1
GATE ME 2025
MCQ (Single Correct Answer)
+1
-0.33

The ceiling function of a real number $x$, denoted by $\operatorname{ce}(x)$, is defined as the smallest integer that is greater than or equal to $x$. Similarly, the floor function, denoted by $f l(x)$, is defined as the largest integer that is smaller than or equal to $x$. Which one of the following statements is NOT correct for all possible values of $x$ ?

A
$\operatorname{ce}(x) \geq x$
B
$f l(x) \leq x$
C
$\operatorname{ce}(x) \geq f l(x)$
D
$f l(x)<\operatorname{ce}(x)$
2
GATE ME 2024
MCQ (Single Correct Answer)
+1
-0.33

Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}

A

21

B

29

C

37

D

23

3
GATE ME 2024
MCQ (Single Correct Answer)
+1
-0.33

In the following series, identify the number that needs to be changed to form the Fibonacci series.

1, 1, 2, 3, 6, 8, 13, 21, …

A

8

B

21

C

6

D

13

4
GATE ME 2024
MCQ (Single Correct Answer)
+1
-0.33

The real variables $x, y, z$, and the real constants $p, q, r$ satisfy

$\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$

Given that the denominators are non-zero, the value of $px + qy + rz$ is

A

0

B

1

C

pqr

D

$p^2 + q^2 + r^2$

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