1
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

e4 denotes the exponential of a square matrix A. Suppose $$\lambda$$ is an eigen value and v is the corresponding eigen-vector of matrix A.

Consider the following two statements:

Statement 1 : e$$\lambda$$ is an eigen value of eA.

Statement 2 : v is an eigen-vector of eA.

Which one of the following options is correct?

A
Statement 1 is true and statement 2 is false.
B
Statement 1 is false and statement 2 is true.
C
Both the statements are correct.
D
Both the statements are false.
2
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Let $$f(x) = \int\limits_0^x {{e^t}(t - 1)(t - 2)dt} $$. Then f(x) decreases in the interval.

A
x $$\in$$ (1, 2)
B
x $$\in$$ (2, 3)
C
x $$\in$$ (0, 1)
D
x $$\in$$ (0.5, 1)
3
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Consider a matrix $$A = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 2} \cr 0 & 1 & 1 \cr } } \right]$$. The matrix A satisfies the equation 6A$$-$$1 = A2 + cA + dI, where c and d are scalars and I is the identify matrix. Then (c + d) is equal to

A
5
B
17
C
$$-$$6
D
11
4
GATE EE 2022
MCQ (Single Correct Answer)
+1
-0.33

Let $$f(x,y,z) = 4{x^2} + 7xy + 3x{z^2}$$. The direction in which the function f(x, y, z) increases most rapidly at point P = (1, 0, 2) is

A
$$20\widehat i + 7\widehat j$$
B
$$20\widehat i + 7\widehat j + 12\widehat k$$
C
$$20\widehat i + 12\widehat k$$
D
$$20\widehat i$$
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