Exam Details
IIT JEE 1982
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Questions
61
Duration
180 mins
Package
IIT-JEE Advance - Previous Year Papers
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61questions
Easy
34
55.7%
Medium
24
39.3%
Hard
3
4.9%
Question type distribution
61questions
MCQ
31
50.8%
Subjective
22
36.1%
Fill in the blanks
7
11.5%
Numerical Answer Type (NAT)
1
1.6%
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PYP
IIT JEE 1982
The outer electronic configuration of the ground state chromium atom is 3d4 4s2
PYP
IIT JEE 1982
MgCl2.6H2O on heating give anhydrous MgCl2
PYP
IIT JEE 1982
If p, q, r are any real numbers, then
PYP
IIT JEE 1982
At room temparature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse through identical pin holes from opposite ends of a glass tube of one metre length and of uniform cross-section. Ammonium chloride is first formed at a distance of 60 cm from the end through which HCL gas is sent in. What is the value of P?
PYP
IIT JEE 1982
Hydroxylamine reduces iron (III) according to the equation:
2NH2OH + 4Fe3+ $$\to$$ N2O(g) $$ \uparrow $$ + H2O + 4Fe2+ + 4H+
Iron (II) thus produced is estimated by titration with a standard permanganate solution. The reaction is :
$$MnO_4^-$$ + 5Fe2+ + 8H+ $$\to$$ Mn2+ + 5Fe3+ + 4H2O
A 10 ml sample of hydroxylamine solution was Diluted to 1 litre. 50 ml of this diluted solution was boiled with an excess of iron (III) solution. The resulting solution required 12 ml of 0.02 M KMnO4 solution for complete oxidation of iron (II). Calculate the weight of hydroxylamine in one litre of the original solution. (H = 1, N = 14, O = 16, K =39, Mn = 55, Fe = 56)
2NH2OH + 4Fe3+ $$\to$$ N2O(g) $$ \uparrow $$ + H2O + 4Fe2+ + 4H+
Iron (II) thus produced is estimated by titration with a standard permanganate solution. The reaction is :
$$MnO_4^-$$ + 5Fe2+ + 8H+ $$\to$$ Mn2+ + 5Fe3+ + 4H2O
A 10 ml sample of hydroxylamine solution was Diluted to 1 litre. 50 ml of this diluted solution was boiled with an excess of iron (III) solution. The resulting solution required 12 ml of 0.02 M KMnO4 solution for complete oxidation of iron (II). Calculate the weight of hydroxylamine in one litre of the original solution. (H = 1, N = 14, O = 16, K =39, Mn = 55, Fe = 56)
PYP
IIT JEE 1982
Calculate the wavelength in Angstrom of the photon that is emitted when an electron in the Bohr orbit, n = 2 returns to the orbit, n = 1 in the hydrogen atom. The ionization potential of the ground state hydrogen atom is 2.17 $$\times$$ 10-11 erg per atom.
PYP
IIT JEE 1982
$$A$$ and $$B$$ are two candidates seeking admission in $$IIT.$$ The probability that $$A$$ is selected is $$0.5$$ and the probability that both $$A$$ and $$B$$ are selected is atmost $$0.3$$. Is it possible that the probability of $$B$$ getting selected is $$0.9$$ ?
PYP
IIT JEE 1982
Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.
PYP
IIT JEE 1982
Prove that $${7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)$$ is divisible by 25 for any natural number $$n$$.
PYP
IIT JEE 1982
$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are natural numbers. Two squares will be called ' neighbours ' if they have exactly one common side. A natural number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighbouring squares.Show that this is possible only if all the numbers used are equal.
