Given below are some sample questions from the set of CBSE Class 10 Mathematics: Important 2 Marks Questions:

Q.  Find the number of all three-digit natural numbers which are divisible by 9.

Sol.

All three-digit natural numbers which are divisible by 9, are 108, 117, 126, ….., 999.

All these numbers form an AP with, 1st term, a =108

Common difference, d =117 – 108 = 9

And last term, an = 999
Now, a + (n − 1) d = an
∴108 + (n − 1) 9 = 999
⟹ (n − 1)9 = 999 −108 = 891

⟹ (n − 1) = 891 /9 = 99

⟹ n = 99 + 1 = 100

CBSE Class 10 Mathematics Previous Years' Solved Question Papers (2010-2019)

Q. Solve the following system of linear equations by substitution method:

2x – y = 2

x + 3y =15

Sol.

Here,   2x – y = 2

⟹       y = 2x – 2

⟹       x + 3y = 15

Substituting the value of y from (i) in (ii), we get

            x + 6x – 6 = 15

⟹       7x = 21

⟹         x = 3

From (i), y = 2 × 3 – 2 = 4

∴             x = 3 and y = 4

Q. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither an ace nor a king.

Sol.

P (neither an ace nor a king)

                        = 1 – P(either an ace or a king)

                        = 1 – [P(an ace) + P (a king)]

                        = 1 – [4/52  +  4/52]

                        = 1 – 8/52

                        = 44/52  =  11/13        

Q. Solve for x : 12x² – 6(a² + b²)x + 3a²b² = 0.

Sol.

12x² – 6(a² + b²)x + 3a²b² = 0.

4x² − 2(a² + b²)x + a²b² = 0.

4x² − 2a²x − 2b²x + a²b² = 0

2x(2x – 2a) − b²(2x − a²) = 0

(2x − b²)( 2x − a²) = 0

⟹ x = b²/2 or x = a²/2