1
GATE ECE 2022
+1
-0.33

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.

What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $$\times$$ 4 grid using the unit squares as building blocks?

A
15
B
20
C
21
D
26
2
GATE ECE 2022
+1
-0.33

Consider the following inequalities.

(i) 2x $$-$$ 1 > 7

(ii) 2x $$-$$ 9 < 1

Which one of the following expressions below satisfies the above two inequalities?

A
x $$\le$$ $$-$$4
B
$$-$$4 < x $$\le$$ 4
C
4 < x < 5
D
x $$\ge$$ 5
3
GATE ECE 2022
+1
-0.33

Four points P(0, 1), Q(0, $$-$$3), R($$-$$2, $$-$$1), and S(2, $$-$$1) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?

A
4
B
$$4\sqrt 2$$
C
8
D
$$8\sqrt 2$$
4
GATE ECE 2022
+1
-0.33

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.

Let X, Y and Z represent the following operations:

X : rotation of the square by 180 degree with respect to the S-Q axis.

Y : rotation of the square by 180 degree with respect to the P-R axis.

Z : rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.

Consider the following three distinct sequences of operation (which are applied in the left to right order).

(1) XYZZ

(2) XY

(3) ZZZZ

Which one of the following statements is correct as per the information provided above?

A
The sequence of operations (1) and (2) are equivalent
B
The sequence of operations (1) and (3) are equivalent
C
The sequence of operations (2) and (3) are equivalent
D
The sequence of operations (1), (2) and (3) are equivalent
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