IIT-JEE 1991

The hybridization of carbon atoms in C-C single bond of HC \(\equiv\) C - CH = CH2 is

Write the IUPAC name for the following :

Arrange the following :
Increasing strength of hydrogen bonding (X-H-X):
O, S, F, Cl, N

The linear structure is assumed by :

The decomposition of N2O5 according to the equation:
2N2O5 (g) \(\to\) 4NO2(g) + O2(g)
is a first order reaction. After 30 min. from the start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm of ...

Zinc granules are added in excess to a 500 ml. of 1.0 M nickel nitrate solution at 25oC until the equilibrium is reached. If the standard reduction potential of Zn2+ | Zn and Ni2+ | Ni are -0.75 V and -0.24 V respectively, find out the conc...

The current of 1.70 A is passed through 300.0 ml of 0.160 M solution of a ZnSO4 for 230 sec. with a current efficiency of 90%. Find out the molarity of Zn2+ after the deposition of Zn. Assume the volume of the solution to remain constant du...

Calculate the volume occupied by 5.0 g of acetylene gas at 50oC and 740 mm pressure.

Arrange of the following in :
Increasing order of ionic size:
N3-, Na+, F-, O2-, Mg2+

Arrange of the following in :
Increasing order of basic character
MgO, SrO, K2O, NiO, Cs2O

Arrange of the following in :
Arrange the following ions in order of their increasing radii:
Li+, Mg2+, K+, Al3+

The volume strength of 1.5 N H2O2 solution is

Write down the balanced equation for the reaction when:
Carbon dioxide is passed through a suspension of lime stone in water.

The degree of dissociation of calcium nitrate in a dilute aqueous solution, containing 7.0 g. of the salt per 100 gm of water at 100oC is 70%. If the vapour pressure of water at 100oC is 760 mm, calculate the vapour pressure of the solution...

The weight of \(1 \times 10^{22}\) molecules of CuSO4.5H2O is ____.

A 1.0 g sample of Fe2O3 solid of 55.2% purity is dissolved in acid and reduced by heating the solution with zinc dust. The resultant solution is cooled and made upto 100.0 ml. An aliquot of 25.0 ml of this solution requires 17.0 ml of 0.016...

A solution of 0.2 g of a compound containing Cu2+ and \(C_2O_4^{2-}\) ions on titration with 0.02M \(KMnO_4\) in presence of \(H_2SO_4\) consumes 22.6 ml. of the oxidant. The resultant solution in neutralized with Na2CO3, acidified with di...

The oxidation state of the most electronegative element in the products of the reaction. BaO2 with dil. H2SO4 are

Read the following statement and explanation and answer as per the options given below:
STATEMENT (S): In the titration of Na2CO3 with HCl using methyl orange indicator, the volume required at the equivalence point is twice that of the acid...

A window of perimeter \(P\) (including the base of the arch) is in the form of a rectangle surmounded by a semi circle. The semi-circular portion is fitted with coloured glass while the rectangular part is fitted with clear glass transmits ...

Sketch the curves and identify the region bounded by
\(x = {1 \over 2},x = 2,y = \ln \,x\) and \(y = {2^x}.\) Find the area of this region.

If \('f\) is a continuous function with \(\int\limits_0^x {f\left( t \right)dt \to \infty }\) as \(\left| x \right| \to \infty ,\) then show that every line \(y=mx\)

intersects the curve $${y^2} + \int\limits_0^x {f\left( t \right)dt = ...

Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y = 10, find the equation of the circles.

If a circle passes through the points of intersection of the coordinate axes with the lines \(\lambda \,x - y + 1 = 0\) and x - 2y + 3 = 0, then the value of \(\lambda\) = .........

Evaluate \(\,\int\limits_0^\pi {{{x\,\sin \,2x\,\sin \left( {{\pi \over 2}\cos x} \right)} \over {2x - \pi }}dx}\)

Find \({{{dy} \over {dx}}}\) at \(x=-1\), when
\({\left( {\sin y} \right)^{\sin \left( {{\pi \over 2}x} \right)}} + {{\sqrt 3 } \over 2}{\sec ^{ - 1}}\left( {2x} \right) + {2^x}\tan \left( {In\left( {x + 2} \right)} \right) = 0\)

Using induction or otherwise, prove that for any non-negative integers \(m\), \(n\), \(r\) and \(k\) ,
$$\sum\limits_{m = 0}^k {\left( {n - m} \right)} {{\left( {r + m} \right)!} \over {m!}} = {{\left( {r + k + 1} \right)!} \over {k!}}\left...

Three normals are drawn from the point \((c, 0)\) to the curve \({y^2} = x.\) Show that \(c\) must be greater than \(1/2\). One normal is always the \(x\)-axis. Find \(c\) for which the other two normals are perpendicular to each other.

Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the sitting arrangements can be made...

In a test an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The probability that he make a guess is \(1/3\) and the probability that he copies the answer is \(1/6\). The probability th...

If the mean and the variance of binomial variate \(X\) are \(2\) and \(1\) respectively, then the probability that \(X\) takes a value greater than one is equal to ...............

For any two events \(A\) and \(B\) in a simple space

In a triangle of base a the ratio of the other two sides is \(r\left( { < 1} \right)\). Show that the altitude of the triangle is less than of equal to \({{ar} \over {1 - {r^2}}}\)

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine the sides of the triangle.

A man notices two objects in a straight line due west. After walking a distance \(c\) due north he observes that the objects subtend an angle \(\alpha\) at his eye; and, after walking a further distance \(2c\) due north, an angle $$\beta ...

The product of \(n\) positive numbers is unity. Then their sum is

If \({S_1}\), \({S_2}\), \({S_3}\),.............,\({S_n}\) are the sums of infinite geometric series whose first terms are 1, 2, 3, ...................,n and whose common ratios are \({1 \over 2}\), \({1 \over 3}\), \({1 \over 4}\),...........

Let p be the first of the n arithmetic means between two numbers and q the first of n harmonic means between the same numbers. Show that q does not lie between p and \(\,{\left( {{{n + 1} \over {n - 1}}} \right)^2}\,p\).

Find the equation of the line passing through the point \((2, 3)\) and making intercept of length 2 units between the lines \(y + 2x = 3\) and \(y + 2x = 5\).

Show that all chords of the curve \(3{x^2} - {y^2} - 2x + 4y = 0,\) which subtend a right angle at the origin, pass through a fixed point. Find the coordinates of the point.

Let the algebraic sum of the perpendicular distances from the points \(\left( {2,0} \right),\,\left( {0,\,2} \right)\) \(\left( {1,\,1} \right)\) to a variable straight line be zero; then the line passes through a fixed point whose cordinat...

If \(\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \right)\,In\,\,2} \right)} \right\}\) satiesfies the equation \({x^2} - 9x + 8 = 0,\) find the value of $${{\cos x} \over {\...

The value of
\(\sin {\pi \over {14}}\sin {{3\pi } \over {14}}\sin {{5\pi } \over {14}}\sin {{7\pi } \over {14}}\sin {{9\pi } \over {14}}\sin {{11\pi } \over {14}}\sin {{13\pi } \over {14}}\) is equal to ______.

Given that \(\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overrightarrow a .\overrightarrow b = 3\) and \(\overrightarrow a \times \overrightarrow b = \overrightarrow c ,\) then $$\ove...

Determine the value of \('c'\) so that for all real \(x,\) the vector
\(cx\widehat i - 6\widehat j - 3\widehat k\) and \(x\widehat i + 2\widehat j + 2cx\widehat k\) make an obtuse angle with each other.