12

Q1. Addition of -4x and 6x is

• -2x
• 2x
• -24x
• 5x

Solution

-4x + 6x = 2x

Q2. For what value of x, the given algebraic expression 8x³ - 7x² + 12x - 13 becomes 0

• -1
• 1
• 2
• -2

Solution

Trying all the given options, (A) At x = -1, we have 8 x (-1)³ – 7 x (-1)² + 12 x (-1) - 13 = -8 - 7 - 12 - 13 = -40 (B) At x = 1, we have 8 x (1)³ – 7 x (1)² + 12 x (1) - 13 = 8 - 7 + 12 - 13 = 0 (C) At x = 2, we have 8 x (2)³ – 7 x (2)² + 12 x (2) - 13 = 64 - 28 + 24 - 13 = 47 (D) At x = -2, we have 8 x (-2)³ – 7 x (-2)² + 12 x (-2) - 13 = -64 - 28 - 24 - 13 = -129 Thus, at x = 1 the expression becomes 0.

Q3. x² - 2x + 3 - A = -3x² + 4x - 9, then A =

• 4x² + 6x - 12
• -4x² - 6x + 12
• 4x² - 6x + 12
• 4x² + 6x + 12

Solution

x² - 2x + 3 - A = -3x² + 4x - 9 Thus, -A = -3x² + 4x - 9 - (x² - 2x + 3) -A = -3x² + 4x - 9 - x² + 2x - 3 -A = -4x² + 6x - 12 Hence, A = 4x² - 6x + 12

Q4. Write the expression for: "y multiplied by 6 and then 2 subtracted from the product"

• 6y + 2
• 6y – 2
• 2y – 6
• 2y + 6

Solution

6y - 2.

Q5. The expression 21b - 32 + 7b - 20b on simplification gives

• 8b + 32
• 8b - 32
• 32 - 8b
• 24b

Solution

21b - 32 + 7b - 20b = 21b + 7b - 20b - 32 = 8b - 32

Q6. Simplify: (2xy + 4yz + 9) - (3yz - 3xy - 1)

• -xy + yz + 10
• -xy + yz
• xy + yz + 10
• xy - yz + 10

Solution

(2xy + 4yz + 9) - (3yz - 3xy - 1) = 2xy + 4yz + 9 - 3yz + 3xy + 1 = (2xy + 3xy) + (4yz - 3yz) + (9 + 1) = xy + yz + 10

Q7. Which of the following pair of algebraic expression will add up to give 12xy - 7?

• -7xy + 12; 12xy - 2; 9xy + 8 and -2xy - 25
• 2xy - 3; 13xy + 14; -2xy - 18 and -xy - 5
• 3xy + 2; 12xy - 13; -14xy + 12 and 13xy - 19
• 3xy; - 7 + 4xy; 9xy - 13 and 17

Solution

Adding like terms in each of the options provided, we get (A) -7xy + 12; 12xy - 2; 9xy + 8 and -2xy - 25 -7xy + 12xy + 9xy - 2xy + 12 - 2 + 8 - 25 = 12xy -7 Hence, option (A) is the correct answer.

Q8. Choose the constant term in the expression "x⁴ - 6x² + 2x - 3".

• 1
• -6
• 3
• -3

Solution

-3 is the constant term.

Q9. Which of the following is an example of binomial?

• 3x
• -x + 1
• 2x² + x + 1
• x⁴ + x - 1

Solution

-x + 1 is an example of binomial as it contains two terms.

Q10. For what value of k, we have 7x² - 5x + k = -4, given that x = -2,

• 22
• -42
• -22
• 42

Solution

Substituting the value of x in the given expression, we get 7 × (-2)² -5 × (-2) + k = -4 7 × 4 + 10 + k = -4 28 + 10 + k = -4 38 + k = -4 Thus, k = -42

Q11. The value of x for which the equation "4x = 12" is satisfied is

• 1
• 2
• 3
• 4

Solution

4x = 12 gives x = 3

Q12. The sum of all the numerical coefficients including constant, for a given algebraic expression 17x²y  - 12xy³ + 31x³ - 37 is

• -1
• 73
• 1
• -73

Solution

17 + (-12) + 31 + (-37) = -1

Q13. An algebraic expression obtained by multiplying x² with 12 and subtracting 5 from it is ______ .

• 12x² - 5
• 7x²
• 5 - 12x²
• -7x²

Solution

Multiplying x² with 12 gives 12x² And, subtracting 5 from 12x² gives 12x² - 5

Q14. Suppose n is the number of coins in my pocket. Four times the number of coins in my pocket plus 5 more is 29 can be written as

• 4n + 5 = 29
• 5n + 5 = 30
• 8n + 3 = 12
• 7n + 10 = 11

Solution

4 times the number of coins = 4n Four times the number of coins plus 5 more = 4 n + 5 According to given statement: 4n + 5 = 29

Q15. Simplify the following: (3a + 2) + (2b - 1)

• 3a + 2b + 1
• 3a + 2b
• 3a + b + 1
• a + 2b + 1

Solution

(3a + 2) + (2b - 1) = 3a + 2 + 2b - 1 = 3a + 2b + 1

Q16. Simplify: (p² + q²) - (q² - r²) - (r² + p²)

• 2
• 1
• 0
• 3

Solution

(p² + q²) - (q² - r²) - (r² + p²) = (p² - p²) + (q² - q²) + (r² - r²) = 0

Q17. The solution of equation "6y + 5 = 35" is:

• 2
• 3
• 4
• 5

Solution

6y + 5 = 35 Or, 6y = 35 - 5 = 30 Or, y = 30/6 = 5

Q18. Subtract 4x from 4y.

• 4(x - y)
• 4(y - x)
• (y - x)
• 4(y + x)

Solution

4y - 4x = 4(y - x).

Q19. Identify constant from the options:

• x
• a
• 3
• p

Solution

3 is a constant and remaining are variables.

Q20. Pratham's father age is 5 more than the 3 times his age. If its father age is 35 year, find the age of Pratham.

• 5 years
• 10 years
• 15 years
• 12 years

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