R S Aggarwal Solutions for Exercise 1: EXERCISE 11A

How many $3$-digit numbers are divisible by $7$?

How many $2$-digit numbers are divisible by $3$?

In an $AP$, it is being given that $\frac{T_4}{T_7}=\frac{2}{3}$. Find $T_7+T_{10}$.

The digits of a $3$-digit number are in $AP$ and their sum is $15$. The number obtained by reversing the digits is $594$ less than the original number. Find the number.

Find the number of terms common to the two arithmetic progressions $5, 9, 13, 17, \dots , 217$ and $3, 9, 15, 21, \dots , 321$.

We know that the sum of the interior angles of a triangle is $180°$. Show that the sum of the interior angles of polygons with $3, 4, 5, 6,\dots$ sides form an arithmetic progression. Find the sum of the interior angles for a $21$-sided polygon.     [Enter the value excluding degree symbol]

A side of an equilateral triangle is $24 \mathrm{cm}$ long. A second equilateral triangle is inscribed in it by joining the midpoints of the sides of the first triangle. The process is continued. If the perimeter of the sixth inscribed equilateral triangle is $k \mathrm{cm}$, then find the value of $k$ in decimal.

A man starts repaying a loan as the first instalment of $₹10000$. If he increases the instalments by $₹500$ every month, what amount will he pay in ${30}^{\mathrm{th}}$ instalment?

[Enter value excluding units]