List of top Questions asked in GATE ME

The relative humidity of ambient air at 300 K is 50% with a partial pressure of water vapor equal to \( p_v \). The saturation pressure of water at 300 K is \( p_{sat} \). The correct relation for the air-water mixture is

The ordinary differential equation \( \frac{dy}{dt} = -\pi y \) subject to an initial condition \( y(0) = 1 \) is solved numerically using the following scheme:
\[ \frac{y(t_{n+1}) - y(t_n)}{h} = -\pi y(t_n) \] \text{where } \( h \) is the time step, \( t_n = nh \), and \( n = 0, 1, 2, \dots \). \text{This numerical scheme is stable for all values of } h \text{ in the interval} ________.

Consider a binomial random variable \( X \). If \( X_1, X_2, \dots, X_n \) are independent and identically distributed samples from the distribution of \( X \) with sum \( Y = \sum_{i=1}^{n} X_i \), then the distribution of \( Y \) as \( n \to \infty \) can be approximated as

The correct sequence of machining operations to be performed to finish a large diameter through hole is

In modern CNC machine tools, the backlash has been eliminated by

Five persons P, Q, R, S, and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.
The number of distinct seating arrangements possible is:

If \( y(x) \) satisfies the differential equation \[ (\sin x) \frac{dy}{dx} + y \cos x = 1, \] subject to the condition \( y(\pi/2) = \pi/2 \), then \( y(\pi/6) \) is

The value of \[ \lim_{x \to 0} \frac{1 - \cos x}{x^2} \] is

“\( \oplus \)” means “-”, “\( \otimes \)” means “:”,
If “\( \Delta \)” means “+”, and “\( \nabla \)” means “×”,
then, the value of the expression \( \Delta 2 \oplus 3 \Delta ((4 \otimes 2) \nabla 4) \) =

"The increased consumption of leafy vegetables in the recent months is a clear indication that the people in the state have begun to lead a healthy lifestyle." Which of the following can be logically inferred from the information presented in the above statement?

Oxpeckers and rhinos manifest a symbiotic relationship in the wild. The oxpeckers warn the rhinos about approaching poachers, thus possibly saving the lives of the rhinos. Oxpeckers also feed on the parasitic ticks found on rhinos. In the symbiotic relationship described above, the primary benefits for oxpeckers and rhinos respectively are,

The number of hens, ducks and goats in farm P are 65, 91 and 169, respectively. The total number of hens, ducks and goats in a nearby farm Q is 416. The ratio of hens:ducks:goats in farm Q is 5:14:13. All the hens, ducks and goats are sent from farm Q to farm P.
The new ratio of hens:ducks:goats in farm P is

Ms. X came out of a building through its front door to find her shadow due to the morning sun falling to her right side with the building to her back. From this, it can be inferred that the building is facing ________

Consider the following sentences:
(i) After his surgery, Raja hardly could walk.
(ii) After his surgery, Raja could barely walk.
(iii) After his surgery, Raja barely could walk.
(iv) After his surgery, Raja could hardly walk.
Which of the above sentences are grammatically CORRECT?

What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}