Algebraic Expressions

Q. The sum of the two numbers is given to be $27$ and their product is $180$. What will be the two numbers?

1. $9,18$
2. $12,15$
3. $13,14$
4. $11,16$

Q. On His Birthday, Manoj planned that this time he celebrates his birthday in a small orphanage centre. He bought apples to give to children and adults working there. Manoj donated 2 apples to each children and 3 apples to each adult working there along with birthday cake. He distributed 60 total apple.
If the number of adults is 12, then find the number of children?

1. 15
2. 12
3. 18
4. 14

Q. Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.

Q.

Write a verbal statement for the algebraic expression: 4x + 8

1. 8 less than 4 times a number x

2. 4 less than 8 times a number x

3. 8 more than 4 times a number x

4. 4 more than 4 times a number x

Q. If $x^3-6x^2+11x-6$ = ($x-1$)($x-2$)($x+a$),
then $a$ = .

1. 2
2. -2
3. 3
4. -3

Q.

Degree of the zero polynomial is,

1. $1$
2. Any natural number
3. $0$
4. Not defined

Q. Question 6
The equation x = 7, in two variables, can be written as:


A) 1.x + 1.y = 7
B) 1.x + 0.y = 7
C) 0.x + 1.y = 7
D) 1.x - 1.y = 7

Q. Determine whether the given value of the variable is a solution of the corresponding equation or not. (i) 2x2 + 5x – 3 = 0, x = –3 (ii) 3x 2 + x – 2 = 0, 3 2

Q.

What are the number of values that satisfy the equation $2x+3=0$?

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

3. 1

4. All of the above

Q.
Identify like terms among the following:
3x, 2y, 4z, x, 5y, xz (2 marks)

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.
इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : If the supplement of an angle is four times of its complement angle, then the sum of three times of its complement with two times of its supplement angle is 330°.
A : यदि एक कोण का संपूरक कोण इसके पूरक कोण का चार गुना है, तब इसके पूरक के तीन गुना तथा इसके संपूरक के दो गुना का योगफल 330° है।

R : Two angles are called complementary angles if their sum is 90° and two angles are called supplementary angles if their sum is 180°.
R : दो कोण पूरक कोण कहलाते हैं यदि उनका योगफल 90° है तथा दो कोण संपूरक कोण कहलाते हैं यदि उनका योगफल 180° है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. divide the sum of -4/7 and -5/2 with the difference of 4/2 and 3/7

Q. At the end of the year 2016, the population of villages Kovad, Varud, Chikhali is 5x² $-$3 y² , 7 y² + 2 xy and 9 x² + 4 xy respectively. At the beginning of the year 2017, x² + xy $-$ y² , 5 xy and 3 x² + xy persons from each of the three villages respectively went to another village for education then what is the remaining total population of these three villages ?

Q. Number of terms in the expression $3x+4y+x$ is

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

Q.

Write in the simplest form: a⁶ x a⁴ x a^-5

1. a⁴

2. a⁵

3. a¹

4. a³

Q. The sum of the first of two numbers added to $3$ times the second number is $30$ and $2$ times the first number added to the second number gives $20$. The numbers are

1. $7$ and $8$
2. $6$ and $8$
3. $6$ and $9$
4. $6$ and $7$

Q.

Find the sum of the expression

$x^2-xy+yz;2xy+yz-2x^2;3yz+3x^2+xy$

Q.

In the expression $xy+3x+4y$, $3x$ is a___.

Q. Oranges are bought at $5$ for Rs.$10$ and sold at $6$ for Rs.$15$. Find profit or loss as percent.

Q. $\text{If}(x-3)\text{and}(x-2)\text{are two factors of the polynomial}{x}^3-6x^2+11x-6,\text{then find the third factor.}$

Q. If x⁸¹ + 81 is divided by x + 1, then the remainder is

यदि x⁸¹ + 81 को x + 1 द्वारा विभाजित किया जाता है, तब शेषफल है

1. 80
   
2. 82
   
3. –80
   
4. –82
   

Q. Solve: $50a^3-2a$

Q. Take away $x+y+3$ from $-x+2y+5$ and then the result from $x+y+2$. The final result will be equal to

1. $4x$
2. $6x$
3. $-3x$
4. $3x$

Q.

Find p(0), p(1) and p(2) for each of the following polynomials:
$1\left)p\right(y)=y^2-y+1$
$2\left)p\right(t)=2+t+2t^2-t^3$ [4 MARKS]

Q. $\text{Subtract:}2x^2+6-4x\text{from}3x^2-6x+8.$

1. $x^2-2x+2$
2. $2x^2-2x+2$
3. $x^2+2x+2$
4. $x^2-8x+2$

Q.

$4a^2-(4b^2+4bc+c^2$)

1. $(2a-2b-c)(2a+2b+c)$

2. $(2a-2b-c)(2a+2b-c)$

3. $(2a-2b-c)(2a-2b+c)$

4. $(2a+2b-c)(2a+2b+c)$

Q. $p\left(x\right)=x^4+2x^3-2x^2+x-1$ and $q\left(x\right)=x^2+2x-3$.
Then $p\left(x\right)$ is divisible by $q\left(x\right)$, if we

1. Add $(x-2)$
2. Add $(x-3)$
3. Add $(2-x)$
4. Add $(3-x)$

Q. Say true or false.

1. True
2. False

Q. A number when divided by 296 leaves 75 as remainder, If the same number is divided by 37, the remainder obtained is

1. 2
2. 1
3. 11
4. 8

Q. Burst out algebraic expressions from the following.

1. x
2. y + 2
3. x + 4 = 3
4. y = mx + c
5. x = 1
6. y - 2x + 3
7. 45
8. 7 - 2x