IIT-JEE 1996

Paper was held on
Thu, Apr 11, 1996 9:00 AM

## Chemistry

A 3.00 g sample containing Fe3O4, Fe2O3 and an inert impure substance is treated with excess of KI solution in presence

View Question The orbital angular momentum of an electron in 2s orbital is

View Question Calculate the wave number for the shortest wavelength transition in the Balmer series of atomic hydrogen.

View Question Consider the hydrogen atom to be a proton embedded in a cavity of radius a0 (Bohr radius) whose charge is neutralised by

View Question Which of the following has the maximum number of unpaired electrons?

View Question When N2, the N-N bond distance _____ and when O2 goes to $$O_2^+$$ the O-O bond distance ___.

View Question The number and type of bonds between two carbon atoms in CaC2 are:

View Question Among the following species, identity the isostructural pairs NF3, $$NO_3^-$$, BF3, H3O+ , HN3

View Question A mixture of ideal gas is cooled upto liquid helium temperature (4.22K) to form an ideal solution

View Question The following compounds have been arranged in order of their increasing thermal stabilities. Identify the correct order

View Question Explain the difference in the nature of bonding in LiF and LiI.

View Question The molar volume of liquid benzene (density = 0.877 g mL-1) increases by a factor of 2750 as it vaporises at 20oC and th

View Question The standard reduction potential for Cu2+|Cu is +0.34 V. Calculate the reduction potential at pH = 14 for the above coup

View Question The ionisation constant of $$NH_4^+$$ in water is 5.6 $$\times$$ 10-10 at 25oC. The rate constant for the reaction of $$

View Question ## Mathematics

General value of $$\theta $$ satisfying the equation $${\tan ^2}\theta + \sec \,2\,\theta = 1$$ is _________.

View Question $${\sec ^2}\theta = {{4xy} \over {{{\left( {x + y} \right)}^2}}}\,$$ is true if and only if

View Question The value of the expression
$$1 \bullet \left( {2 - \omega } \right)\left( {2 - {\omega ^2}} \right) + 2 \bullet \left(

View Question For positive integers $${n_1},\,{n_2}$$ the value of the expression $${\left( {1 + i} \right)^{^{{n_1}}}} + {\left( {1 +

View Question Find all non-zero complex numbers Z satisfying $$\overline Z = i{Z^2}$$.

View Question Find all values of $$\theta $$ in the interval $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ satisfying the equ

View Question Let n and k be positive such that $$n \ge {{k(k + 1)} \over 2}$$ . The number of solutions $$\,({x_1},\,{x_2},\,.....{x_

View Question Using mathematical induction prove that for every integer $$n \ge 1,\,\,\left( {{3^{2n}} - 1} \right)$$ is divisible by

View Question For any odd integer $$n$$ $$ \ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3

View Question The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are i

View Question A rectangle $$PQRS$$ has its side $$PQ$$ parallel to the line $$y = mx$$ and vertices $$P, Q$$ and $$S$$ on the lines $$

View Question The intercept on the line y = x by the circle $${x^2} + {y^2} - 2x = 0$$ is AB. Equation of the circle with AB as a dia

View Question The angle between a pair of tangents drawn from a point P to the circle $${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,

View Question A circle passes through three points A, B and C with the line segment AC as its diameter. A line passing through A angle

View Question Find the intervals of value of a for which the line y + x = 0 bisects two chords drawn from a point $$\left( {{{1\, + \,

View Question An ellipse has eccentricity $${1 \over 2}$$ and one focus at the point $$P\left( {{1 \over 2},1} \right)$$. Its one dire

View Question Points $$A, B$$ and $$C$$ lie on the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$A, B$$ and $$C$$, taken

View Question From a point $$A$$ common tangents are drawn to the circle $${x^2} + {y^2} = {a^2}/2$$ and parabola $${y^2} = 4ax$$. Fin

View Question If $$x{e^{xy}} = y + {\sin ^2}x,$$ then at $$x = 0,{{dy} \over {dx}} = ..............$$

View Question In a triangle $$ABC$$, $$a:b:c=4:5:6$$. The ratio of the radius of the circumcircle to that of the incircle is .........

View Question A curve $$y=f(x)$$ passes through the point $$P(1, 1)$$. The normal to the curve at $$P$$ is $$a(y-1)+(x-1)=0$$. If the

View Question Determine the points of maxima and minima of the function
$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x >

View Question Let $$f\left( x \right) = \left\{ {\matrix{
{x{e^{ax}},\,\,\,\,\,\,\,x \le 0} \cr
{x + a{x^2} - {x^3},\,x > 0

View Question Evaluate $$\int {{{\left( {x + 1} \right)} \over {x{{\left( {1 + x{e^x}} \right)}^2}}}dx} $$.

View Question If for nonzero $$x$$, $$af(x)+$$ $$bf\left( {{1 \over x}} \right) = {1 \over x} - 5$$ where $$a \ne b,$$ then
$$\int_1^

View Question For $$n>0,$$ $$\int_0^{2\pi } {{{x{{\sin }^{2n}}x} \over {{{\sin }^{2n}}x + {{\cos }^{2n}}x}}} dx = $$

View Question Let $${A_n}$$ be the area bounded by the curve $$y = {\left( {\tan x} \right)^n}$$ and the
lines $$x=0,$$ $$y=0,$$ and

View Question Determine the equation of the curve passing through the origin, in the form $$y=f(x),$$ which satisfies the differential

View Question For the three events $$A, B,$$ and $$C,P$$ (exactly one of the events $$A$$ or $$B$$ occurs) $$=P$$ (exactly one of the

View Question In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, $$3$$ in the front an

View Question A nonzero vector $$\overrightarrow a $$ is parallel to the line of intersection of the plane determined by the vectors $

View Question If $$\overrightarrow b \,$$ and $$\overrightarrow c \,$$ are two non-collinear unit vectors and $$\overrightarrow a \,$$

View Question The position vectors of the vertices $$A, B$$ and $$C$$ of a tetrahedron $$ABCD$$ are $$\widehat i + \widehat j + \wideh

View Question ## Physics

Two guns, situated on the top of a hill of height 10 m, fire one shot each with the same speed $$5\sqrt 3 $$ m s-1 at so

View Question