QBManager

ALGEBAIC EXPRESSIONS

295449 Subtract the second expression from the first m $^{1}$ n - 8 + mn $^{1}$ and 7 - m $^{1}$ n - mn $^{1}$ .

1 m

^{1}

+ 2mn

^{1}

- 14

2 2m

^{1}

n + 2mn

^{1}

- 15

3 2m

^{1}

n + 2n

^{1}

- 14

4 2n

^{1}

mn + 2mn

^{1}

- 15

Explanation:

2m $^{1}$ n + 2mn $^{1}$ - 15
m $^{1}$ n - 8 + mn $^{1}$ - (7 - m $^{1}$ n - mn $^{1}$ )
= m $^{1}$ n - 8 + mn $^{1}$ + m $^{1}$ n - 7 + mn $^{1}$
= 2m $^{1}$ n + 2mn $^{1}$ - 15

ALGEBAIC EXPRESSIONS

295450 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The value of 9x -38 when x = 4 is -2.
Reason (R): Numerical coefficient is defined as a fixed number that is multiplied to a variable.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

ALGEBAIC EXPRESSIONS

295451 If $f (x) = \frac{5}{3} x^{2}$ then $f (\frac{3}{5})$ is:

1

\frac{1}{5}

2

\frac{1}{3}

3

\frac{3}{5}

4

\frac{4}{5}

Explanation:

$\frac{3}{5}$
$f(x) = \frac{5}{3} x^{2} f (\frac{3}{5}) = \frac{5}{3} (\frac{3}{5})^{2} \Rightarrow \frac{5}{3} \times \frac{3}{5} \times \frac{3}{5} \Rightarrow \frac{3}{5}$

ALGEBAIC EXPRESSIONS

295452 If x is a natural number, then the minimum value of (x $^{1}$ - 6x + 12) is:

1 3

2 7

3 6

4 12

Explanation:

3
Given: f(x) = x $^{1}$ - 6x + 12 Minimum value of f (x) is at x = x $_{\1}$ , where x $_{\1}$ ? is that value of x where f'(x) = 0 Here,
f'(x) = 2x - 6 So, f(x) = 0 = 2x - 6 x = x $_{\1}$ ?= 3
$∴$ maximum value of f(x) is = f(3) = 3 $^{1}$ - 6 (3) + 12 = 21 - 18 = 3

ALGEBAIC EXPRESSIONS

295449 Subtract the second expression from the first m $^{1}$ n - 8 + mn $^{1}$ and 7 - m $^{1}$ n - mn $^{1}$ .

1 m

^{1}

+ 2mn

^{1}

- 14

2 2m

^{1}

n + 2mn

^{1}

- 15

3 2m

^{1}

n + 2n

^{1}

- 14

4 2n

^{1}

mn + 2mn

^{1}

- 15

Explanation:

2m $^{1}$ n + 2mn $^{1}$ - 15
m $^{1}$ n - 8 + mn $^{1}$ - (7 - m $^{1}$ n - mn $^{1}$ )
= m $^{1}$ n - 8 + mn $^{1}$ + m $^{1}$ n - 7 + mn $^{1}$
= 2m $^{1}$ n + 2mn $^{1}$ - 15

ALGEBAIC EXPRESSIONS

295450 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The value of 9x -38 when x = 4 is -2.
Reason (R): Numerical coefficient is defined as a fixed number that is multiplied to a variable.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

ALGEBAIC EXPRESSIONS

295451 If $f (x) = \frac{5}{3} x^{2}$ then $f (\frac{3}{5})$ is:

1

\frac{1}{5}

2

\frac{1}{3}

3

\frac{3}{5}

4

\frac{4}{5}

Explanation:

$\frac{3}{5}$
$f(x) = \frac{5}{3} x^{2} f (\frac{3}{5}) = \frac{5}{3} (\frac{3}{5})^{2} \Rightarrow \frac{5}{3} \times \frac{3}{5} \times \frac{3}{5} \Rightarrow \frac{3}{5}$

ALGEBAIC EXPRESSIONS

295452 If x is a natural number, then the minimum value of (x $^{1}$ - 6x + 12) is:

1 3

2 7

3 6

4 12

Explanation:

3
Given: f(x) = x $^{1}$ - 6x + 12 Minimum value of f (x) is at x = x $_{\1}$ , where x $_{\1}$ ? is that value of x where f'(x) = 0 Here,
f'(x) = 2x - 6 So, f(x) = 0 = 2x - 6 x = x $_{\1}$ ?= 3
$∴$ maximum value of f(x) is = f(3) = 3 $^{1}$ - 6 (3) + 12 = 21 - 18 = 3

ALGEBAIC EXPRESSIONS

295449 Subtract the second expression from the first m $^{1}$ n - 8 + mn $^{1}$ and 7 - m $^{1}$ n - mn $^{1}$ .

1 m

^{1}

+ 2mn

^{1}

- 14

2 2m

^{1}

n + 2mn

^{1}

- 15

3 2m

^{1}

n + 2n

^{1}

- 14

4 2n

^{1}

mn + 2mn

^{1}

- 15

Explanation:

2m $^{1}$ n + 2mn $^{1}$ - 15
m $^{1}$ n - 8 + mn $^{1}$ - (7 - m $^{1}$ n - mn $^{1}$ )
= m $^{1}$ n - 8 + mn $^{1}$ + m $^{1}$ n - 7 + mn $^{1}$
= 2m $^{1}$ n + 2mn $^{1}$ - 15

ALGEBAIC EXPRESSIONS

295450 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The value of 9x -38 when x = 4 is -2.
Reason (R): Numerical coefficient is defined as a fixed number that is multiplied to a variable.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

ALGEBAIC EXPRESSIONS

295451 If $f (x) = \frac{5}{3} x^{2}$ then $f (\frac{3}{5})$ is:

1

\frac{1}{5}

2

\frac{1}{3}

3

\frac{3}{5}

4

\frac{4}{5}

Explanation:

$\frac{3}{5}$
$f(x) = \frac{5}{3} x^{2} f (\frac{3}{5}) = \frac{5}{3} (\frac{3}{5})^{2} \Rightarrow \frac{5}{3} \times \frac{3}{5} \times \frac{3}{5} \Rightarrow \frac{3}{5}$

ALGEBAIC EXPRESSIONS

295452 If x is a natural number, then the minimum value of (x $^{1}$ - 6x + 12) is:

1 3

2 7

3 6

4 12

Explanation:

3
Given: f(x) = x $^{1}$ - 6x + 12 Minimum value of f (x) is at x = x $_{\1}$ , where x $_{\1}$ ? is that value of x where f'(x) = 0 Here,
f'(x) = 2x - 6 So, f(x) = 0 = 2x - 6 x = x $_{\1}$ ?= 3
$∴$ maximum value of f(x) is = f(3) = 3 $^{1}$ - 6 (3) + 12 = 21 - 18 = 3

ALGEBAIC EXPRESSIONS

295449 Subtract the second expression from the first m $^{1}$ n - 8 + mn $^{1}$ and 7 - m $^{1}$ n - mn $^{1}$ .

1 m

^{1}

+ 2mn

^{1}

- 14

2 2m

^{1}

n + 2mn

^{1}

- 15

3 2m

^{1}

n + 2n

^{1}

- 14

4 2n

^{1}

mn + 2mn

^{1}

- 15

Explanation:

2m $^{1}$ n + 2mn $^{1}$ - 15
m $^{1}$ n - 8 + mn $^{1}$ - (7 - m $^{1}$ n - mn $^{1}$ )
= m $^{1}$ n - 8 + mn $^{1}$ + m $^{1}$ n - 7 + mn $^{1}$
= 2m $^{1}$ n + 2mn $^{1}$ - 15

ALGEBAIC EXPRESSIONS

295450 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion (A): The value of 9x -38 when x = 4 is -2.
Reason (R): Numerical coefficient is defined as a fixed number that is multiplied to a variable.

1 Both A and R are true and R is the correct explanation of A.

2 Both A and R are true but R is not the correct explanation of A.

3 A is true but R is false.

4 A is false but R is true.

ALGEBAIC EXPRESSIONS

295451 If $f (x) = \frac{5}{3} x^{2}$ then $f (\frac{3}{5})$ is:

1

\frac{1}{5}

2

\frac{1}{3}

3

\frac{3}{5}

4

\frac{4}{5}

Explanation:

$\frac{3}{5}$
$f(x) = \frac{5}{3} x^{2} f (\frac{3}{5}) = \frac{5}{3} (\frac{3}{5})^{2} \Rightarrow \frac{5}{3} \times \frac{3}{5} \times \frac{3}{5} \Rightarrow \frac{3}{5}$

ALGEBAIC EXPRESSIONS

295452 If x is a natural number, then the minimum value of (x $^{1}$ - 6x + 12) is:

1 3

2 7

3 6

4 12

Explanation:

3
Given: f(x) = x $^{1}$ - 6x + 12 Minimum value of f (x) is at x = x $_{\1}$ , where x $_{\1}$ ? is that value of x where f'(x) = 0 Here,
f'(x) = 2x - 6 So, f(x) = 0 = 2x - 6 x = x $_{\1}$ ?= 3
$∴$ maximum value of f(x) is = f(3) = 3 $^{1}$ - 6 (3) + 12 = 21 - 18 = 3