1
GATE CE 2023 Set 1
MCQ (Single Correct Answer)
+1
-0.33
In cement concrete mix design, with the increase in water-cement ratio, which one of the following statements is TRUE?
A
Compressive strength decreases but workability increases 
B
Compressive strength increases but workability decreases
C
Both compressive strength and workability decrease 
D
Both compressive strength and workability increase
2
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
3
GATE CE 2023 Set 1
MCQ (More than One Correct Answer)
+1
-0
If M is an arbitrary real n × n matrix, then which of the following matrices will have non-negative eigenvalues? 
A
M2
B
MMT
C
MTM
D
(MT)2
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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