Embibe Experts Solutions for Chapter: Algebraic Expressions, Exercise 1: Exercise

Mohit was observing a number pattern and noted the values.

What is $y$, when $x=n$?

The volume of a cone is given by the formula, $\frac{1}{3}\pi r^{2}h$, where $r$ is its radius at the base, $h$ is its vertical height, and $h^2=l^2-r^2$, where $l$ is length to its top from a point on the edge at the base.

Given, $l=25 \mathrm{cm}$, $r=15 \mathrm{cm}$, which of the following gives the volume of the cone?

The perimeter of a triangle is given by $\left(8x^2+4x+9\right) \mathrm{cm}$ and its two sides are $\left(8x^2-2\right) \mathrm{cm}$ and $\left(4x+1\right) \mathrm{cm}$. What is its third side?

Shown below is several pieces of a ribbon joined together. The length of each peice is given as algebraic expressions.

$A=24ab-10b-18a$, $B=30ab+12b+14a$, $C=54ab$, $D=15ab+4a$

What is the length, $E$ of the arrangement?

Manoj added a monomial, a binomial and a trinomial.  Which of the following is definite about the number of terms in the resulting polynomial?
 

Srihari purchased a rectangular plot where it length is $9 \mathrm{ft}$ more than twice its width. If the width is $x \mathrm{ft}$, then what is its perimeter?

The figure below shows a park, $ABCD$. Inside the park, $PQRS$ is garden area. The area of $ABCD$ and $PQRS$ are $7x^2-5x+5$ and $x^2-5$ respectively.

What is the area of the region shaded in the above figure?

Vinod subtracted $7x^3-5x+8$ from an expression and got, $8x^2-x+4$.

Which of the following is the expression from which he subtracted, $7x^3-5x+8$?