1
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

A partial differential equation

$$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0$$

is defined for the two-dimensional field $T: T(x, y)$, inside a planar square domain of size 2 m × 2 m. Three boundary edges of the square domain are maintained at value $T = 50$, whereas the fourth boundary edge is maintained at $T = 100$.

The value of $T$ at the center of the domain is

A

50.0

B

62.5

C

75.0

D

87.5

2
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication.

P: $(A + B)^T = A^T + B^T$

Q: $(AB)^T = B^T A^T$

Which one of the following options is CORRECT?

A

P is TRUE and Q is FALSE

B

Both P and Q are TRUE

C

P is FALSE and Q is TRUE

D

Both P and Q are FALSE

3
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

The second derivative of a function $f$ is computed using the fourth-order Central Divided Difference method with a step length $h$. The CORRECT expression for the second derivative is

A

$\frac{1}{12h^2} \left[ -f_{i+2} + 16 f_{i+1} - 30 f_i + 16 f_{i-1} - f_{i-2} \right]$

B

$\frac{1}{12h^2} \left[ f_{i+2} + 16 f_{i+1} - 30 f_i + 16 f_{i-1} - f_{i-2} \right]$

C

$\frac{1}{12h^2} \left[ -f_{i+2} + 16 f_{i+1} - 30 f_i + 16 f_{i-1} + f_{i-2} \right]$

D

$\frac{1}{12h^2} \left[ -f_{i+2} - 16 f_{i+1} + 30 f_i - 16 f_{i-1} - f_{i-2} \right]$

4
GATE CE 2024 Set 2
MCQ (Single Correct Answer)
+1
-0.33

The function $f(x) = x^3 - 27x + 4$, $1 \leq x \leq 6$ has

A

Maxima point

B

Minima point

C

Saddle point

D

Inflection point

EXAM MAP