IIT-JEE 1984

Paper was held on
Wed, Apr 11, 1984 9:00 AM

## Chemistry

2.68 $$\times$$ 10-3 moles of a solution containing an ion An+ require 1.61 $$\times$$ 10-3 moles of $$MnO_4^-$$ for the

View Question Correct set of four quantum numbers for the valence (outermost) electron of rubidium (Z = 37) is

View Question The increasing order (lowest first) for the values of e/m (charges/mass) for electron (e), proton (p), neutron (n) and

View Question Which electronic level would allow the hydrogen atom to absorb a photon but not to emit a photon?

View Question An isotone of $${}_{32}^{76}Ge$$ is

View Question Many elements have non-integral atomic masses because:

View Question When alpha particles are sent through a thin metal foil, most of them go straight through the foil because

View Question The electron energy in hydrogen atom is given by E = (-21.7 $$\times$$ 10-12)/n2 ergs. Calculate the energy required to

View Question On hybridization of one s and one p orbitals we get:

View Question The total energy of one mole of an ideal monatomic gas at 27o is _______ calories.

View Question Cp - Cv for an ideal gas is _______

View Question Equal weights of methane and hydrogen are mixed in an empty container at 25oC. The fraction of the total pressure exerte

View Question The hydration energy of Mg++ is larger than that of:

View Question The IUPAC name of the compound having the formula is :

View Question When 16.8 g of white solid X were heated, 4.4 g of acid
gas A, that turned lime water milky was driven off together
with

View Question ## Mathematics

There exists a value of $$\theta $$ between 0 and $$2\pi $$ that satisfies the equation $$\,\,{\sin ^4}\theta - 2{\sin

View Question If the complex numbers, $${Z_1},{Z_2}$$ and $${Z_3}$$ represent the vertics of an equilateral triangle such that
$$\lef

View Question $$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}}

View Question If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, then show that (1- $${{a_1}}$$) (1- $${{a

View Question Find the values of $$x \in \left( { - \pi , + \pi } \right)$$ which satisfy the equation $${g^{(1 + \left| {\cos x} \rig

View Question For real $$x$$, the function $$\,{{\left( {x - a} \right)\left( {x - b} \right)} \over {x - c}}$$ will assume all real v

View Question If the product of the roots of the equation $$\,{x^2} - 3\,k\,x + 2\,{e^{2lnk}} - 1 = 0\,\,\,\,is\,7$$, then the roots a

View Question If a < b < c < d, then the roots of the equation (x - a) (x - c) + 2 ( x - b) (x - d) = 0 are real and distinct

View Question The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has

View Question If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval

View Question The side AB, BC and CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. The number of triangles t

View Question If $$p$$ be a natural number then prove that $${p^{n + 1}} + {\left( {p + 1} \right)^{2n - 1}}$$ is divisible by $${p^2}

View Question Given $${s_n} = 1 + q + {q^2} + ...... + {q^2};$$
$${S_n} = 1 + {{q + 1} \over 2} + {\left( {{{q + 1} \over 2}} \right)

View Question The sum of integers from 1 to 100 that are divisible by 2 or 5 is ............

View Question If $$a > 0,\,b > 0$$ and $$\,c > 0,$$ prove that $$\,c > 0,$$ prove that $$\left( {a + b + c} \right)\left(

View Question If $$n$$ is a natural number such that
$$n = {p_1}{}^{{\alpha _1}}{p_2}{}^{{\alpha _2}}.{p_3}{}^{{\alpha _3}}........{p

View Question If $$a,\,b$$ and $$c$$ are in A.P., then the straight line $$ax + by + c = 0$$ will always pass through a fixed point wh

View Question Two equal sides of an isosceles triangle are given by the equations $$7x - y + 3 = 0$$ and $$x + y - 3 = 0$$ and its thi

View Question The lines 3x - 4y + 4 = 0 and 6x - 8y - 7 = 0 are tangents to the same circle. The radius of this circle is ............

View Question The locus of the mid-point of a chord of the circle $${x^2} + {y^2} = 4$$ which subtends a right angle at the origin is

View Question The abscissa of the two points A and B are the roots of the equation $${x^2}\, + \,2ax\, - {b^2} = 0$$ and their ordinat

View Question If $$\alpha $$ be a repeated root of a quadratic equation $$f(x)=0$$ and $$A(x), B(x)$$ and $$C(x)$$ be polynomials of d

View Question For a triangle $$ABC$$ it is given that $$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilater

View Question With usual notation, if in a triangle $$ABC$$;
$${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$

View Question The numerical value of $$\tan \left\{ {2{{\tan }^{ - 1}}\left( {{1 \over 5}} \right) - {\pi \over 4}} \right\}$$ is eq

View Question For $$0 < a < x,$$ the minimum value of the function $$lo{g_a}x + {\log _x}a$$ is $$2$$.

View Question Evaluate the following $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$

View Question Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$

View Question Given a function $$f(x)$$ such that
(i) it is integrable over every interval on the real line and
(ii) $$f(t+x)=f(x),$

View Question Find the area of the region bounded by the $$x$$-axis and the curves defined by
$$$y = \tan x, - {\pi \over 3} \le x \

View Question Three identical dice are rolled. The probability that the same number will appear on each of them is

View Question A box contains $$24$$ identical balls of which $$12$$ are white and $$12$$ are black. The balls are drawn at random from

View Question If $$M$$ and $$N$$ are any two events, the probability that exactly one of them occurs is

View Question In a certain city only two newspapers $$A$$ and $$B$$ are published, it is known that $$25$$% of the city population rea

View Question $$A, B, C$$ and $$D,$$ are four points in a plane with position vectors $$a, b, c$$ and $$d$$ respectively such that
$$$

View Question The points with position vectors $$a+b,$$ $$a-b,$$ and $$a+kb$$ are collinear for all real values of $$k.$$

View Question ## Physics

Four person K, L, M, N are initially at the four corners of a square of side d. Each person now moves with a uniform spe

View Question A projectile fired from the ground follows a parabolic path. The speed of the projectile is minimum at the top of its pa

View Question A block of mass 1 kg lies on a horizontal surface in a truck. The coefficient of static friction between the block and t

View Question A simple pendulum with a bob of mass m swings with an angular amplitude of $$40^\circ $$. When its angular displacement

View Question A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in the time

View Question