IIT-JEE 2001 Screening

The common features among the species CN-, CO and NO+ are :

The reaction, \(3Cl{O^ - }(aq)\)\(\to ClO_3^ - (aq) + 2C{l^ - }(aq)\) is an example of :

The set representing the correct order of first ionization potential is

In the standardization of Na2S2O3 using K2Cr2O7 by iodometry, the equivalent weight of K2Cr2O7 is:

An aqueous solution of 6.3 g oxalic acid dihydrate is made up to 250ml. the volume of
0.1N NaOH required to completely neutralize 10ml of this solution is :

The quantum numbers +1/2 and -1/2 for the electron spin represent

The wavelength associated with a golf ball weighing 200 g and moving at speed of 5 m/h is of the order

The triangle formed by the tangent to the curve \(f\left( x \right) = {x^2} + bx - b\) at the point \((1, 1)\) and the coordinate axex, lies in the first quadrant. If its area is \(2\), then the value of \(b\) is

Let \(f\left( x \right) = \left( {1 + {b^2}} \right){x^2} + 2bx + 1\) and let \(m(b)\) be the minimum value of \(f(x)\). As \(b\) varies, the range of \(m(b)\) is

If \(f\left( x \right) = x{e^{x\left( {1 - x} \right)}},\) then \(f(x)\) is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Let A B be a chord of the circle \({x^2} + {y^2} = {r^2}\) subtending a right angle at the centre. Then the locus of the centriod of the triangle PAB as P moves on the circle is

Let \({z_1}\) and \({z_2}\) be \({n^{th}}\) roots of unity which subtend a right angle at the origin. Then \(n\) must be of the form

The complex numbers \({z_1},\,{z_2}\) and \({z_3}\) satisfying \({{{z_1} - {z_3}} \over {{z_2} - {z_3}}} = {{1 - i\sqrt 3 } \over 2}\,\) are the vertices of a triangle which is

The value of \(\int\limits_{ - \pi }^\pi {{{{{\cos }^2}x} \over {1 + {a^x}}}dx,\,a > 0,}\) is

Let \(f:\left( {0,\infty } \right) \to R\) and \(F\left( x \right) = \int\limits_0^x {f\left( t \right)dt.}\) If \(F\left( {{x^2}} \right) = {x^2}\left( {1 + x} \right)\), then \(f(4)\) equals

If \({\sin ^{ - 1}}\left( {x - {{{x^2}} \over 2} + {{{x^3}} \over 4} - ....} \right)\)
\($ + {\cos ^{ - 1}}\left( {{x^2} - {{{x^4}} \over 2} + {{{x^6}} \over 4} - ....} \right) = {\pi \over 2}\)$
for \(0 < \left| x \right| < \sqrt 2 ,\) ...

In the binomial expansion of \({\left( {a - b} \right)^n},\,n \ge 5,\) the sum of the \({5^{th}}\) and \({6^{th}}\) terms is zero. Then \(a/b\) equals

The equation of the directrix of the parabola \({y^2} + 4y + 4x + 2 = 0\)

The equation of the common tangent touching the circle \({\left( {x - 3} \right)^2} + {y^2} = 9\) and the parabola \({y^2} = 4x\) above the \(x\)-axis is

Let \({T_n}\) denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If \({T_{n + 1}} - {T_n} = 21\), then n equals

A man from the top of a \(100\) metres high tower sees a car moving towards the tower at an angle of depression of \({30^ \circ }\). After some time,the angle of depression becomes \({60^ \circ }\). The distance (in metres) travelled by the...

Let \(\alpha\), \(\beta\) be the roots of \({x^2} - x + p = 0\) and \(\gamma ,\delta\) be the roots of \({x^2} - 4x + q = 0.\) If \(\alpha ,\beta ,\gamma ,\delta\) are in G.P., then the integral values of \(p\) and \(q\) respectively, a...

If the sum of the first \(2n\) terms of the A.P.\(2,5,8,......,\) is equal to the sum of the first \(n\) terms of the A.P.\(57,59,61,.....,\) then \(n\) equals

Let the positive numbers \(a,b,c,d\) be in A.P. Then \(abc,\) \(abd,\) \(acd,\) \(bcd,\) are

Area of the parallelogram formed by the lines \(y = mx\), \(y = mx + 1\), \(y = nx\) and \(y = nx + 1\) equals

The number of integer values of \(m\), for which the \(x\)-coordinate of the point of intersection of the lines \(3x + 4y = 9\) and \(y = mx + 1\) is also an integer, is

The number of distinct real roots of \(\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right|\,\)
\(\, = 0\) in the interval $$ - {\pi \over ...

If \(\alpha + \beta = \pi /2\) and \(\beta + \gamma = \alpha ,\) then \(\tan \,\alpha \,\) equals

The maximum value of \(\left( {\cos {\alpha _1}} \right).\left( {\cos {\alpha _2}} \right).....\left( {\cos {\alpha _n}} \right),\) under the restrictions \(0 \le {\alpha _1},{\alpha _2},....,{\alpha _n} \le {\pi \over 2}\) vand $$\left( ...

Let \(\overrightarrow a = \overrightarrow i - \overrightarrow k ,\overrightarrow b = x\overrightarrow i + \overrightarrow j + \left( {1 - x} \right)\overrightarrow k\) and
$$\overrightarrow c = y\overrightarrow i - x\overrightarrow...

If \(\overrightarrow a \,,\,\overrightarrow b\) and \(\overrightarrow c\) are unit vectors, then $${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\ove...

The pulleys and strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, the angle \(\theta\) should be

A particle executes simple harmonic motion between x = - A to x = + A. The time taken for it to go from 0 to \({A \over 2}\) is T1 and to go from \({A \over 2}\) to A is T2. Then

A quantity X is given by \({\varepsilon _0}L{{\Delta V} \over {\Delta t}}\) where \({\varepsilon _0}\) is the permittivity of the free space, L is a length, \({\Delta V}\) is a potential difference and \({\Delta t}\) is a time interval. The...