List of practice Questions

The sum of two roots of the equation \(x^4 - x^3 - 16x^2 + 4x + 48 = 0\) is zero. If \(\alpha, \beta, \gamma, \delta\) are the roots of this equation, then \(\alpha^4 + \beta^4 + \gamma^4 + \delta^4\) is:
If \( \alpha, \beta \) (\(\alpha<\beta\)) are the values of \( x \) such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of \( 2\alpha + 3\beta + 4\gamma \) is:
Given the two parabolas: \[ S = y^2 - 4ax = 0, \quad S' = y^2 + ax = 0 \] where \( P(t) \) is a point on the parabola \( S' = 0 \). If \( A \) and \( B \) are the feet of the perpendiculars from \( P \) to the coordinate axes and \( AB \) is a tangent to the parabola \( S = 0 \) at the point \( Q(t_1) \), then the value of \( t_1 \) is:
If \( A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} \) is a singular matrix, then the quadratic equation having the roots \( k \) and \( \frac{1}{k} \) is:
An aircraft executes a horizontal loop of radius 9 km at a constant speed of 540 km/h. The wings of the aircraft are banked at an angle of
Which of the following steps are not involved in gravimetric analysis:
A(1, -2, 1) and B(2, -1, 2) are the end points of a line segment. If \(D(\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from \(C(1, 2, 3)\) to AB, then \(\alpha^2 + \beta^2 + \gamma^2 =\)
An organic compound containing phosphorus on oxidation with \( Na_2O_2 \) gives a compound \( X \). When \( X \) is boiled with \( HNO_3 \) and treated with a reagent, it gives a yellow precipitate \( Y \). Identify \( X \) and \( Y \).
If \( A = \begin{bmatrix} 1 & 8 \\ 0 & 1 \end{bmatrix} \), then \( A^8 = \)

Staying in comfort at home gives one more happiness than travelling.
 

Match the persons given in column 'A' with opinions/characteristics given in column 'B' 



 

The wavenumber of the first spectral line of the Lyman series of He\(^+\) ion is \( x \) m\(^{-1}\). What is the wavenumber (in m\(^{-1}\)) of the second spectral line of the Balmer series of Li\(^{2+}\) ion?
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
Choose the correct statements from the following: I) In vapour phase, \( BeCl_2 \) exists as a chlorobridged dimer.
II) \( BeSO_4 \) is readily soluble in water.
III) \( BeO \) is completely basic in nature.
IV) \( BeCO_3 \), being unstable, is kept in the atmosphere of \( CO_2 \).
V) \( BeCO_3 \) is less soluble among all the carbonates of group 2 elements.
Observe the following species: (i) \( NH_3 \) (ii) \( AlCl_3 \) (iii) \( SnCl_4 \) (iv) \( CO_2 \) (v) \( Ag^+ \) (vi) \( HSO_4^- \) How many of the above species act as Lewis acids?
P is a variable point such that the distance of P from A(4,0) is twice the distance of P from B(-4,0). If the line \( 3y - 3x - 20 = 0 \) intersects the locus of P at the points C and D, then the distance between C and D is:
A massless spring of length \( l \) and spring constant \( k \) oscillates with a time period \( T \) when loaded with a mass \( m \). The spring is now cut into three equal parts and connected in parallel. The frequency of oscillation of the combination when it is loaded with a mass \( 4m \) is: \vspace{0.5cm}
In \( \triangle ABC \), if \( AB:BC:CA = 6:4.5 \), then \( R : r = \)
The normality of a 20-volume solution of hydrogen peroxide is:

In the given reaction sequence, identify Z.

Reaction of conversion of Y to Z in the given reaction corresponds to: 

A solid is dissolved in 1 L water. The enthalpy of its solution (\(\Delta H_{{sol}}^\circ\)) is 'x' kJ/mol. The hydration enthalpy (\(\Delta H_{{hyd}}^\circ\)) for the same reaction is 'y' kJ/mol. What is lattice enthalpy (\(\Delta H_{{lattice}}^\circ\)) of the solid in kJ/mol? 

The region in the output voltage versus input voltage graph where a transistor can be used as an amplifier is?
The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is 100 Hz. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is:
A solid sphere rolls down without slipping from the top of an inclined plane of height 28 m and angle of inclination 30°. The velocity of the sphere when it reaches the bottom of the plane is (Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \))