IIT-JEE 1995 Screening

Number of paired electrons in O2 molecules is

Which one is most ionic

Which has most stable +2 oxidation state?

A 3p orbital has

The slope of the tangent to a curve \(y = f\left( x \right)\) at \(\left[ {x,\,f\left( x \right)} \right]\) is \(2x+1\). If the curve passes through the point \(\left( {1,2} \right)\), then the area bounded by the curve, the \(x\)-axis and ...

The function \(f\left( x \right) = {{in\,\left( {\pi + x} \right)} \over {in\,\left( {e + x} \right)}}\) is

On the interval \(\left[ {0,1} \right]\) the function \({x^{25}}{\left( {1 - x} \right)^{75}}\) takes its maximum value at the point

If \(\omega \,\left( { \ne 1} \right)\) is a cube root of unity and \({\left( {1 + \omega } \right)^7} = A + B\,\omega\) then \(A\) and \(B\) are respectively

Let \(z\) and \(\omega\) be two non zero complex numbers such that
\(\left| z \right| = \left| \omega \right|\) and \({\rm A}rg\,z + {\rm A}rg\,\omega = \pi ,\) then \(z\) equals

Let \(z\) and \(\omega\) be two complex numbers such that
\(\left| z \right| \le 1,\) \(\left| \omega \right| \le 1\) and \(\left| {z + i\omega } \right| = \left| {z - i\overline \omega } \right| = 2\) then \(z\) equals

The value of \(\int\limits_\pi ^{2\pi } {\left[ {2\,\sin x} \right]\,dx}\) where [ . ] represents the greatest integer function is

If \(f\left( x \right)\,\,\, = \,\,\,A\sin \left( {{{\pi x} \over 2}} \right)\,\,\, + \,\,\,B,\,\,\,f'\left( {{1 \over 2}} \right) = \sqrt 2\) and
\(\int\limits_0^1 {f\left( x \right)dx = {{2A} \over \pi },}\) then constants \(A\) and $$...

The radius of the circle passing through the foci of the ellipse \({{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1\), and having its centre at \((0, 3)\) is

The value of the integral \(\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,\) is

Consider a circle with its centre lying on the focus of the parabola \({y^2} = 2px\) such that it touches the directrix of the parabola. Then a point of intersection of the circle and parabola is

Let \(0 < P\left( A \right) < 1,0 < P\left( B \right) < 1\) and
\(P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)\) then

The probability of India winning a test match against West Indies is \(1/2\). Assuming independence from match to match the probability that in a \(5\) match series India's second win occurs at third test is

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

In a triangle \(ABC\), \(\angle B = {\pi \over 3}\) and \(\angle C = {\pi \over 4}\). Let \(D\) divide \(BC\) internally in the ratio \(1:3\) then \({{\sin \angle BAD} \over {\sin \angle CAD}}\) is equal to

\(\,3{\left( {\sin x - \cos x} \right)^4} + 6{\left( {\sin x + \cos x} \right)^2} + 4\left( {{{\sin }^6}x + {{\cos }^6}x} \right) =\)

The general values of \(\theta\) satisfying the equation \(2{\sin ^2}\theta - 3\sin \theta - 2 = 0\) is

Let \(\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \widehat k - \widehat i.\) If \(\overrightarrow d\) is a unit vector such that $$\overrightarrow a .\overrightarrow d =...

If \(\overrightarrow a ,\) \(\overrightarrow b\) and \(\overrightarrow c\) are three non coplanar vectors, then
$$\left( {\overrightarrow a + \overrightarrow b + \overrightarrow c } \right).\left[ {\left( {\overrightarrow a + \overri...

If \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) are non coplanar unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\left( {\overrightarrow b + \overrightarr...

Let \(\overrightarrow u ,\overrightarrow v\) and \(\overrightarrow w\) be vectors such that \(\overrightarrow u + \overrightarrow v + \overrightarrow w = 0.\) If $$\left| {\overrightarrow u } \right| = 3,\left| {\overrightarrow v } \ri...

The pairs of physical quantities that have the same dimensions is (are):