1) A letter is chosen at random from the word “MATHEMATICS”.
Find the probability that:

(i) The chosen letter is a vowel.
(ii) The chosen letter is not a vowel.

2) The word MATH is coded as 14-21-28.

Now, the secret code 22-4-13-17 belongs to which word?

3) What is the probability of drawing a red card from a standard deck of 52 playing cards?

4) Five students stand in a row.

• P is to the left of Q.

• R is to the right of Q.

• S is between P and Q.

• T is not at either end.

Who must be in the middle?

5) How many lines of symmetries and rotational symmetries are in below figure?

6) Which letter has both a horizontal and a vertical axis of symmetry?

7) How many of the following letters have rotational symmetry of order more than 1?

R, B, S, H, O, P, W, X, Z

8) Five friends — A, B, C, D, and E — are sitting in a row facing north.

• A is to the immediate right of B.

• C is at one of the ends.

• D is between C and B.

• E is not sitting next to A.

Who is sitting in the middle?

9) A word is coded by this rule:

Code = (Number of letters) × 2 + (Number of vowels) × 3

Using this rule:

MATH → 11
SCIENCE → 20

What is the code for GEOMETRY?

10) Look at the pattern carefully:

3 → 10
5 → 26
8 → 65
12 → ?

What number should replace the question mark?

11) A father is 30 years older than his son.
After 5 years, he will be 4 times as old as his son.
What is the present age of the father?

12) Look at the sequence:

2, 6, 12, 20, 30, ___

What is the next term?

13) Find the missing number:

Rule is same in every row.

14) What is the probability of drawing a queen from a standard deck of 52 playing cards?

15) How many lines of symmetry and what is the order of rotational symmetry respectively are there in the given regular polygon?

16) A cubical box has the numbers 1, 4, 6, 4, 8, 3 written on its faces.
It is rolled once. Find the probability of:

(i) getting 4.
(ii) getting the largest number.

17) Find the next term:

1, 4, 10, 22, 46, ___

18) A machine follows this rule:

For any two-digit number AB, output = (A + B) × (A − B)

Example: For 72 → (7+2) × (7−2)=9 × 5 = 45

Now compute the output for 94.

19) A cubical box has the numbers 2, 3, 5, 7, 2, 9 written on its faces.
It is rolled once. Find the probability of:

(i) getting 2.
(ii) getting a prime number.

20) In a secret code:

🔺 + 🔺 + 🔺 = 27
🔺 + ⭐ + ⭐ = 19
⭐ + ⚫ + ⚫ = 13

Find:

🔺 × ⭐ + ⚫