SSC (Marathi Semi-English) १० वीं कक्षा - Maharashtra State Board Important Questions

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. 

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`

Find the sum of first 'n' even natural numbers.

Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)

Find the sum of all odd numbers between 351 and 373.

Calculate the sum of 35 terms in an AP, whose fourth term is 16 and ninth term is 31.

Find the middle term of the AP. 95, 86, 77, ........, – 247.

Find the sum of all even numbers from 1 to 250.