SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions

Six year before, the age of mother was equal to the square of her son's age. Three year hence, her age will be thrice the age of her son then. Find the present ages of the mother and son.

Simplify `sqrt(50)`

What is the sum of first 10 terms of the A. P. 15,10,5,........?

Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .

Here a = 1 , d =b`[    ], t_n = 149`

t_n = a + (n-1) d 

∴ 149 =`[  ]     ∴149 = 2n -  [  ]`
∴ n =`[  ]`

Select the correct alternative and write it. 

What is the sum of first n natural numbers ? 

Select the correct alternative and write it. 

If a share is at premium, then - 

The sum of third and seventh term of an A. P. is 6 and their product is 8. Find the first term and the common difference of the A. P. 

If the second term and the fourth term of an A.P. are 12 and 20 respectively, then find the sum of first 25 terms:

The 11^th term and the 21^st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term. 

Find the sum of all members from 50 to 250 which divisible by 6 and find t13.

Obtain the sum of the first 56 terms of an A.P. whose 18^th and 39^th terms are 52 and 148 respectively.

For a given A.P. a = 3.5, d = 0, then t_n = _______.

Find the 23rd term of the following A.P.: 9, 4,-1,-6,-11.

Find second and third terms of an A.P. whose first term is – 2 and the common difference is – 2.

In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)

Find t₅ if a = 3 आणि d = −3

If a = 6 and d = 10, then find S₁₀ 

How many two-digit numbers are divisible by 5?

Activity :-  Two-digit numbers divisible by 5 are, 10, 15, 20, ......, 95.

Here, d = 5, therefore this sequence is an A.P.

Here, a = 10, d = 5, t_n = 95, n = ?

t_n = a + (n − 1) `square`

`square` = 10 + (n – 1) × 5

`square` = (n – 1) × 5

`square` = (n – 1)

Therefore n = `square`

There are `square` two-digit numbers divisible by 5

A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment

Complete the following activity to find the 19^th term of an A.P. 7, 13, 19, 25, ........ :

Activity: 

Given A.P. : 7, 13, 19, 25, ..........

Here first term a = 7; t₁₉ = ?

t_n + a + `(square)`d .........(formula)

∴ t₁₉ = 7 + (19 – 1) `square`

∴ t₁₉ = 7 + `square`

∴ t₁₉ = `square`