IIT-JEE 1982

Paper was held on
Sun, Apr 11, 1982 9:00 AM

## Chemistry

The oxidation number of carbon in CH2O is

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Hydroxylamine reduces iron (III) according to the equation:
2NH2OH + 4Fe3+ $$\to$$ N2O(g) $$ \uparrow $$ + H2O + 4Fe2+

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The mass of a hydrogen atom is ______ kg.

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Isotopes of an element differ in the number of ______ in their nuclei.

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When there are two electrons in the same orbital, they have _____ spins.

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The outer electronic configuration of the ground state chromium atom is 3d4 4s2

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Calculate the wavelength in Angstrom of the photon that is emitted when an electron in the Bohr orbit, n = 2 returns to

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The energy released when an electron is added to a neutral gaseous atom is called ______ of the atom.

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The element with the highest first ionization potential is

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There are ______ $$\pi$$ bonds in a nitrogen molecule.

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____ hybrid orbitals of nitrogen atom are involved in the formation of ammonium ion.

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The ion that is isoelectronic with CO is

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Among the following, the molecule that is linear is

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The compound with no dipole moment is

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Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average kinetic energy of a helium atom is

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At room temparature, ammonia gas at 1 atm pressure and hydrogen chloride gas at P atm pressure are allowed to effuse thr

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MgCl2.6H2O on heating give anhydrous MgCl2

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How will you prepare bleaching powder from slaked lime.

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Write down the balanced equations for the reaction when:
An alkaline solution of potassium ferricyanide is reacted with

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## Mathematics

If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\sqrt 3 } \over 2} - {i \over 2}} \right)^

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The inequality |z-4| < |z-2| represents the region given by

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Without using tables, prove that $$\left( {\sin \,{{12}^ \circ }} \right)\left( {\sin \,{{48}^ \circ }} \right)\left( {

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$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$ by $$n$$, where $$m$$ and $$n$$ are nat

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Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real solution.

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The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............

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If $$2 + i\sqrt 3 $$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,.

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The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is

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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

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If p, q, r are any real numbers, then

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The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is

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The larger of $${99^{50}} + {100^{50}}$$ and $${101^{50}}$$ is ..............

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The sum of the coefficients of the plynomial $${\left( {1 + x - 3{x^2}} \right)^{2163}}$$ is ...............

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Prove that $${7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)$$ is divisible by 25 for any natural number

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In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions, where i = 1, 2,..., k. No student gave

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Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the nu

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Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chai

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The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\,{C_3}} $$ is equal to

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The third term of a geometric progression is 4. The product of the first five terms is

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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 -

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Does there exist a geometric progression containing $$27, 8$$ and $$12$$ as three of its terms? If it exits, how many su

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$$y = {10^x}$$ is the reflection of $${\log _{10}}\,x$$ in the line whose equation is ...........

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The set of lines $$ax + by + c = 0,$$ where $$3a + 2b + 4c = 0$$ is concurrent at the point ..........

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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 canno

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$$A$$ is point on the parabola $${y^2} = 4ax$$. The normal at $$A$$ cuts the parabola again at point $$B$$. If $$AB$$ su

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If $$y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$$ and $$f'\left( x \right) = \sin {x^2}$$, then $${{dy} \over

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Let $$f$$ be a twice differentiable function such that
$$f''\left( x \right) = - f\left( x \right),$$ and $$f'\left( x

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A vertical pole stands at a point $$Q$$ on a horizontal ground. $$A$$ and $$B$$ are points on the ground, $$d$$ meters a

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If $$f(x)$$ and $$g(x)$$ are differentiable function for $$0 \le x \le 1$$ such that $$f(0)=2$$, $$g(0)=0$$, $$f(1)=6$$;

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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}

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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

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Find the value of $$\int\limits_{ - 1}^{3/2} {\left| {x\sin \,\pi \,x} \right|\,dx} $$

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Show that $$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} = {\pi \over 2}\int\limits_0^\pi {f\left( {\sin x} \righ

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For any real $$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}$$ is a point on the
hyperb

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If $$A$$ and $$B$$ are two events such that $$P\left( A \right) > 0,$$ and $$P\left( B \right) \ne 1,$$ then $$P\left

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$$A$$ and $$B$$ are two candidates seeking admission in $$IIT.$$ The probability that $$A$$ is selected is $$0.5$$ and t

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For non-zero vectors $${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow c },$$ $$\left| {\left( {\overrightarrow

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$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polygon with $$n$$ sides and $$O$$ is its cen

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Find all values of $$\lambda $$ such that $$x, y, z,$$$$\, \ne $$$$(0,0,0)$$ and
$$\left( {\overrightarrow i + \overri

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## Physics

Write the dimensions of the followings in terms of mass, time, length and charge
(i) magnetic flux
(ii) rigidity modulus

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A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity changes to 5 m/s northwards. The average ac

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In the arrangement shown in Fig. the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulley

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