List of practice Questions

The solution of the differential equation
{x⁴+6x²+2(x+y)} dx-xdy=0
subject to the condition y(1)=0 is

Which of the following statement is not correct?

Let A and B be 2 × 2 matrices, then which of the following is correct?

Let f (x) be defined on [0, 3] by \(f(x) =   \begin{cases}     x,\text{if x is a rational number}       \\  3-x\text{, if x is an irrational number}   \end{cases}\) Then f(x) is continuous in the interval at:

If A is symmetric real valued matrix of dimension 2022, then eigenvalues of A are

Which one of the following rings is an integral domain?

Let f: G→H be a group homomorphism from group G into group H with kernel K. If the order of G, H and K are 50, 25 and 10 respectively then the order of f(G) is

The equation (2x + y + 1) dx + (x + 2y +1) dy = 0 represents a family of:

The value of surface integral \(\iint_S(9x\hat{i}-2\hat{j}-z\hat{k}).\hat{n}dS\) over the surface S of the sphere x²+y²+z²=9 where \(\hat{n}\) is the unit outward normal to surface element dS is:

The line integral of function \(F = yz\hat{i}\), in the counter clockwise direction, along the circle x² + y² = 1 at z = 1 is

If \(\overrightarrow{r}=x_1\hat{a}_{x_1}+x_2\hat{a}_{x_2}+x_3\hat{a}_{x_3}\) and \(|\overrightarrow{r}|=r\) then \(div(r^2\nabla(In\;r))\)is

The area of surface of solid generated by the revolution of line segment y = 2x from x = 0 to x = 2 about x-axis is equal to:

To evaluate the double integral \(\int_0^8\left(\int\limits_{y/2}^{(y/2)+1}\left(\frac{2x-y}{2}\right)dx\right)dy\), we make the substitution \(u=\frac{2x-y}{2}\)and \(v=\frac{y}{2}\). The integral will reduce to

If \(\Phi(z)=c_0+c_1z^{-1}\), then \(\oint_{|z|=1}\frac{1+\Phi(z)}{z}dz\) is

For Matrix \(A = \begin{vmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1  \end {vmatrix}\), the sum and differences of maximum & minimum 1 eight value of Matrix are 4 and 8, then the eigen values for the Matrix A are. 

The solution of \(x ^2 \frac{d^2y}{dx^2}+x+\frac{dy}{dx}+y=\sin(\log x^2)\).

If x is continuous random variable. and a probability density function \(f(x) = ke^{-3xl}, x ∈ (-\infty,\infty).\) The value of k is

The system matrix of a linear time invariant continuous time system is given by \(A= \begin{bmatrix} 0 & 1 \\ -4 & -5 \end{bmatrix}\)
What are the roots of characteristics equation.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The state transition matrix represents the free response of the system.
Reason R: The state transition matrix satisfies the homogeneous state equation
In the light of the above statements, choose the most appropriate answer from the options given below :

The bus admittance matrix of a power system is given as.
1     2                3
\( 1\\2\\3 \begin{bmatrix}-j50 &+j10 &+j5\\+j10&-j30&+j10\\+j5&+j10&-j25\end{bmatrix}\)
The impedance of line between bus 2 and bus 3 will be equal to____

A solar photovoltaic system feeds power to a motor of 1hp at the shaft. The motor has an efficiency of 85%. Each module has 40 multi crestline Silicone solar cells arranged in 9x5 matrix? The cell is 130 mm×130 mm and the cell efficiency is 13%. Calculate the number of photovoltaic modules required, assuming global radiation incident to the panel as 1kW/m²

A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to be subtend an angle twice as before. Find the height of the tower?

If tanα=1/3, tanβ=1/7 and 2α + β = m, then sin 2m is equal.

If an angle a is divided into two parts A and B such that A-B=x and tan A: tan B=k:1, then the value of sinx is

The base of a tower is 80m away from a point A on the ground. If the angle of elevation of the top of the tower from A is 45. Calculate the height of the tower.