1
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

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

The smallest positive root of the equation $$x^5 - 5 x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$$ lies in the range

A

0 < x ≤ 2

B

2 < x ≤ 4

C

6 ≤ x ≤ 8

D

10 ≤ x ≤ 100

3
GATE CE 2023 Set 1
MCQ (Single Correct Answer)
+1
-0.33

For the integral $\rm I=\displaystyle\int^1_{-1}\frac{1}{x^2}dx$

which of the following statements is TRUE? 

A
I = 0
B
I = 2 
C
I = -2 
D
The integral does not converge
4
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+1
-0

The following function is defined over the interval [-L, L]:

f(x) = px4 + qx5.

If it is expressed as a Fourier series, 

$\rm f(x)=a_0 +\displaystyle\sum^\infty_{n=1} \left\{a_n \sin\left( \frac{\pi x}{L} \right) +b_n\cos\left( \frac{\pi x}{L} \right) \right\} $,

which options amongst the following are true?

A
an, n = 1, 2, ..., ∞ depend on p
B
an, n = 1, 2, ..., ∞ depend on q
C
bn, n = 1, 2, ..., ∞ depend on p
D
bn, n = 1, 2, ..., ∞ depend on q
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