1
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
2
GATE ECE 2021
+1
-0.33
p and q are positive integers and $${p \over q} + {q \over p} = 3$$, then $${{{p^2}} \over {{q^2}}} + {{{q^2}} \over {{p^2}}}$$ =
A
11
B
3
C
9
D
7
3
GATE ECE 2021
+1
-0.33
The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 yeas ago?
A
9,92,500
B
9,95,006
C
12,51,506
D
10,00,000
4
GATE ECE 2019
+1
-0.33
Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second respectively from right side of the shelf. The number of different orders in which P, Q and T may be arranged is ________.
A
6
B
2
C
12
D
120
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