1
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

2
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

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

3
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

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

Consider two Ordinary Differential Equations (ODEs):

P: $ \dfrac{dy}{dx} = \dfrac{x^4 + 3x^2 y^2 + 2y^4}{x^3 y} $

Q: $ \dfrac{dy}{dx} = -\dfrac{y^2}{x^2} $

Which one of the following options is CORRECT?

A

P is a homogeneous ODE and Q is an exact ODE.

B

P is a homogeneous ODE and Q is not an exact ODE.

C

P is a nonhomogeneous ODE and Q is an exact ODE.

D

P is a nonhomogeneous ODE and Q is not an exact ODE.

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