Variable and Constants

Q. What do we call an algebraic expression with same variables ?

Q.

If a pen costs $₹x$ and a pencil costs $₹y$ , what is the cost of $5$ pens and $9$ pencils ?

Q.

X^m = Yⁿ = Z^q , XYZ = 1 and m is not equal to 0, then find 1/m + 1/n + 1/p

Q.

State true or false.
The total number of variables in the equation 3a + b + 6ab = 0 is 3.

1. 3

2. 12

Q. Arrange the following type of equations in the ascending order of their degree.

1. Cubic
2. Quadratic
3. Linear
4. Biquadratic

Q. The total number of variables in the equation 3a + b + 6ab = 0 is

1. 1
2. 2
3. 3

Q.

Give first step that you will use to separate the variables in each of the following:

x - 5 = 0

Q.

State true or false.
The total number of variables in the equation 3a + b = 5 is 3.

1. 12

2. 3

Q.

Which of the following is a linear expression ?

a) $x^2\times y+xy+1$

b) $x+y+1$

c) $x^3\times y+xy+1$

d) $4x^2+1$

1. $4x^2+1$

2. $x^2\times y+xy+1$

3. $x+y+1$

4. $x^3\times y+xy+1$

Q. Find the value of m in the given equation:$7m+\frac{19}{2}=13$

1. $4$
2. $\frac{1}{2}$
3. $\frac{2}{5}$
4. None of the above

Q.

The linear expression equivalent to 5xy - 2k - xy( 8z + 5 ) is 5xy - 2k - 8xyz.

1. False

2. True

Q.

Question 77

In questions 60 to 79, state whether the statements are True or False.
Amount received after depositing ₹ 800 for a period of 3 yr at the rate of 12 % per annum is ₹ 896.

Q.

The equation with a variable 5t - 4 = 1 is satisfied for 't' = 1.

1. No

2. Yes

Q.

12x - 4 is a linear expression .

1. True

2. False

Q. Justin takes the subway to commute for work, and he spends $\$8$ on lunch every day. In 20 days, he spent a total of $\$210$ on both lunch and subway tickets. If due to money shortage, he decides to spend only $\$85$ for the next ten days for lunch and travel, then how much should he reduce from the usual amount spent on lunch per day?

1. $\$2.75$
2. $\$1.5$
3. $\$2$
4. $\$2.5$

Q.

17+5p=12 What is the value of x

Q. If $\frac{x}{pq}+\frac{x}{qr}+\frac{x}{pr}=p+q+r$, then find the value of$x$.

1. $pqr$
2. $\frac{pq}{r}$
3. $\frac{p}{qr}$
4. $\frac{q}{pr}$

Q.

The total number of variables in the equation 3a + b + 6ab = 0 is 3.

1. 12

2. 3

Q.

The cost of one food packet is ₹ 45 with a fixed delivery charge of ₹ 10. The total cost of $y$ food packets is given by ___.

1. ₹ (45 + 10y)

2. ₹ (45y + 10)

3. ₹ (45 - 10y)

4. ₹ (45 + 10 + y)

Q. Find the value of $x$ in $kx+a=mx+b$.

1. $\frac{b-a}{k-m}$
2. $\frac{a-b}{k-m}$
3. $\frac{k-m}{a-b}$
4. $\frac{m-k}{a-b}$

Q. If $\frac{x+c}{x+1}=c+1$. Express $x$ in terms of $c$.
Given c is a constant, $c\ne 0$, $c\ne -1$ and $x\ne -1$.

1. $\frac{-1}{c}$
2. $\frac{c-1}{c}$
3. $\frac{c-1}{c+1}$
4. $c-2$

Q.

The total number of variables in the equation 3a + b + 6ab = 0 is 3.

1. 3

2. 12

Q.

Write the variables and constants of the following expressions.

(i) 18 + x − y (ii) 7p − 4q + 5

Q. How many variables are there in the expression (xy + 5)?

1. 0
2. 1
3. 2
4. 3

Q. How many variables are there in the expression (xy + 5)?

1. 3
2. 1
3. 2
4. 0

Q.

The variable used in the equation 2p + 8 = 18 is ___ .

Q. If y = x /x + a, then prove: x dy / dx = y [ 1 – y].

Q.

Two prizes are to be distributed in a quiz contest. The value of the second prize is ${\frac{5}{6}}^{th}$ of the value of the first prize. If the first prize is Rs. 3000, the second prize is Rs.___.

Q. There are three consecutive numbers whose sum is 129. Find the square of the middle one.

1. 1936
2. 1849
3. 1764
4. 1829