List of practice Questions

Consider the following cell reaction
\(\text{Cd}_{(s)} + \text{Hg}_2\text{SO}_{4(s)} + \frac{9}{5} \text{H}_2\text{O}_{(l)} \rightleftharpoons \text{CdSO}_4 \cdot \frac{9}{5} \text{H}_2\text{O}_{(s)} + 2\text{Hg}_{(l)}\)
The value of \(E_{cell}^0\) is \(4.315\text{ V}\) at \(25^\circ\text{C}\). If \(\Delta H^0 = -825.2\text{ kJ mol}^{-1}\), the standard entropy change \(\Delta S^0\) in J K\(^{-1}\) is \(\dots\dots\dots\). (Nearest integer)
[Given : Faraday constant = \(96487\text{ C mol}^{-1}\)]

For a first order reaction, the ratio of the time for \(75%\) completion of a reaction to the time for \(50%\) completion is \(\dots\dots\dots\). (Integer answer)

The number of halogen/(s) forming halic (V) acid is ____________

The number of hydrogen bonded water molecule(s) associated with stoichiometry \( CuSO_4 \cdot 5H_2O \) is ____________

The total number of reagents from those given below, that can convert nitrobenzene into aniline is ___________. (Integer answer)
I. \( Sn - HCl \)
II. \( Sn - NH_4OH \)
III. \( Fe - HCl \)
IV. \( Zn - HCl \)
V. \( H_2 - Pd \)
VI. \( H_2 - Raney \ Nickel \)}

Consider the sulphides \( HgS, PbS, CuS, Sb_2S_3, As_2S_3 \) and \( CdS \). Number of these sulphides soluble in \( 50% \ HNO_3 \) is _____________

Which of the following is not correct for relation \( R \) on the set of real numbers?

The number of real roots of the equation \( e^{4x} + 2e^{3x} - e^x - 6 = 0 \) is :

If \( a_r = \cos\frac{2r\pi}{9} + i \sin\frac{2r\pi}{9}, r = 1, 2, 3, \dots, i = \sqrt{-1} \), then the determinant \( \begin{vmatrix} a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9 \end{vmatrix} \) is equal to :

If the following system of linear equations
\( 2x + y + z = 5 \)
\( x - y + z = 3 \)
\( x + y + az = b \)
has no solution, then :

The sum of 10 terms of the series \( \frac{3}{1^2 \times 2^2} + \frac{5}{2^2 \times 3^2} + \frac{7}{3^2 \times 4^2} + \dots \) is :

If the function

is continuous at \(x = 0\), then \(\frac{1}{a} + \frac{1}{b} + \frac{4}{k}\) is equal to :}

The function \(f(x) = |x^2 - 2x - 3| \cdot e^{|9x^2 - 12x + 4|}\) is not differentiable at exactly :

The integral \(\int \frac{1}{\sqrt[4]{(x - 1)^3 (x + 2)^5}} \, dx\) is equal to :
(where C is a constant of integration)

If \(\frac{dy}{dx} = \frac{2^{x+y} - 2^x}{2^y}\), \(y(0) = 1\), then \(y(1)\) is equal to :

If \(p\) and \(q\) are the lengths of the perpendiculars from the origin on the lines, \(x \csc \alpha - y \sec \alpha = k \cot 2\alpha\) and \(x \sin \alpha + y \cos \alpha = k \sin 2\alpha\) respectively, then \(k^2\) is equal to :

The length of the latus rectum of a parabola, whose vertex and focus are on the positive \(x\)-axis at a distance \(R\) and \(S\) (\(S>R\)) respectively from the origin, is :

The line \(12x \cos \theta + 5y \sin \theta = 60\) is tangent to which of the following curves ?

Let the equation of the plane, that passes through the point \((1, 4, -3)\) and contains the line of intersection of the planes \(3x - 2y + 4z - 7 = 0\) and \(x + 5y - 2z + 9 = 0\), be \(\alpha x + \beta y + \gamma z + 3 = 0\), then \(\alpha + \beta + \gamma\) is equal to :

A vertical pole fixed to the horizontal ground is divided in the ratio \(3 : 7\) by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a point on the ground \(18\text{ m}\) away from the base of the pole, then the height of the pole (in meters) is :

If \(\left(\frac{3^6}{4^4}\right)k\) is the term independent of \(x\) in the binomial expansion of \(\left(\frac{x}{4} - \frac{12}{x^2}\right)^{12}\), then \(k\) is equal to ___________

A point \(z\) moves in the complex plane such that \(\arg\left(\frac{z-2}{z+2}\right) = \frac{\pi}{4}\), then the minimum value of \(|z - 9\sqrt{2} - 2i|^2\) is equal to _________

If 'R' is the least value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is increasing on \([1, 2]\) and 'S' is the greatest value of 'a' such that the function \(f(x) = x^2 + ax + 1\) is decreasing on \([1, 2]\), then the value of \(|R-S|\) is \dots\dots.

Let \([t]\) denote the greatest integer \(\leq t\). Then the value of \(8 \cdot \int_{-1/2}^{1} ([2x] + |x|) \, dx\) is _________

If \(x \phi(x) = \int_{5}^{x} (3t^2 - 2\phi'(t))dt\), \(x>-2\), and \(\phi(0)=4\), then \(\phi(2)\) is ___________