List of top Questions asked in GATE XE- 2021

Gauri said that she can play the keyboard $\underline{\hspace{2cm}}$ her sister.

A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like $\underline{\hspace{2cm}}$

If $\theta$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then $\cos \theta =$

If $\left(x-\dfrac{1}{2}\right)^2 - \left(x-\dfrac{3}{2}\right)^2 = x + 2$, then the value of $x$ is:

Pen : Write :: Knife : $\underline{\hspace{2cm}}$
Which one of the following options maintains a similar logical relation in the above?

Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.
Which one of the following statements is the CORRECT inference of the above passage?

A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece, when assembled, will form a rectangle?
The piece can be moved, rotated or flipped to assemble with the above piece. \includegraphics[width=0.152\linewidth]{image7.png} \includegraphics[width=0.85\linewidth]{image07.png}

The number of students in three classes is in the ratio $3:13:6$. If 18 students are added to each class, the ratio changes to $15:35:21$.
The total number of students in all the three classes in the beginning was:

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year. The ratio of the selling price in Year 2 to the selling price in Year 3 is $\underline{\hspace{1cm}}$.
\includegraphics[width=0.75\linewidth]{image9.png}

Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
Observation I: S is taller than R.
Observation II: Q is the shortest of all.
Observation III: U is taller than only one student.
Observation IV: T is taller than S but is not the tallest.
The number of students that are taller than R is the same as the number of students shorter than $\underline{\hspace{2cm}.}$

Let \[ f(x, y) = x^4 + y^4 - 2x^2 + 4xy - 2y^2 + \alpha \] be a real valued function. Then, which one of the following statements is TRUE for all $ \alpha $?

Let \[ u(x, y) = (x^2 - y^2)v(x, y) \] be such that both $ u(x, y) $ and $ v(x, y) $ satisfy the Laplace equation in a domain $ \Omega $ of the xy-plane. Then, which one of the following is TRUE in $ \Omega $?

The figure shows a schematic of Indian Ocean surface circulation. This pattern is representative of the circulation in which month of the year?

The figure shows vertical variation of two chemicals P and Q measured in the Pacific Ocean. Identify the correct combination showing (P, Q) pair from the list below.

Match unit operation in Column I with its application in food processing in Column II.

Binary polymer blends of polypropylene and polyamide 6 are immiscible. From a thermodynamic viewpoint this is due to $\underline{\hspace{2cm}}$.

Equal and opposite forces of a constant magnitude $ F $ are applied at the two ends of a thin elastomeric rod, which is held at a temperature $ T_1 $ (where $ T_g < T_1 < T_m $, and $ T_g $ and $ T_m $ are the glass transition temperature and melting temperature respectively). If the temperature is increased to $ T_2 $ (where $ T_g < T_2 < T_m $ and $ T_2 > T_1 $), the rod will $\underline{\hspace{2cm}}$.

Match the Additive to its Function.

Match the polymer processing operation with respect to its typical range of shear rate.

Shear stress ($ \sigma $) and shear viscosity ($ \eta $) are plotted as functions of the shear rate ($ \dot{\gamma} $) for idealized "solid-like with yielding (1)" and "liquid-like (2)" materials.

Associate the shear stress and viscosity plots with the appropriate material responses.

The plateau modulus of polystyrene has a value of 0.2 × 10⁶ Pa at 150 °C. Given, the density of polystyrene is 1.05 g/cm³, the universal gas constant, $ R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} $, and the monomer molecular weight is 104 g/mol. The molecular weight between entanglements (rounded off to the nearest integer) of polystyrene chains is $\underline{\hspace{2cm}}$ g/mol.

A single screw extruder is operating at a rotational speed of 2 revolutions per second for the extrusion of a Newtonian polymer under open-discharge conditions (in absence of a die, the pressure drop, $ \Delta p = 0 $). The extruder has a screw diameter, $ D = 5 \, \text{cm} $, a channel depth, $ H = 0.4 \, \text{cm} $, distance between flights, $ W = 1 \, \text{cm} $, and a helix angle, $ \theta = 20^\circ $. Assume the value of $ \pi = 3.14 $. The volumetric flow rate (rounded off to 2 decimal places) is $\underline{\hspace{2cm}}$ cm³/s.

At 215 °C, the viscosity of a polystyrene of molecular weight 250 × 10³ g/mol is 8.0 × 10³ Pa·s. The critical molecular weight of polystyrene, $ M_c = 35 \times 10^3 $ g/mol. For a similar polystyrene of molecular weight 500 × 10³ g/mol, the viscosity (rounded off to nearest integer) will be $\underline{\hspace{2cm}}$ × 10³ Pa·s.

There are two different PTFE polymer specimens of the following density $ \rho $ and % crystallinity. For PTFE-specimen-1, $ \rho = 2.144 \, \text{g/cm}^3 $ and % crystallinity is 50. For PTFE- specimen-2, $ \rho = 2.215 \, \text{g/cm}^3 $ and % crystallinity is 75. Assuming the polymer is pure and defect free, the density (rounded off to 3 decimal places) of 100% amorphous PTFE specimen will be $\underline{\hspace{2cm}}$ g/cm³.

If
$h$ is the mass specific enthalpy,
$s$ is the mass specific entropy,
$P$ is the pressure,
$T$ is the temperature,
$C_V$ is the mass specific heat at constant volume,
$C_P$ is the mass specific heat at constant pressure,
$\beta$ is the coefficient of thermal expansion,
$v$ is the mass specific volume,
$\kappa$ is the isothermal compressibility,
then the partial derivative $\left( \frac{\partial h}{\partial s} \right)_P$ is