List of top Questions asked in GATE AE- 2021

In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equal parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in cm², is

1. Some football players play cricket.
2. All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q. The probability that any point picked randomly within the square falls in the shaded area is

The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk on to the stage and start speaking. In my opinion, it is no less important for public speakers to rehearse their talks." Based on the above passage, which one of the following is TRUE?

On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P. The distance of point Q to point O, in the same units, should be $\underline{\hspace{2cm}}$

Four persons P, Q, R, and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:

$ \oplus $ and $ \odot $ are two operators on numbers $ p $ and $ q $ such that
$ p \odot q = p - q$ and $p \oplus q = p \times q. $
Then, $ (9 \odot (6 \oplus 7)) \odot (7 \oplus (6 \odot 5)) = ? $

Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled on each die is:

The mirror image of the above text about the x-axis is

Which of the following sentences are grammatically correct?
(i) Arun and Aparna are here.
(ii) Arun and Aparna is here.
(iii) Arun's families is here.
(iv) Arun's family is here.

An airplane (5500 kg) initiates a pull-up at 225 m/s with curvature radius 775 m. CG, CP, and tail point T are shown. Thrust and drag cancel. Tail force is vertical. Find the tail force (round to one decimal place).

A 3 m × 1 m signboard is subjected to a wind pressure of 7.5 kPa. It is supported by a hollow square pole of outer dimension 250 mm and inner dimension $d$ (unknown). The yield strength is 240 MPa. Find $d$ (round off to nearest integer).

Two cantilever beams AB and DC touch at their free ends through a roller. Both beams have a 50 mm × 50 mm square cross section and modulus $E = 70\ \text{GPa}$. Beam AB carries a UDL of 20 kN/m. Determine the compressive force at the roller (round off to one decimal place).

A two-cell wing box has wall thickness 1.5 mm and shear modulus $G = 27\ \text{GPa}$. A torque of 12 kNm is applied. Determine the shear stress in wall AD (round off to one decimal place).

At the design conditions of a single-stage axial compressor, the blade angle at rotor exit is $30^\circ$. The absolute velocities at rotor inlet and exit are 140 m/s and 240 m/s, respectively. The relative flow velocities at rotor inlet and exit are 240 m/s and 140 m/s, respectively. Find the blade speed $U$ at the mean radius (round off to two decimal places).

A rigid horizontal bar ABC is supported by two columns BD and CE. BD is fixed at D, CE is pinned at E. A load $P$ is applied at distance $a$ from $B$. The columns are steel with $E = 200$ GPa and cross-section $1.5 \text{ cm} \times 1.5 \text{ cm}$. The lengths are: BD = 75 cm, CE = 125 cm. The value of $a$ for which both columns buckle simultaneously is $\underline{\hspace{2cm}}$ cm (round off to one decimal place).

A large water tank is fixed on a cart with wheels and a vane. The cart is tied to a fixed support with a rope. Water exits through a 5 cm diameter hole as a 10 m/s jet which is deflected by the vane by $60^\circ$. The velocity of the jet after deflection remains 10 m/s. Density of water is $1000\ \text{kg/m}^3$. The tension in the rope is $\underline{\hspace{1cm}}$ N (round off to one decimal place).

Consider a boundary-layer velocity profile:
\[ \frac{u}{U} = \begin{cases} \left( \frac{y}{\delta} \right)^2 & y \le \delta \\ 1 & y > \delta \end{cases} \] The shape factor (ratio of displacement thickness to momentum thickness) is $\underline{\hspace{2cm}}$ (round off to 2 decimal places).

For the matrix \[ \begin{bmatrix} 3 & 1 & 2 \\ 2 & -3 & -1 \\ 1 & 2 & 1 \end{bmatrix} \] find the ratio of the product of eigenvalues to the sum of eigenvalues (round off to nearest integer).

Which of the following statement(s) is/are true?

A conventional fixed-wing aircraft, with a horizontal tail and vertical fin, in steady and level flight is subjected to small perturbations. Which of the following statement(s) is/are true?

A shock moving into a stationary gas can be transformed to a stationary shock by a change in reference frame, as shown in the figure. Which of the following is/are true relating the flow properties in the two reference frames?

To estimate aerodynamic loads on an aircraft flying at 100 km/h at standard sea-level conditions, a one-fifth scale model is tested in a variable-density wind tunnel ensuring similarity of inertial and viscous forces. The pressure used in the wind tunnel is 10 times the atmospheric pressure.
Assuming ideal gas law to hold and the same temperature conditions in model and prototype, the velocity needed in the wind tunnel test-section is ______________.

The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as:

Which of the following statement(s) is/are true about the function defined as $ f(x)= e^{-x} \lvert \cos x \rvert $ for $ x>0 $?