Introduction to Algebra

Q.

Lakshmi is a cashier in a bank. She has currency notes of denominations .$\mathrm{Rs}100$, .$\mathrm{Rs}50$ and .$\mathrm{Rs}10$, respectively. The ratio of the number of these notes is $2:3:5$. The total cash with Lakshmi is .$\mathrm{Rs}400000$. How many notes of each denomination does she have?

Q.

Question 1 (i)

Get the algebraic expression in the following case using variables, constants and arithmetic operations:

Subtraction of z from y.

Q. On transposing a variable or constant from the left hand side to the right hand side of an equation, its sign does not change.

1. False
2. True

Q. The numerical coefficient of the unknown is a number that is by an unknown(s) in a particular term.

1. multiplied
2. divided
3. subtracted
4. added

Q.

Kiran buys of yellow ribbon, of red ribbon and of blue ribbon to decorate a mantap. If the cost of 1 metre of ribbon is Rs. 6/-, find the cost of ribbons bought by him.

Q.

Write the numerical as well as literal coefficient for each of the following.

$-5xy$

Q. The mathematical phrase that contains numbers, variables and operators is an algebraic .

1. equation
2. expression
3. coefficient
4. formula

Q.

Find the rule which gives the number of matchsticks required to make the below matchstick pattern:-

A pattern of the letter $A$as A.

Q. John has $10$ blue and red marbles in his bag. Among these $10$ marbles, the number of blue marbles is $b$ and the number of red marbles is $r$. Which of the following is the correct algebraic equation ?

1. $b+r=10$
2. $b-r=10$
3. $b\times r=10$
4. None of the above

Q.

State which of the following are equations (with a variable). Give a reason for your answer. Identify the variable from the equations with a variable.

$7=11\times 5-12\times 4$

Q.

John has a total of 10 blue, white and red marbles in his bag. If the number of blue marbles is 4 and the number of red marbles is 3, then the number of white marbles is

Q.

Mohan has ‘$3a$’ red marbles and ‘$2b$’ yellow marbles. Total marbles with him are:

1. $6ab$

2. $3a+2b$

3. $5ab$

4. $5(a+b)$

Q. Which hand of the clock represents radius of the inner circle?

1. Hour
2. Minute
3. Second
4. None

Q. Jack drove $60$ miles in one hour. If he maintains his current speed, he will travel a distance of miles in $t$ hours.

Q. What is an equation?

Q. There are $15$ fruits in a basket. The basket contains $a$ number of apples, $g$ number of grapes and $k$ number of kiwis only. What would be the value of $a+g+k?$

1. $10$
2. $12$
3. $15$
4. $18$

Q. Write the equation for the following statement:
Ten times a is 70.

Q. In algebra, a constant is a fixed number, or sometimes a letter such as $x,p,q$ or $d$ to stand for a fixed number.

1. True
2. False

Q.

Write down separately the terms of each of the following algebraic expressions :

$3xy+4x^2{y}^3-5z$$-5z.$

Q. what is diameter formula?

Q. On transposing a variable or constant from the left hand side to the right hand side of an equation, its sign does not change.

1. True
2. False

Q. Alex's elder brother is $y$ years old, and Alex is $5$ years younger than his brother. What is the age of Alex?

1. $y+5$
2. $5-y$
3. $5y$
4. $y-5$

Q. On transposing a variable or constant from the left hand side to the right hand side of an equation, its sign does not change.

1. False
2. True

Q. Which value of $a$ would satisfy the algebraic equation $a+5+(-4)=12?$

1. $9$
2. $10$
3. $11$
4. $12$

Q. Choose the expression with exactly one variable.

1. 2a + b - 7
2. a + 2
3. 1
4. a + b + c

Q.

Write the numerical as well as literal coefficient for each of the following.

$x$

Q. The mathematical phrase that contains numbers, variables and operators is an algebraic .

1. coefficient
2. equation
3. expression
4. formula

Q. Algebra is the mathematics of uncovering the unknowns.

1. True
2. False

Q. The product of two rational numbers is 18/7 and one third of first number is -7/5 then half of the second number is ?

Q. Solve the following equation by trial and error method:
5p+ 2 = 17