List of practice Questions

Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
The points in the Argand plane represented by the complex numbers \(4\hat{i}+3\hat{j}\), \(6\hat{i}-2\hat{j}-3\hat{k}\) and \(\hat{i}-\hat{j}-3\hat{k}\) form
If \( z = x+iy \) and \(x^2+y^2=1\), then \( \frac{1+x+iy}{1+x-iy} = \)
If \( x^6 = (\sqrt{3}-i)^5 \), then the product of all of its roots is
If \( \alpha \neq 0 \) and zero are the roots of the equation \( x^2 - 5kx + (6k^2-2k) = 0 \), then \( \alpha = \)
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is
\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
If \( A = \begin{pmatrix} 1 & 2 & 3 \\ 1 & 3 & 5 \\ 2 & 1 & 6 \end{pmatrix} \) and \( |adj(adj(A))|(adj A)^{-1} = kA \), then k =
Match the following polymers with their applications: \begin{center} \begin{tabular}{|c|c|} \hline List-I (Polymer) & List-II (Used in making)
\hline
Match the following polymers with their applications:
The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm. At \( T \)(K), the gas pressure is \( 2 \) atm. What is the value of \( \frac{x}{m} \)? (\( n = 2 \) and \( k \) = constant)
Consider the following: Statement-I: In the extraction of Al by Hall-Heroult process, pure \( Al_2O_3 \) mixed with \( Na_3AlF_6 \) lowers its melting point and increases conductivity. Statement-II: Zirconium metal is purified by zone refining method. The correct answer is:
Which of the following is not correct?
In which one of the following complexes the metal ion has \( t_{2g}^3 e_g^2 \) configuration?
The composition of a sample of wustite is \( \text{Fe}_{0.93} \text{O}_{1.00} \). Percentage of iron in the form of \( \text{Fe}^{3+} \) ion is nearly:
Consider the following gaseous equilibrium reactions (I), (II) and (III) with equilibrium constants \( K_1 \), \( K_2 \), and \( K_3 \) respectively:
I) \( \frac{1}{2} N_2 + \frac{3}{2} H_2 \rightleftharpoons NH_3 \)
II) \( 2NO \rightleftharpoons N_2 + O_2 \)
III) \( H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2O \)
The correct expression for the equilibrium constant for the gaseous equilibrium reaction: \[ 2NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2NO + 3H_2O \]
Which set of elements form electron-precise hydrides?
The correct order of density of Be, Mg, Ca, Sr is:
Identify the reaction in which diborane is produced on an industrial scale:
Match the following pollutant concentration limits in water with their effects:
The sum of bond order values of \( C_2 \) and \( O_2^{2-} \) is \( x \), which is equal to the sum of bond order values of \( a, b, \) and \( c \). What are \( a, b, \) and \( c \)?
At \( 27^\circ C \) kinetic energy of 4 g of \( H_2 \) is \( x \) J. What is the kinetic energy (in J) of 6.4 g of oxygen at \( 127^\circ C \)?
A long straight wire of circular cross-section of radius \( a \) is carrying a steady current. The current is distributed uniformly across the cross-section of the wire. The ratio of the magnetic fields at points \( 0.5a \) and \( 1.5a \) from the centre of the wire is:
If a wheel with 24 metallic spokes each \( 40 \) cm long is rotated with a speed of \( 180 \) rev/min in a plane normal to the horizontal component of Earth's magnetic field, the emf induced between the axle and the rim of the wheel is \( E \). If the number of spokes is made \( 12 \) and the wheel is rotated with a speed of \( 90 \) rev/min in the same field, the induced emf is: