. unit, then the value of \(a\) is

If one of the diameters of the circle \({x^2} + {y^2} - 2x - 6y + 6 = 0\) is a chord to the circle with centre (2, 1), then the radius of the circle is

If \(\omega\) \(\left( { \ne 1} \right)\) be a cube root of unity and \({\left( {1 + {\omega ^2}} \right)^n} = {\left( {1 + {\omega ^4}} \right)^n},\) then the least positive value of n is

The value of the integral \(\int\limits_0^1 {\sqrt {{{1 - x} \over {1 + x}}} dx}\) is

If \(f(x)\) is differentiable and \(\int\limits_0^{{t^2}} {xf\left( x \right)dx = {2 \over 5}{t^5},}\) then \(f\left( {{4 \over {25}}} \right)\) equals

If \(y=y(x)\) and \({{2 + \sin x} \over {y + 1}}\left( {{{dy} \over {dx}}} \right) = - \cos x,y\left( 0 \right) = 1,\)
then \(y\left( {{\pi \over 2}} \right)\) equals

If \(y\) is a function of \(x\) and log \((x+y)-2xy=0\), then the value of \(y'(0)\) is equal to

If tangents are drawn to the ellipse \({x^2} + 2{y^2} = 2,\) then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

If the line \(62x + \sqrt 6 y = 2\) touches the hyperbola \({x^2} - 2{y^2} = 4\), then the point of contact is

The value of \(x\) for which \(sin\left( {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right) = \cos \left( {{{\tan }^{ - 1}}\,x} \right)\) is

If \({}^{n - 1}{C_r} = \left( {{k^2} - 3} \right)\,{}^n{C_{r + 1,}}\) then \(k \in\)

The angle between the tangents drawn from the point \((1, 4)\) to the parabola \({y^2} = 4x\) is

If three distinct numbers are chosen randomly from the first \(100\) natural numbers, then the probability that all three of them are divisible by both \(2\) and \(3\) is

The sides of a triangle are in the ratio \(1:\sqrt 3 :2\), then the angles of the triangle are in the ratio

If one root is square of the other root of the equation \({x^2} + px + q = 0\), then the realation between \(p\) and \(q\) is

For all \('x',{x^2} + 2ax + 10 - 3a > 0,\) then the interval in which '\(a\)' lies is

An infinite G.P. has first term '\(x\)' and sum '\(5\)', then \(x\) belongs to

Area of the triangle formed by the line \(x + y = 3\) and angle bisectors of the pair of straight line \({x^2} - {y^2} + 2y = 1\) is

Given both \(\theta\) and \(\phi\) are acute angles and \(\sin \,\theta = {1 \over 2},\,\) \(\cos \,\phi = {1 \over 3},\) then the value of \(\theta + \phi\) belongs to

The unit vector which is orthogonal to the vector \(3\overrightarrow i + 2\overrightarrow j + 6\overrightarrow k\) and is coplanar with the vectors \(\,2\widehat i + \widehat j + \widehat k\) and $$\,\widehat i - \widehat j + \widehat k$...

If \(\overrightarrow a = \left( {\widehat i + \widehat j + \widehat k} \right),\overrightarrow a .\overrightarrow b = 1\) and \(\overrightarrow a \times \overrightarrow b = \widehat j - \widehat k,\) then \(\overrightarrow b\) is

A body starts from rest at time t = 0, the acceleration time graph is
shown in the figure. The maximum velocity attained by the body
will be

A particle starts sliding down a frictionless inclined plane. If Sn is the distance traveled by it from time t = n - 1 sec to t = n sec, the ratio Sn / Sn+1 is

A wire of length \(l = 6 \pm 0.06\) cm and \(r = 0.5 \pm 0.005\) cm and mass \(m = 0.3 \pm 0.003\) gm. Maximum percentage error in density is

Pressure depends on distance as, \(P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)\), where \(\alpha\), \(\beta\) are constants, z in distance, k is Boltzman's constant and \(\theta\) is temperature. The ...

A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which
curve correctly represents the variation of potential energy of the block with respect to x