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IIT-JEE 1984

Exam Held on Wed Apr 11 1984 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

2.68 $$\times$$ 10<sup>-3</sup> moles of a solution containing an ion A<sup>n+</...
Correct set of four quantum numbers for the valence (outermost) electron of rubi...
The increasing order (lowest first) for the values of e/m (charges/mass) for el...
Which electronic level would allow the hydrogen atom to absorb a photon but not ...
An isotone of $${}_{32}^{76}Ge$$ is
Many elements have non-integral atomic masses because:
When alpha particles are sent through a thin metal foil, most of them go straigh...
The electron energy in hydrogen atom is given by E = (-21.7 $$\times$$ 10<sup>-1...
On hybridization of one s and one p orbitals we get:
The total energy of one mole of an ideal monatomic gas at 27<sup>o</sup> is ____...
C<sub>p</sub> - C<sub>v</sub> for an ideal gas is _______
Equal weights of methane and hydrogen are mixed in an empty container at 25<sup>...
The hydration energy of Mg<sup>++</sup> is larger than that of:

Mathematics

There exists a value of $$\theta $$ between 0 and $$2\pi $$ that satisfies the e...
If the complex numbers, $${Z_1},{Z_2}$$ and $${Z_3}$$ represent the vertics of a...
$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \r...
If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, t...
Find the values of $$x \in \left( { - \pi , + \pi } \right)$$ which satisfy the ...
For real $$x$$, the function $$\,{{\left( {x - a} \right)\left( {x - b} \right)}...
If the product of the roots of the equation $$\,{x^2} - 3\,k\,x + 2\,{e^{2lnk}} ...
If a &lt; b &lt; c &lt; d, then the roots of the equation (x - a) (x - c) + 2 ( ...
The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has
If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval
The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respect...
If $$p$$ be a natural number then prove that $${p^{n + 1}} + {\left( {p + 1} \ri...
Given $${s_n} = 1 + q + {q^2} + ...... + {q^2};$$ <br>$${S_n} = 1 + {{q + 1} \o...
The sum of integers from 1 to 100 that are divisible by 2 or 5 is ............
If $$a &gt; 0,\,b &gt; 0$$ and $$\,c &gt; 0,$$ prove that $$\,c &gt; 0,$$ prove ...
If $$n$$ is a natural number such that <br>$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{...
If $$a,\,b$$ and $$c$$ are in A.P., then the straight line $$ax + by + c = 0$$ w...
Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3...
The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. T...
The locus of the mid-point of a chord of the circle $${x^2} + {y^2} = 4$$ which ...
The abscissa of the two points A and B are the roots of the equation $${x^2}\, +...
If $$\alpha $$ be a repeated root of a quadratic equation $$f(x)=0$$ and $$A(x),...
For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}...
With usual notation, if in a triangle $$ABC$$; <br>$${{b + c} \over {11}} = {{c...
The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \ri...
For $$0 &lt; a &lt; x,$$ the minimum value of the function $$lo{g_a}x + {\log _x...
Evaluate the following $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{...
Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \ove...
Given a function $$f(x)$$ such that <br>(i) it is integrable over every interva...
Find the area of the region bounded by the $$x$$-axis and the curves defined by ...
Three identical dice are rolled. The probability that the same number will appea...
A box contains $$24$$ identical balls of which $$12$$ are white and $$12$$ are b...
If $$M$$ and $$N$$ are any two events, the probability that exactly one of them ...
In a certain city only two newspapers $$A$$ and $$B$$ are published, it is known...
$$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, ...
The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear fo...

Physics

Four person K, L, M, N are initially at the four corners of a square of side d. ...
A projectile fired from the ground follows a parabolic path. The speed of the pr...
A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of...
A simple pendulum with a bob of mass m swings with an angular amplitude of $$40^...
A body is moved along a straight line by a machine delivering constant power. Th...

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