List of top Questions asked in GATE ES

Assuming \( s>|a| \); the Laplace transform of \( f(x) = \cosh(ax) \) is:

You conducted a batch experiment in the lab for 10 minutes to degrade a toxic compound, which follows first-order kinetics. The compound degrades from \( 2 \times 10^{-3} \, {M} \) to \( 2 \times 10^{-4} \, {M} \). The information from the lab experiment will be used to design a plug flow reactor in field conditions.
Given field conditions:
• Flow rate of contaminated water to be treated: 1 m\(^3\)/hour
• Concentration of toxic compound in contaminated water: \( 5 \times 10^{-1} \, {M} \)
• Target concentration of toxic compound in treated water: \( 1 \times 10^{-4} \, {M} \)
• Temperature is the same in lab and field conditions.
The required volume of the plug flow reactor is ________ m\(^3\). (rounded off to two decimal places)

A homogeneous isotropic confined aquifer of uniform thickness 30 m has hydraulic conductivity of 5 m/day and porosity of 0.3. There are two observation wells X and Y along a radial line from a fully penetrating pumping well at 100 m and 200 m distance, respectively. The well is pumped at a uniform rate to produce steady drawdown of 5 m at X and 3 m at Y. If a non-reactive pollutant enters at the observation well Y, then the time taken by the pollutant (under advection) to reach the observation well X is ________ days. (rounded off to two decimal places)

A tank has inflow, outflow, and a stirring mechanism. Initially, the tank holds 500 L of a brine solution of concentration 200 g/L. At \( t = 0 \), an inflow of another brine solution of concentration 100 g/L starts entering the tank at the rate of 15 L/minute. At the same time, the outflow of thoroughly stirred mixture also takes place at the same rate so that the volume of brine in the tank remains constant. The brine concentration \( C \) (g/L) in the tank at any time \( t \) (minute) can be expressed by the following differential equation: \[ \frac{dC}{dt} + 0.03 C = 3 \] The brine concentration in the tank at \( t = 1.5 \) hour is ________ g/L. (rounded off to two decimal places)

For a gradually varied flow, consider the following statements:
P: \( y_n>y_c>y \) in M3 surface profile
Q: \( y_n<y_c<y \) in S1 surface profile
where, \( y_n \) is normal depth, \( y_c \) is critical depth, and \( y \) is flow depth.
Choose the correct option from the following:

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹1000(X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts?

If a real variable \( x \) satisfies \( 3^{x^2} = 27 \times 9^x \), then the value of \( \frac{2^{x^2}}{(2^x)^2} \) is:

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let \( a_1 \) and \( a_2 \) (in years) denote the ages of the brothers and \( a_1<a_2 \). Which one of the following statements is correct about their age on the day when they attain the same weight?

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.

A rectangle has a length \(L\) and a width \(W\), where \(L>W\). If the width, \(W\), is increased by 10%, which one of the following statements is correct for all values of \(L\) and \(W\)?
Select the most appropriate option to complete the above sentence.

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?

A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with \( U \leq 4 \) is:

We __________ tennis in the lawn when it suddenly started to rain.
Select the most appropriate option to complete the above sentence.

Courage : Bravery :: Yearning :
Select the most appropriate option to complete the analogy.

With reference to the gate shown in the figure, the gate will start opening automatically when the water level 'h' above the hinge is ________ m (rounded off to 2 decimal places).

Ten cards in a pack are numbered as 1, 2, 3, . . .10. The probability of drawing a card with an even number or a number which is a multiple of 5 from the pack is

Hardness in water is NOT caused by ______

The maximum coordination number of \( \text{Sn}^{4+} \) is \(\_\_\_\_\)

Rod shaped bacterial cells are called _______.

Tuberculosis is predominantly caused by ________.

Which one of the following conversions belongs to nonsymbiotic nitrogen fixation?

Crown corrosion of reinforced cement concrete sewer is caused by ______

The processes of removal of particles in a rapid sand filter with their description is given in the table.

Process	Description
(i) Straining	P: Removes only particles in the water large enough to get caught in the pores of the filter
(ii) Sedimentation	Q: Larger and heavier particles do not follow the fluid streamline around the sand grain and settle on the grain
(iii) Interception	R: Particles that do follow the streamline, but are too large and are caught because they brush up against the sand grains
(iv) Diffusion	S: Very small particles are experiencing Brownian motion and may collide with the sand grains by chance

Select the correct match.

The environmental temperature increases by 6°C/km with height at a particular location. The stability condition of the atmosphere at the location is ______,