1
GATE CSE 2022
+1
-0.33

A function y(x) is defined in the interval [0, 1] on the x-axis as

$$y(x) = \left\{ \matrix{ 2\,if\,0 \le x < {1 \over 3} \hfill \cr 3\,if\,{1 \over 3} \le x < {3 \over 4} \hfill \cr 1\,if\,{3 \over 4} \le x < 1 \hfill \cr} \right.$$

Which one of the following is the area under the curve for the interval [0, 1] on the x-axis?

A
$${5 \over 6}$$
B
$${6 \over 5}$$
C
$${{13} \over 6}$$
D
$${6 \over {13}}$$
2
GATE CSE 2022
+1
-0.33

Let r be a root of the equation x2 + 2x + 6 = 0. Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is

A
51
B
$$-$$ 51
C
126
D
$$-$$ 126
3
GATE CSE 2022
+1
-0.33

Given below are four statements :

Statement 1 : All students are inquisitive.

Statement 2 : Some students are inquisitive.

Statement 3 : No student is inquisitive.

Statement 4 : Some students are not inquisitive.

From the given four statements, find the two statements that CANNOT BE TRUE simultaneously, assuming that there is at least one student in the class.

A
Statement 1 and Statement 3
B
Statement 1 and Statement 2
C
Statement 2 and Statement 4
D
Statement 3 and Statement 4
4
GATE CSE 2022
+1
-0.33

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters.

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.

A
B
C
D
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