IIT-JEE 1985

All molecules with polar bonds have dipole moment.

SnCl2 is a non-linear molecule

How many sigma bonds and how many pi-bonds are present in a benzene molecule?

The molecule having one unpaired electron is

Calculate the root mean square velocity of ozone kept in a closes vessel at 20oC and 82 cm mercury pressure.

Rate of diffusion of a gas is

Kinetic Energy of a Molecule is zero at 0oC.

A gas in a closed container will exert much higher pressure due to gravity at the bottom than at the top.

Hydrogen gas will not reduce

On Mulliken scale, the average of ionization potential and electron affinity is known as _____.

Arrange the following in:
Decreasing ionic size:
Mg2+, O2-, Na+, F-

Arrange the following in:
Increasing acidic property:
ZnO, Na2O2, P2O5, MgO

Arrange the following in:
Increasing first ionisation potential :
Mg, Al, Si, Na

The oxide that gives hydrogen peroxide on treatment with a dilute acid is

Sodium dissolved in liquid ammonia conducts electricity because ________.

Write down the balanced equations for the reaction when:
Calcium phosphate is heated with a mixture of sand and carbon;

Molecular formula of Glauber's salt is:

Five ml of 8N nitric acid, 4.8ml of 5N hydrochloric acid and a certain volume of 17M sulphuric acid are mixed together and made upto 2 litre. Thirty ml of this acid mixture neutralise 42.9 ml of sodium carbonate solution containing one gram...

Bohr Model can explain

Electromangnetic radiation with maximum wavelength is:

Give reasons why the ground state outermost electronic configuration of silicon is:

What is the maximum number of electrons that may be present in all atomic orbitals with principal quantum number 3 and azimuthal quantum number 2?

The radius of an atomic nucleus is of the order of

Let \(f\left( x \right) = {\sin ^3}x + \lambda {\sin ^2}x, - {\pi \over 2} < x < {\pi \over 2}.\) Find the intervals in which \(\lambda\) should lie in order that \(f(x)\) has exactly one minimum and exactly one maximum.

Find all the tangents to the curve
\(y = \cos \left( {x + y} \right),\,\, - 2\pi \le x \le 2\pi ,\) that are parallel to the line \(x+2y=0\).

Sketch the region bounded by the curves \(y = \sqrt {5 - {x^2}}\) and \(y = \left| {x - 1} \right|\) and find its area.

From the origin chords are drawn to the circle \({(x - 1)^2} + {y^2} = 1\). The equation of the locus of the mid-points of these chords is.............

Let \({x^2} + {y^2} - 4x - 2y - 11 = 0\) be a circle. A pair of tangentas from the point (4, 5) with a pair of radi from a quadrilateral of area............................

No tangent can be drawn from the point (5/2, 1) to the circumcircle of the triangle with vertices \(\left( {1,\sqrt 3 } \right)\,\,\left( {1, - \sqrt 3 } \right),\,\,\left( {3,\sqrt 3 } \right)\).

If three complex numbers are in A.P. then they lie on a circle in the complex plane.

If \(a,\,b,\,c\) and \(u,\,v,\,w\) are complex numbers representing the vertics of two triangles such that \(c = \left( {1 - r} \right)a + rb\) and \(w = \left( {1 - r} \right)u + rv,\) where \(w = \left( {1 - r} \right)u + rv,\) is a compl...

If \({z_1}\) = a + ib and \({z_2}\) = c + id are complex numbers such that \(\left| {{z_1}} \right| = \left| {{z_2}} \right| = 1\) and \({\mathop{\rm Re}\nolimits} ({z_1}\,{\overline z _2}) = 0\), then the pair of complex numbers \({w_1}\)...

Evaluate the following : \(\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx\)

For any integer \(n\) the integral ...........
\(\int\limits_0^\pi {{e^{{{\cos }^2}x}}{{\cos }^3}\left( {2n + 1} \right)xdx}\) has the value

If \(f\left( x \right) = {\log _x}\left( {In\,x} \right),\) then \(f'\left( x \right)\) at \(x=e\) is ................

If \({f_r}\left( x \right),{g_r}\left( x \right),{h_r}\left( x \right),r = 1,2,3\) are polynomials in \(x\) such that \({f_r}\left( a \right) = {g_r}\left( a \right) = {h_r}\left( a \right),r = 1,2,3\)
and $$F\left( x \right) = \left| {\ma...

Evaluate the following \(\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} }\)

Use method of mathematical induction \({2.7^n} + {3.5^n} - 5\) is divisible by \(24\) for all \(n > 0\)

If \(\left| {\matrix{ a & {{a^2}} & {1 + {a^3}} \cr b & {{b^2}} & {1 + {b^3}} \cr c & {{c^2}} & {1 + {c^3}} \cr } } \right| = 0\) and the vectors
$$\overrightarrow A = \left( {1,a,{a^2}} \right),\,\,\overrightarrow B = \...

7 relatives of a man comprises 4 ladies and 3 gentlemen ; his wife has also 7 relatives ; 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man's relativ...

The product of any r consecutive natural numbers is always divisible by r!

In a multiple-choice question there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks the correct answers. The candidate decides to tick the answers at random, If he ...

\(P\left( {A \cup B} \right) = P\left( {A \cap B} \right)\) if and only if the relation between \(P(A)\) and \(P(B)\) is .............

A box contains \(100\) tickets numbered \(1, 2, ....., 100.\) Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than \(10.\) The minimum number on them is \(5\) with probability .......

In a triangle \(ABC\), if cot \(A\), cot \(B\), cot \(C\) are in A.P., then \({a^2},{b^2},{c^2}\), are in ............... progression.

In a triangle \(ABC\), the median to the side \(BC\) is of length
\(${1 \over {\sqrt {11 - 6\sqrt 3 } }}\)$ and it divides the angle \(A\) into angles \({30^ \circ }\) and \({45^ \circ }\). Find the length of the side \(BC\).

The set of all real numbers \(a\) such that \({a^2} + 2a,2a + 3\) and \({a^2} + 3a + 8\) are the sides of a triangle is ...........

A ladder rests against a wall at an angle \(\alpha\) to the horizintal. Its foot is pulled away from the wall through a distance \(a\), so that it slides \(a\) distance \(b\) down the wall making an angle \(\beta\) with the horizontal. Sh...

Solve for \(x\) ; \({\left( {5 + 2\sqrt 6 } \right)^{{x^2} - 3}} + {\left( {5 - 2\sqrt 6 } \right)^{{x^2} - 3}} = 10\)

If \({\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)\), then x lies in the interval-