Expression Formation

Q.

α, β and γ are the zeroes of cubic polynomial $p\left(x\right)=a{x}^3+b{x}^2+cx+d$, $(a\ne 0)$. Then product of their zeroes [αβγ] is?

Q.

$3x-5y-4=0$ and $9x=2y+7$; solve it with the elimination method.

Q.

Suppose the vectors ${\mathrm{x}}_1$, ${\mathrm{x}}_2$ and $x_3$ are the solutions of system of linear equation, $\mathrm{Ax}=\mathrm{b}$ when the vector is on the right side is equal to ${\mathrm{b}}_1$, ${\mathrm{b}}_2$ and ${\mathrm{b}}_3$ respectively. If ${\mathrm{x}}_1=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$, ${\mathrm{x}}_2=\left[\begin{array}{c}0\\ 2\\ 1\end{array}\right]$, ${\mathrm{x}}_3=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$, ${\mathrm{b}}_1=\left[\begin{array}{c}1\\ 0\\ 0\end{array}\right]$, ${\mathrm{b}}_2=\left[\begin{array}{c}0\\ 2\\ 0\end{array}\right]$, ${\mathrm{b}}_3=\left[\begin{array}{c}0\\ 2\\ 2\end{array}\right]$ , then the determinant of $\mathrm{A}$ is equal to

1. $2$

2. $\frac{1}{2}$

3. $\frac{3}{2}$

4. $4$

Q.

Solve the following equation: $1.6=\frac{y}{1.5}$

Q.

Q.

If $5$ is added to three times the product of numbers $m$ and $n.$

Express the above statement as an algebraic expression.

1. $5(mn+3)$
2. $3(mn+5)$
3. $(3mn+5)$
4. $(3m+n+5)$

Q.

Question 1 (v)

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

Numbers $x$ and $y$ both squared and added.

Q.

Give one example of a Biquadratic Polynomial.

Q.

Question 1 (iii)

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

The number z is multiplied by itself.

Q.

Factorise the expression and divide them as directed: $4yz\left(z^2+6z-16\right)÷2y\left(z+8\right)$.

Q.

Question 76

A taxi service charges Rs 8 per km levies a fixed charge of Rs 50. Write an algebraic expression for the above situation, if the taxi is hired for x km.

Q.

Question 4 (iii)

If a = 2, b = -2, find the value of:
$a^2-b^2$

Q.

Complete the pattern

-11, -8, -5, -2, -----, -----, -----

Q.

Solve: $0.5x-(0.8-0.2x)=0.2-0.3x$

Q.

The difference of two numbers is $4$, if the difference of their reciprocals is $\frac{4}{21}$, find the numbers.

Q.

Write an algebraic expression for the following :

Three times the sum of $x$ and $y$

Q.

Question 78

Sonu and Raj have to collect different kinds of leaves for a science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.

Q. A pencil costs Rs 5 more than an eraser. The total cost of 5 pencils and 10 erasers is Rs 100. What is the cost of a single pencil and a single eraser?

1. Eraser - Rs 15
   Pencil - Rs 20
2. Eraser - Rs 10
   Pencil - Rs 15
3. Eraser - Rs 5
   Pencil - Rs 10
4. None of the above

Q.

Question 77

Shiv works in a mall and gets paid Rs. 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.

Q.

Write the following in algebraic form:

The product of $x$ and $y$ added to the sum of $x$ and $y$.

Q.

Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

(a)

(b)

(c)

If the number of digits formed is taken to be n, the number of segments required to form n digits is given by the algebraic expression appearing on the right of each pattern.

How many segments are required to form 5, 10, 100 digits of the kind −

, , .

Q.

Question 84

Rohan's mother gave him Rs. $3x{y}^2$ and his father gave him Rs. $5(x{y}^2+2)$.Out of this money, he spent Rs. $(10-3x{y}^2)$ on his birthday party. How much money is left with him?

Q.

Which of the following is always even.

1. Sum of three odd numbers

2. Sum of two odd numbers

3. Sum of one even and one odd number

4. None of these

Q.

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

(i) $3\sqrt{t}+t\sqrt{2}$

(ii) $y+\frac{2}{y}$

(iii) $x^{10}+y^3+t^{50}$

Q. 8 is subtracted from three times the product of numbers p, q and r. Express the above statement as an algebraic expression.

1. $3pqr-8$
2. $3pqr+8$
3. $8-3pqr$
4. $3pq+q-8$

Q. 'x' packets with 6 sweets each are divided equally among 10 children. How many sweets does each child get?

1. 6x
2. 3x - 5
3. 6x - 10
4. $\frac{3x}{5}$

Q.

Question 83 (a)

A wire is (7x -3) metres long. A length of (3x -4) metres is cut for use. Now, answer the following question:

How much wire is left?

Q.

Question 1 (vii)

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

Product of numbers y and z subtracted from10.

Q.

The degree of a polynomial $A$ is $7$ and that of polynomial $AB$ is $56$, then find the degree of polynomial $B$.

1. $49$

2. $42$

3. $50$

4. $48$

Q.

Question 95 (ii)

What's the Error?

A student wrote an algebraic expression for "5 less than a number n divided by 3" as $\frac{n}{3}-5$. What error did the student make?