PYP
IIT JEE 1982
Without using tables, prove that $$\left( {\sin \,{{12}^ \circ }} \right)\left( {\sin \,{{48}^ \circ }} \right)\left( {\sin \,{{54}^ \circ }} \right) = {1 \over 8}.$$
PYP
IIT JEE 1982
Let $$f$$ be a twice differentiable function such that
$$f''\left( x \right) = - f\left( x \right),$$ and $$f'\left( x \right) = g\left( x \right),h\left( x \right) = {\left[ {f\left( x \right)} \right]^2} + {\left[ {g\left( x \right)} \right]^2}$$
Find $$h\left( {10} \right)$$ if $$h(5)=11$$
PYP
IIT JEE 1982
$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polygon with $$n$$ sides and $$O$$ is its centre. Show that
$$\sum\limits_{i = 1}^{n - 1} {\left( {\overrightarrow {O{A_i}} \times {{\overrightarrow {OA} }_{i + 1}}} \right) = \left( {1 - n} \right)\left( {{{\overrightarrow {OA} }_2} \times {{\overrightarrow {OA} }_1}} \right)} $$
$$\sum\limits_{i = 1}^{n - 1} {\left( {\overrightarrow {O{A_i}} \times {{\overrightarrow {OA} }_{i + 1}}} \right) = \left( {1 - n} \right)\left( {{{\overrightarrow {OA} }_2} \times {{\overrightarrow {OA} }_1}} \right)} $$
PYP
IIT JEE 1982
If $$a{x^2} + {b \over x} \ge c$$ for all positive $$x$$ where $$a>0$$ and $$b>0$$ show that $$27a{b^2} \ge 4{c^3}$$.
PYP
IIT JEE 1982
If $$f(x)$$ and $$g(x)$$ are differentiable function for $$0 \le x \le 1$$ such that $$f(0)=2$$, $$g(0)=0$$, $$f(1)=6$$; $$g(1)=2$$, then show that there exist $$c$$ satisfying $$0 < c < 1$$ and $$f'(c)=2g'(c)$$.
PYP
IIT JEE 1982
For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
hyperbola $${x^2} - {y^2} = 1$$. Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to $${t_1}$$ and $$-{t_1}$$ is $${t_1}$$.
PYP
IIT JEE 1982
There are ______ $$\pi$$ bonds in a nitrogen molecule.
PYP
IIT JEE 1982
Show that $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} = {\pi \over 2}\int\limits_0^\pi {f\left( {\sin x} \right)dx.} $$
PYP
IIT JEE 1982
Isotopes of an element differ in the number of ______ in their nuclei.
PYP
IIT JEE 1982
____ hybrid orbitals of nitrogen atom are involved in the formation of ammonium ion.
PYP
IIT JEE 1982
If $$2 + i\sqrt 3 $$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,....................).
PYP
IIT JEE 1982
The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............
PYP
IIT JEE 1982
$$y = {10^x}$$ is the reflection of $${\log _{10}}\,x$$ in the line whose equation is ...........
PYP
IIT JEE 1982
The sum of the coefficients of the plynomial $${\left( {1 + x - 3{x^2}} \right)^{2163}}$$ is ...............
PYP
IIT JEE 1982
In the arrangement shown in Fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed.
Mass M moves upwards with a speed
Mass M moves upwards with a speed
PYP
IIT JEE 1982
The oxidation number of carbon in CH2O is
PYP
IIT JEE 1982
The ion that is isoelectronic with CO is
PYP
IIT JEE 1982
If A and B are points in the plane such that PA/PB = k (constant) for all P on a given circle, then the value of k cannot be equal to ..........................................
PYP
IIT JEE 1982
A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average acceleration in this time is
PYP
IIT JEE 1982
The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is
PYP
IIT JEE 1982
Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is
PYP
IIT JEE 1982
The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is
PYP
IIT JEE 1982
The element with the highest first ionization potential is
PYP
IIT JEE 1982
The compound with no dipole moment is
PYP
IIT JEE 1982
Among the following, the molecule that is linear is
PYP
IIT JEE 1982
Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at
PYP
IIT JEE 1982
If $$x,\,y$$ and $$z$$ are $$pth$$, $$qth$$ and $$rth$$ terms respectively of an A.P. and also of a G.P., then $${x^{y - z}}\,{y^{z - x}}\,{z^{x - y}}$$ is equal to :
PYP
IIT JEE 1982
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated are
PYP
IIT JEE 1982
The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to
PYP
IIT JEE 1982
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4; and then the men select the chairs from amongst the remaining. The number of possible arrangements is
PYP
IIT JEE 1982
The third term of a geometric progression is 4. The product of the first five terms is
PYP
IIT JEE 1982
If $$A$$ and $$B$$ are two events such that $$P\left( A \right) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left( {{{\overline A } \over {\overline B }}} \right)$$ is equal to
PYP
IIT JEE 1982
For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right).\overrightarrow c } \right| = \left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|\left| {\overrightarrow c } \right|$$ holds if and only if
PYP
IIT JEE 1982
The inequality |z-4| < |z-2| represents the region given by
PYP
IIT JEE 1982
The area bounded by the curves $$y=f(x)$$, the $$x$$-axis and the ordinates $$x=1$$ and $$x=b$$ is $$(b-1)$$ sin $$(3b+4)$$. Then $$f(x)$$ is
PYP
IIT JEE 1982
If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^5},$$ then
PYP
IIT JEE 1982
Write the dimensions of the followings in terms of mass, time, length and charge
(i) magnetic flux
(ii) rigidity modulus
(i) magnetic flux
(ii) rigidity modulus
PYP
IIT JEE 1982
The mass of a hydrogen atom is ______ kg.
