Logical Reasoning — UPSC CSE CSAT PYQs

What comes at X and Y respectively in the following sequence ?
January, January, December, October, X, March, October, Y, September

A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct ?
I. The minimum number of cuts is 9.
II. The number of smaller pieces which are not painted on any face is 6.
Select the correct answer using the code given below :

If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to ?

Consider the following statements :
I. If A <= B > C < D > E > F >= G = H; then B is always greater than E.
II. If P > Q = R >= S = T <= U = V > W; then S is always less than V.
Which of the statements given above is/are correct ?

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR - PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S) ?

Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence ?

What is X in the sequence 24, X, 12, 18, 36, 90 ?

If P = +, Q = -, R = x, S = div, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20 :

A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows :
P : I did not steal. Q stole it.
Q : R did not steal. I did not steal.
R : I did not steal. I do not know who did it.
Who stole the mobile phone ?

Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct ?
I. The result of the match between P and Q is a draw with the score 0 - 0.
II. The number of goals scored by R against Q is 1.
Which of the statements given above is/are correct ?