1
UPSC Civil Service Prelims Paper II 2023 (CSAT)
+2.5
-0.833

There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:

1. It is possible that exactly one letter goes into an incorrect envelope.

2. There are only six ways in which only two letters can go into the correct envelopes.

Which of the statements given above is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
2
UPSC Civil Service Prelims Paper II 2023 (CSAT)
+2.5
-0.833
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions?
A
12
B
18
C
36
D
72
3
UPSC Civil Service Prelims Paper II 2023 (CSAT)
+2.5
-0.833
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points?
A
16
B
18
C
20
D
24
4
UPSC Civil Service Prelims Paper II 2023 (CSAT)
+2.5
-0.833

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements:

1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.

2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.

Which of the above statements is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
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