PYP
IIT JEE 1982
When there are two electrons in the same orbital, they have _____ spins.
PYP
IIT JEE 1982
The energy released when an electron is added to a neutral gaseous atom is called ______ of the atom.
PYP
IIT JEE 1982
How will you prepare bleaching powder from slaked lime.
PYP
IIT JEE 1982
Write down the balanced equations for the reaction when:
An alkaline solution of potassium ferricyanide is reacted with hydrogen peroxide.
An alkaline solution of potassium ferricyanide is reacted with hydrogen peroxide.
PYP
IIT JEE 1982
Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many such progressions are possible ?
PYP
IIT JEE 1982
The larger of $${99^{50}} + {100^{50}}$$ and $${101^{50}}$$ is ..............
PYP
IIT JEE 1982
In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave more than k wrong answers. The total number of wrong answers given is.....................................
PYP
IIT JEE 1982
Find all values of $$\lambda $$ such that $$x, y, z,$$$$\, \ne $$$$(0,0,0)$$ and
$$\left( {\overrightarrow i + \overrightarrow j + 3\overrightarrow k } \right)x + \left( {3\overrightarrow i - 3\overrightarrow j + \overrightarrow k } \right)y + \left( { - 4\overrightarrow i + 5\overrightarrow j } \right)z$$
$$ = \lambda \left( {x\overrightarrow i \times \overrightarrow j \,\,y + \overrightarrow k \,z} \right)$$ where $$\overrightarrow i ,\,\,\overrightarrow j ,\,\,\overrightarrow k $$ are unit vectors along the coordinate axes.
$$\left( {\overrightarrow i + \overrightarrow j + 3\overrightarrow k } \right)x + \left( {3\overrightarrow i - 3\overrightarrow j + \overrightarrow k } \right)y + \left( { - 4\overrightarrow i + 5\overrightarrow j } \right)z$$
$$ = \lambda \left( {x\overrightarrow i \times \overrightarrow j \,\,y + \overrightarrow k \,z} \right)$$ where $$\overrightarrow i ,\,\,\overrightarrow j ,\,\,\overrightarrow k $$ are unit vectors along the coordinate axes.
PYP
IIT JEE 1982
A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters apart. The pole subtends angles $$\alpha $$ and $$\beta $$ at $$A$$ and $$B$$ respectively. $$AB$$ subtends an angle $$\gamma $$ and $$Q$$. Find the height of the pole.
PYP
IIT JEE 1982
The set of lines $$ax + by + c = 0,$$ where $$3a + 2b + 4c = 0$$ is concurrent at the point ..........
PYP
IIT JEE 1982
$$A$$ is point on the parabola $${y^2} = 4ax$$. The normal at $$A$$ cuts the parabola again at point $$B$$. If $$AB$$ subtends a right angle at the vertex of the parabola. Find the slope of $$AB$$.
PYP
IIT JEE 1982
If $$y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$$ and $$f'\left( x \right) = \sin {x^2}$$, then $${{dy} \over {dx}} = ..........$$
PYP
IIT JEE 1982
Find the value of $$\int\limits_{ - 1}^{3/2} {\left| {x\sin \,\pi \,x} \right|\,dx} $$
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