IIT-JEE 1986

Write the IUPAC name of :
CH3CH2CH = CHCOOH

The hydrogen bond is strongest in

The bond between two identical non-metal atoms has a pair of electrons

The hybridisation of sulphur in sulphur dioxide is

CO2 is isostructural with

Write the lewis dot structure of the following:
O3, COCl2

The average velocity of an ideal gas molecule at 27oC is 0.3m/sec. The average velocity at 927oC will be

The rate of diffusion of gas is _______ proportional to both ________ and square root of molecular mass.

Give reasons of the following:
Hydrogen peroxide is a better oxidising agent than water.

Arrange the following in:
Increasing size:
Cl-, S2-, Ca2+, Ar

Complete and balance the following equation:
Mn2+ + PbO2 \(\to\) \(MnO_4^-\) + H2O

Complete and balance the following equation:
Ag+ + AsH3 \(\to\) H3AsO3 + H+

Arrange the following in increasing oxidation number of iodine.
I2, HI, HIO4, ICl

Complete and balance the following equation:
\(ClO_3^-\) + I- + H2SO4 \(\to\) Cl- + \(HSO_4^-\)

Complete and balance the following equation:
S + OH- \(\to\) S2- + \(S_2O_3^-\)

The softness of group I-A metals increases down the group with increasing atomic number.

The pair of compound which cannot exist together in solution is:

The vapour pressure of ethanol and methanol are 44.5 and 88.7 mm Hg respectively. An ideal solution is formed at the same temperature by mixing 60 g of ethanol with 40 g of methanol. Calculate the total vapour pressure of the solution and t...

A molal solution is one that contains one mole of solute in

Which one of the following sets of quantum numbers represents an impossible arrangement?

Rutherford's alpha particle scattering experiment eventually led to the conclusion that:

The ratio of the energy of a photon of 2000Å wavelength to that 4000Å radiation is

The sum of the number of neutrons and proton in the isotope of hydrogen is

The electron density in the XY plane in 3dx2 - y2 orbital is zero

If the line \(ax+by+c=0\) is a normal to the curve \(xy=1\), then

Let \(P\left( x \right) = {a_0} + {a_1}{x^2} + {a_2}{x^4} + ...... + {a_n}{x^{2n}}\) be a polynomial in a real variable \(x\) with
\(0 < {a_0} < {a_1} < {a_2} < ..... < {a_n}.\) The function \(P(x)\) has

From the point A(0, 3) on the circle \({x^2} + 4x + {(y - 3)^2} = 0\), a chord AB is drawn and extended to a point M such that AM = 2AB. The equation of the locus of M is..........................

Lines 5x + 12y - 10 = 0 and 5x - 12y - 40 = 0 touch a circle \(C_1\) of diameter 6. If the centre of \(C_1\) lies in the first quadrant, find the equation of the circle \(C_2\) which is concentric with \(C_1\) and cuts intercepts of length ...

The equation of the line passing through the points of intersection of the circles \(3{x^2} + 3{y^2} - 2x + 12y - 9 = 0\) and \({x^2} + {y^2} - 6x + 2y - 15 = 0\) is..............................

Show that the area of the triangle on the Argand diagram formed by the complex numbers z, iz and z + iz is \({1 \over 2}\,{\left| z \right|^2}\) .

Let \({z_1}\) and \({z_2}\) be complex numbers such that \({z_1}\) \(\ne\) \({z_2}\) and \(\left| {{z_1}} \right| =\,\left| {{z_2}} \right|\). If \({z_1}\) has positive real and \({z_2}\) has negative imaginary part, then $${{{z_1}\, ...

Evaluate : \(\int\limits_0^\pi {{{x\,dx} \over {1 + \cos \,\alpha \,\sin x}},0 < \alpha < \pi }\)

The derivative of \({\sec ^{ - 1}}\left( {{1 \over {2{x^2} - 1}}} \right)\) with respect to \(\sqrt {1 - {x^2}}\) at \(x = {1 \over 2}\) is ...............

The principal value of \({\sin ^{ - 1}}\left( {\sin {{2\pi } \over 3}} \right)\) is

If \({C_r}\) stands for \({}^n{C_r},\) then the sum of the series
$${{2\left( {{n \over 2}} \right){\mkern 1mu} !{\mkern 1mu} \left( {{n \over 2}} \right){\mkern 1mu} !} \over {n!}}\left[ {C_0^2 - 2C_1^2 + 3C_2^2 - } \right......... + {\l...

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

A student appears for tests, \(I\), \(II\) and \(III\). The student is successful if he passes either in tests \(I\) and \(II\) or tests \(I\) and \(III\). The probabilities of student passing in tests \(I\), \(II\) and \(III\) are \(p, q\)...

A lot contains \(20\) articles. The probability that the lot contains exactly \(2\) defective articles is \(0.4\) and the probability that the lot contains exactly \(3\) defective articles is \(0.6\). Articles are drawn from the lot at rand...

The probability that at least one of the events \(A\) and \(B\) occurs is \(0.6\). If \(A\) and \(B\) occur simultaneously with probability \(0.2,\) then \(P\left( {\overline A } \right) + P\left( {\overline B } \right)\) is

If \({{1 + 3p} \over 3},\,\,\,{{1 - p} \over 4}\) and \(\,{{1 - 2p} \over 2}\) are the probabilities of three mutually exclusive events, then the set of all values of \(p\) is ..............

If in a triangle \(ABC\), \(\cos A\cos B + \sin A\sin B\sin C = 1,\) Show that \(a:b:c = 1:1:\sqrt 2\)

There exists a triangle \(ABC\) satisfying the conditions

For \(a \le 0,\) determine all real roots of the equation \(${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0\)$

If the quadratic equations \({x^2} + ax + b = 0\) and \({x^2} + bx + a = 0\) \((a \ne b)\) have a common root, then the numerical value of a + b is..........................

If \(S\) is the set of all real \(x\) such that \({{2x - 1} \over {2{x^3} + 3{x^2} + x}}\) is positive, then \(S\) contains

If \(a,\,b\) and \(c\) are distinct positive numbers, then the expression
\(\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc\) is

The solution of equation \({\log _7}\,{\log _5}\,\left( {\sqrt {x + 5} + \sqrt x } \right) = 0\) is ........................

The solution of the equation \(lo{g_7}\) \(lo{g_5}\) \(\left( {\sqrt {x + 5} + \sqrt x } \right) = 0\) is .............

All points lying inside the triangle formed by the points \(\left( {1,\,3} \right),\,\left( {5,\,0} \right)\) and \(\left( { - 1,\,2} \right)\) satisfy

The points \(\left( {0,{8 \over 3}} \right),\,\,\left( {1,\,3} \right)\) and \(\left( {82,\,30} \right)\) are vertices of