List of top Questions asked in TS PGECET- 2026

Compared to Single yarn, in Double or folded yarns the Uniformity will

Habutai is a Silk fabric consists of \((\text{in } g/m^{2})\)

The percentage of Moisture Regain of Silk is

The following is considered as one of the fibre properties, prior selection to Spinning of Cotton

Which of the following are having potential as Composite material from New Natural fibres?

Compared to Cotton, the special feature of Wool is

In the binomial distribution \(B(n,p)\), the variance \((\sigma^{2})\) and the mean \((\mu)\) are related by

40's Cotton count refers to

\[ \lim_{n\rightarrow\infty}\frac{5n^{2}+4}{7n^{2}+6n}= \]

If \(y_{1}=x^{2}\) is a known solution of \[ x^{2}y^{\prime\prime}-3xy^{\prime}+4y=0, \] then the second independent solution \(y_{2}\) is

The solution of \[ \frac{dy}{dx}+y=f(x), \] where \[ f(x)= \begin{cases} x, & 0\le x \\ 0, & x\ge1, \end{cases} \] with the conditions \[ y(0)=0,\qquad y(1)=e^{-1}, \] is

Assertion (A): If \(X\sim N(\mu,\sigma^{2})\), then \[ P(X<\mu)=0.5. \] Reason (R): Normal distribution is symmetric about its mean.

Consider the differential equation \[ \frac{dy}{dx}=x^{2}-y,\qquad y(0)=1. \] Using the Simple Euler's Method with a step size of \(h=0.1\), the value of \(y(0.1)\) is

If \[ \vec{v}=(x+y+1)\hat{i}+\hat{j}+(-x-y)\hat{k}, \] then the value of \[ \vec{v}\cdot(\nabla\times\vec{v}) \] is

If \[ f(x,y,z,w)=x^{2}e^{2y+3z}\cos(4w), \] then \[ \frac{\partial f}{\partial z} \] at \((2,0,-2,1)\) is

Let \(A\) and \(B\) be any two \(n\times n\) matrices and \[ tr(A)=\sum_{i=1}^{n}a_{ii}, \qquad tr(B)=\sum_{i=1}^{n}b_{ii}. \] Consider the following statements:
• Statement-I : \(tr(AB)=tr(BA)\).
• Statement-II : \(tr(A+B)=tr(A)+tr(B)\).
• Statement-III : If \(tr(A)=5,\; tr(A^{2})=13\), then \[ tr(A-I)^2=6, \] where \(A_{3\times3}\) and \(I_{3\times3}\) are matrices. Choose the correct option.

Let the matrix \[ A=\begin{bmatrix} 3& 1 \\ -1& 2 \end{bmatrix} \] and \[ I=\begin{bmatrix} 1& 0 \\ 0& 1 \end{bmatrix}, \] then \[ A^{2}-5A+7I= \]

If \[ \{(2,-3,5),\ (1,\alpha,7),\ (3,\beta,3)\} \] is not a basis of the vector space \(\mathbb{R}^3\), then \((\alpha,\beta)\) lies on the locus:

The tautology \[ \bigl(p \wedge (p \rightarrow q)\bigr) \rightarrow q \] is the basis of the following rule of inference:

What is the output of the following recursive function? \[ \texttt{int\ func1(int\ num1,\ int\ num2)} \]

return (num2 == 0) ? num1 : func1(num2, num1 % num2);
  

Steady-state error of the following second-order system for a unit ramp input is \[ \frac{C(s)}{R(s)} = \frac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}. \] The steady-state error is:

For the given open-loop system, \[ G(s)=\frac{1}{(s+2)(s+4)}, \] the poles of the unity feedback closed-loop system are:

If the transfer function of a controller is given by \[ G_c(s)=\frac{K_1s^2+K_2s+K_3}{s}, \] then the proportional, integral, and derivative constants are:

If \(\alpha\) is ratio \(\frac{\text{T}_{\text{ON}}}{\text{T}}\) of chopper, then the ratio of input voltage to output voltage of step down and step-up chopper respectively are