List of practice Questions

If \(α,β,γ\) are the roots of \(4x^3-6x^2+7x+3=0\), then the value of \(αβ+βγ+γα\) is

A steel deck plate of a tanker is supported by two longitudinal stiffeners as shown in the figure. The width of the plate is \( a \) and its length is 5 times the width. Assume that the long edge is simply supported, and the short edge is free. The plate is loaded by a distributed pressure, \( p = p_0 \sin\left(\frac{\pi y}{a}\right) \), where \( p_0 \) is the pressure at \( y = a/2 \). The flexural rigidity of the plate is \( D \). The plate equation is given by

If \(2\) is a root of the equation \(x^2-px+q=0\) and \(p^2=4q\), then the other root is

If the coefficients of the \( r^{th} \), \( (r+1)^{th \), and \( (r+2)^{th} \) terms in the expansion of \( (1 + x)^n \) are in the ratio \( 4:15:42 \), then \( n - r \) is:}

The rank of matrix \(\begin{bmatrix} k & -1 & 0 \\[0.3em] 0 & k & -1 \\[0.3em] -1 & 0 & k \end{bmatrix}\) is 2, for \( k = \)

If \(A = \begin{bmatrix} 4 & 2 \\[0.3em] -3 & 3 \end{bmatrix}\), then \(A^{-1} =\)

A two-port network is defined by the relation
\(\text{I}_1 = 5V_1 + 3V_2 \)
\(\text{I}_2 = 2V_1 - 7V_2 \)
The value of \( Z_{12} \) is:

An induction motor when started on load does not accelerate up to full speed but runs at \({\frac {1}{17}}\)th of the rated speed. The motor is said to be:

Gold doped GTOs have ______ as compared to the conventional GTOs.

A single phase full-converter using R load is a _____ quadrant converter and that using an RL load without FD is a _____ quadrant converter.

If \(P(A) = \frac{7}{11}\), \( P(B) = \frac{6}{11} \), and \( P(A \cup B) = \frac{8}{11} \), then \( P(A|B) = \) ?}

The general solution of \( z = px + qy + p^2q^2 \) is

If \( \text{div}~\vec{F} \) of any vector \( \vec{F} \) is zero, then it is

If \( f(z) \) is analytic at \( z_0 \), then it is

If \( \bar{x} = 4 \), \( \bar{y} = 8 \), \( \sigma_x = 2 \), \( \sigma_y = 3 \), and \( r = 0.3 \), then the line of regression of \( y \) on \( x \) is

One of the two events must occur. The chance of one is \( \frac{2}{3} \) of the other, then odds in favour of the other are

The speed time curve of the urban service has no

Matrix \( A \) has \( x \) rows and \( x + 5 \) columns. Matrix \( B \) has \( y \) rows and \( 11 - y \) columns. Both \( AB \) and \( BA \) exist, then

The minimum value of the function \( x^2 + y^2 + z^2 \) if \( x + y + z = 3a \)

Particular integral of the partial differential equation \( \frac{\partial^2 z}{\partial x^2} - 2 \frac{\partial^2 z}{\partial x \partial y} + \frac{\partial^2 z}{\partial y^2} = 2x \cos y \) is