IIT-JEE 1998

Paper was held on
Sat, Apr 11, 1998 9:00 AM

## Chemistry

An aqueous solution containing 0.10 g KIO3 (formula weight = 214.0) was treated with an excess of KI solution. The solut

View Question The orbital diagram in which the Aufbau principle is violated is

View Question The energy of an electron in the first Bohr orbit of H atom is -13.6 eV. The possible energy value(s) of the excited sta

View Question Decrease in atomic number is observed during

View Question Which of the following statement(s) is (are) correct?

View Question ASSERTION:
Nuclide $${}_{13}^{30}Al$$ is less stable than $${}_{20}^{40}Ca$$
REASON:
Nuclides having odd number of proto

View Question The geometry and the type of hybrid orbital present about the central atom in BF3 is

View Question Interpret the non-linear shape of H2S molecule and non-planar shape of PCl3 using valence shell electron pair repulsion

View Question Read the following Assertion and Reason and answer as per the options given below
Assetion: LiCl is predominantly a cov

View Question Highly pure dilute solution of sodium in liquid ammonia

View Question Work out the following using chemical equation :
Chlorination of calcium hydroxide produces bleaching powder.

View Question Hydrogen peroxide acts both as an oxidising and as a reducing agent in alkaline solution towards certain first row trans

View Question A solution of a nonvolatile solute in water freezes at -0.30oC. The vapour pressure of pure water at 298 K s 23.51 mm Hg

View Question Calculate the equilibrium constant for the reaction:
2Fe3+ + 3I- $$\leftrightharpoons$$ 2Fe2+ + $$I_3^-$$. The standard

View Question Find the solubility product of a saturated solution of Ag2CrO4 in water at 298 K if the emf of the cell Ag|Ag+ (satd. Ag

View Question The rate constant of a reaction is 1.5 $$\times$$ 107 s-1 at 50oC and 4.5 $$\times$$ 107 s-1 at 100oC. Evaluate the Arrh

View Question ## Mathematics

If $${\omega}$$ is an imaginary cube root of unity, then $${(1\, + \omega \, - {\omega ^2})^7}$$ equals

View Question The value of the sum $$\,\,\sum\limits_{n = 1}^{13} {({i^n}} + {i^{n + 1}})$$ , where i = $$\sqrt { - 1} $$, equals

View Question If $$\,\left| {\matrix{
{6i} & { - 3i} & 1 \cr
4 & {3i} & { - 1} \cr
{20} & 3 & i

View Question The number of values of $$x\,\,$$ in the interval $$\left[ {0,\,5\pi } \right]$$ satisfying the equation $$3\,{\sin ^2}x

View Question Which of the following number(s) is /are rational?

View Question Prove that $$\tan \,\alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot 8\alpha = \cot \alpha $$

View Question Number of divisor of the form 4$$n$$$$ + 2\left( {n \ge 0} \right)$$ of the integer 240 is

View Question If $${a_n} = \sum\limits_{r = 0}^n {{1 \over {{}^n{C_r}}},\,\,\,then\,\,\,\sum\limits_{r = 0}^n {{r \over {{}^n{C_r}}}}

View Question An n-digit number is a positive number with exactly digits. Nine hundred distinct n-digit numbers are to be formed using

View Question Let $$p$$ be a prime and $$m$$ a positive integer. By mathematical induction on $$m$$, or otherwise, prove that whenever

View Question Let $$n$$ be an odd integer. If $$\sin n\theta = \sum\limits_{r = 0}^n {{b_r}{{\sin }^r}\theta ,} $$ for every value of

View Question Let $${T_r}$$ be the $${r^{th}}$$ term of an A.P., for $$r=1, 2, 3, ....$$ If for some positive integers $$m$$, $$n$$ we

View Question If $$x > 1,y > 1,z > 1$$ are in G.P., then $${1 \over {1 + In\,x}},{1 \over {1 + In\,y}},{1 \over {1 + In\,z}}$

View Question The diagonals of a parralleogram $$PQRS$$ are along the lines $$x + 3y = 4$$ and $$6x - 2y = 7$$. Then $$PQRS$$ must be

View Question If $$\left( {P\left( {1,2} \right),\,Q\left( {4,6} \right),\,R\left( {5,7} \right)} \right)$$ and $$S\left( {a,b} \right

View Question If the vertices $$P, Q, R$$ of a triangle $$PQR$$ are rational points, which of the following points of the triangle $$P

View Question Using co-ordinate geometry, prove that the three altitudes of any triangle are concurrent.

View Question If the circle $${x^2}\, + \,{y^2} = \,{a^2}$$ intersects the hyperbola $$xy = {c^2}$$ in four points $$P\,({x_1},\,{y_1}

View Question The number of common tangents to the circles $${x^2}\, + \,{y^2} = 4$$ and $${x^2}\, + \,{y^2}\, - 6x\, - 8y = 24$$ is

View Question $$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C

View Question The number of values of $$c$$ such that the straight line $$y=4x + c$$ touches the curve $$\left( {{x^2}/4} \right) + {

View Question If $$P=(x, y)$$, $${F_1} = \left( {3,0} \right),\,{F_2} = \left( { - 3,0} \right)$$ and $$16{x^2} + 25{y^2} = 400,$$ the

View Question The angle between a pair of tangents drawn from a point $$P$$ to the parabola $${y^2} = 4ax$$ is $${45^ \circ }$$. Show

View Question If$$\,\,\,$$ $$y = {{a{x^2}} \over {\left( {x - a} \right)\left( {x - b} \right)\left( {x - c} \right)}} + {{bx} \over {

View Question If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then

View Question Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of th

View Question A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose $${60^ \circ }$$ an

View Question Prove that a triangle $$ABC$$ is equilateral if and only if $$\tan A + \tan B + \tan C = 3\sqrt 3 $$.

View Question The number of values of $$x$$ where the function
$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attai

View Question If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real number $$x$$, then the minimum value of $$f$$

View Question Let $$h\left( x \right) = f\left( x \right) - {\left( {f\left( x \right)} \right)^2} + {\left( {f\left( x \right)} \righ

View Question A curve $$C$$ has the property that if the tangent drawn at any point $$P$$ on $$C$$ meets the co-ordinate axes at $$A$$

View Question Suppose $$f(x)$$ is a function satisfying the following conditions
(a) $$f(0)=2,f(1)=1$$,
(b) $$f$$has a minimum value

View Question If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is

View Question Let $$f\left( x \right) = x - \left[ x \right],$$ for every real number $$x$$, where $$\left[ x \right]$$ is the integra

View Question Prove that $$\int_0^1 {{{\tan }^{ - 1}}} \,\left( {{1 \over {1 - x + {x^2}}}} \right)dx = 2\int_0^1 {{{\tan }^{ - 1}}} \

View Question The order of the differential equation whose general solution is given by
$$y = \left( {{C_1} + {C_2}} \right)\cos \left

View Question If from each of the three boxes containing $$3$$ white and $$1$$ black, $$2$$ white and $$2$$ black, $$1$$ white and $$3

View Question If $$\overline E $$ and $$\overline F $$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0

View Question If $$E$$ and $$F$$ are events with $$P\left( E \right) \le P\left( F \right)$$ and $$P\left( {E \cap F} \right) > 0,$

View Question There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random or

View Question Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed

View Question A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing o

View Question Three players, $$A,B$$ and $$C,$$ toss a coin cyclically in that order (that is $$A, B, C, A, B, C, A, B,...$$) till a h

View Question Let $${C_1}$$ and $${C_2}$$ be the graphs of the functions $$y = {x^2}$$ and $$y = 2x,$$ $$0 \le x \le 1$$ respectively.

View Question If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vector

View Question For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?

View Question Which of the following expressions are meaningful?

View Question Prove, by vector methods or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line p

View Question For any two vectors $$u$$ and $$v,$$ prove that
(a) $${\left( {u\,.\,v} \right)^2} + {\left| {u \times v} \right|^2} =

View Question ## Physics

The SI unit of inductance, the henry can be written as

View Question Let [$${\mathrm\varepsilon}_\mathrm o$$] denote the dimentional formula of the permittivity of the vacuum, and [$$\mu_o$

View Question