IIT-JEE 1983

Which one among the following does not have the hydrogen bond?

Linear overlap of two atomic p-orbitals leads to a sigma bond.

Carbon tetrachloride has no net dipole moment because of

The types of bonds present in CuSO4.5H2O are only

Heavy water is

The absorption of hydrogen by palladium is commonly known as ______.

Complete and balance the following equation:
Ce3+ + \(S_2O_8^{-2} \to\) \(SO_4^{-2}\) + Ce4+

Complete and balance the following equations:
Cl2 + OH- \(\to\) Cl- + ClO-

Complete and balance the following equation:
Zn + \(NO_3^- \to\) Zn2+ + \(NH_4^+\)

Complete and balance the following equation:
\(Cr_2O_7^{2-}\) + C2H4O \(\to\) C2H4O2 + Cr3+

Complete and balance the following equation:
HNO3 + HCl \(\to\) NO + Cl2

An organic compound CxH2yOy was burnt with twice the amount of oxygen needed for complete combustion of CO2 and H2O. The hot gases when cooled to 0oC and 1 atm pressure, measured 2.24 litres. The water collected during cooling weighed 0.9 g...

3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molality if the solution is _____.

The density of a 3 M Sodium thiosulphate solution (Na2S2O3) is 1.25 g per ml. Calculate (i) the percentage by weight of sodium thiosulphate, (ii) the mole fraction of sodium thiosulphate and (iii) the molalities of Na+ and \(S_2O_3^{-2}\) ...

4.08 g of a mixture of BaO and an unknown carbonate MCO3 was heated strongly. The residue weighed 3.64 g. This was dissolved in 100 ml of 1 N HCl. The excess acid required 16 ml of 2.5 N NaOH solution for complete neutralization. Identify t...

The energy of the electron in the 3d-orbital is less than that in the 4s-orbital in the hydrogen atom.

The principal quantum number of an atom is related to the

Any p-orbital can accommodate upto

Elements of the same mass number but of different atomic numbers are known as ____.

Rutherford's scattering experiment is related to the size of the

Gamma rays are electromagnetic radiations of wavelengths of 10-6 to 10-5 cm

A vector \(\overrightarrow A\) has components \({A_1},{A_2},{A_3}\) in a right -handed rectangular Cartesian coordinate system \(oxyz.\) The coordinate system is rotated about the \(x\)-axis through an angle \({\pi \over 2}.\) Find the co...

The points with position vectors \(60i+3j,\) \(40i-8j,\) \(ai-52j\) are collinear if

The unit vector perpendicular to the plane determined by \(P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)\) and \(R\left( {0,2,1} \right)\) is ...........

The volume of the parallelopiped whose sides are given by
\(\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i + j - k,\,\overrightarrow {OC} = 3i - k,\) is

The area of the triangle whose vertices are \(A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)\) is ..........

Show that \(1+x\) \(In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}}\) for all \(x \ge 0\)

Find the coordinates of the point on the curve \(y = {x \over {1 + {x^2}}}\)
where the tangent to the curve has the greatest slope.

If \(y = a\,\,In\,x + b{x^2} + x\) has its extreamum values at \(x=-1\) and \(x=2\), then

The function \(y = 2{x^2} - In\,\left| x \right|\) is monotonically increasing for values of \(x\left( {x \ne 0} \right)\) satisfying the inequalities ......... and monotonically decreasing for values of \(x\) satisfying the inequalities .....

If \(x-r\) is a factor of the polynomial \(f\left( x \right) = {a_n}{x^4} + ..... + {a_0},\) repeated \(m\) times \(\left( {1 < m \le n} \right)\), then \(r\) is a root of \(\left( x \right) = 0\) repeated \(m\) times.

If \(a+b+c=0\), then the quadratic equation \(3a{x^2} + 2bx + c = 0\) has

The normal to the curve \(\,x = a\left( {\cos \theta + \theta \sin \theta } \right)\), \(y = a\left( {\sin \theta - \theta \cos \theta } \right)\) at any point \('\theta '\) is such that

The larger of \(\cos \left( {In\,\,\theta } \right)\) and \(In\) \(\left( {\cos \,\,\theta } \right)\) If \({e^{ - \pi /2}} < \theta < {\pi \over 2}\) is ..................

\(AB\) is a diameter of a circle and \(C\) is any point on the circumference of the circle. Then

Find the area bounded by the \(x\)-axis, part of the curve \(y = \left( {1 + {8 \over {{x^2}}}} \right)\) and
the ordinates at \(x=2\) and \(x=4\). If the ordinate at \(x=a\) divides the area into two equal parts, find \(a\).

The point of intersection of the line 4x - 3y - 10 = 0 and the circle \({x^2} + {y^2} - 2x + 4y - 20 = 0\) are ........................and ...................

The equation of the circle passing through (1, 1) and the points of intersection of \({x^2} + {y^2} + 13x - 3y = 0\) and \(2{x^2} + 2{y^2} + 4x - 7y - 25 = 0\) is

The centre of the circle passing through the point (0, 1) and touching the curve \(\,y = {x^2}\) at (2, 4) is

Through a fixed point (h, k) secants are drawn to the circle \(\,{x^2}\, + \,{y^2} = \,{r^2}\). Show that the locus of the mid-points of the secants intercepted by the circle is \(\,{x^2}\, + \,{y^2}\) = \(hx + ky\).

Prove that the complex numbers \({{z_1}}\), \({{z_2}}\) and the origin form an equilateral triangle only if \(z_1^2 + z_2^2 - {z_1}\,{z_2} = 0\).

If \(z = x + iy\) and \(\omega = \left( {1 - iz} \right)/\left( {z - i} \right),\) then \(\,\left| \omega \right| = 1\) implies that, in the complex plane,

The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if

Evaluate : \(\int\limits_0^{\pi /4} {{{\sin x + \cos x} \over {9 + 16\sin 2x}}dx}\)

The value of the integral \(\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx}\) is

If \(\left( {a + bx} \right){e^{y/x}} = x,\) then prove that \({x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {dx}} - y} \right)^2}\)

The derivative of an even function is always an odd function.

Evaluate : \(\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx}\)

The value of \(\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)} \right]\) is

Find all the solution of \(4\) \({\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x\)