Solve The Following Question.1MARKS

Question 11 Mark

Subtract:
$4 a^2+5 b^2-6 c^2+8 \text { from } 2 a^2-3 b^2-4 c^2-5 .$

Answer

$2 a^2-3 b^2-4 c^2-5-\left(4 a^2+5 b^2 2-6 c^2+8\right)$
$=2 a^2-3 b^2-4 c^2-5-4 a^2-5 b^2+6 c^2-8$
$=2 a^2-4 a^2-3 b^2-5 b^2-4 c^2+6 c^2-5-8$
$=-2 a^2-8 b^2+2 c^2-13$

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Question 21 Mark

Write 'T' for true and 'F' for false of the following:
$\frac{\text{x}}{4}+\frac{\text{x}}{6}-\frac{\text{x}}{2}=\frac{3}{4}\Rightarrow\text{x}=-9$

Answer

True
Solution:
$\frac{\text{x}}{4}+\frac{\text{x}}{6}-\frac{\text{x}}{2}=\frac{3}{4}$
$\Rightarrow\frac{3\text{x}+2\text{x}-6\text{x}}{12}=\frac{3}{4}$
$\Rightarrow\frac{-\text{x}}{12}=\frac{3}{4}$
$\Rightarrow-4\text{x}=36$
$\Rightarrow\text{x}=-\frac{36}{4}$
$\Rightarrow\text{x}=-9$

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Question 31 Mark

Write 'T' for true and 'F' for false of the following:
(5a - 9b) - (-6a + 2b) = (-a - 7b)

Answer

FalseSolution:
L.H.S. = (5a - 9b) - (-6a + 2b)
= 5a - 9b + 6a - 2b = (-a - 7b)
= 5a + 6a - 9b - 2b = (-a - 7b)
= (11a - 11b)
This is not equal to (-a - 7b).
Thus, the L.H.S. is not equal to the R.H.S.

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Question 41 Mark

Fill in the blanks.
$x^2-18 x+81$= ( ____ )

Answer

$x^2-18 x+81=(x-9)^2$
Solution:
$x^2-18 x+81$
$=x^2-2 \times x \times 9+9^2$
$=(x-9)^2$

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Question 51 Mark

Write 'T' for true and 'F' for false of the following:
$2\text{x}-5=0\Rightarrow\text{x}=\frac{2}{5}$

Answer

FalseSolution:
$2\text{x} - 5 = 0$
$\Rightarrow 2\text{x}= 5$
$\Rightarrow\text{x} = \frac{5}{2}$

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Question 61 Mark

Write 'T' for true and 'F' for false of the following:
-8 is a monomial.

Answer

True
Solution:
Any expression that contains only one term is called a monomial. It can either be a constant or a variable.

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Question 71 Mark

Fill in the blanks. abc - ab - c + 1 = (_____)(_____)

Answer

(c - 1)(ab - 1)
Solution:
abc - ab - c + 1
= ab(c - 1) - 1(c - 1)
= (c - 1)(ab - 1)

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MCQ 81 Mark

Mark $(\checkmark)$ against the correct answer: $8 x^3-2 x=?$

A
$(4 x -1)(2 x -1) x$
B
$\left(2 x^2+1\right)(2 x-1)$
✓
$2 x(2 x-1)(2 x+1)$
D
None of these

Answer

Correct option: C.

$2 x(2 x-1)(2 x+1)$

$8 x^3-2 x$
$=2 x\left(4 x^2-1\right)$
$=2 x\left((2 x)^2-1^2\right)$
$=2 x(2 x-1)(2 x+1)$

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Question 91 Mark

Fill in the blanks.
$4-36 x^2=$(_____)(_____)(_____)

Answer

$(4)(1-3 x)(1+3 x)$
$4-36 x^2$
$=4\left(1-9 x^2\right)$
$=4\left(12-(3 x)^2\right)$
$=(4)(1-3 x)(1+3 x)$

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Question 101 Mark

Fill in the blanks.
$x^2-14 x+13=$ (_____)(_____)

Answer

$(x-13)(x-1)$
Solution:
$x^2-14 x+13$
$=x^2-13 x-x+13$
$=x(x-13)-1(x-13)$
$=(x-13)(x-1)$

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Question 111 Mark

Mark $(\checkmark)$ against the correct answer:
$\frac{\text{x}+5}{2}+\frac{\text{x}-5}{3}=\frac{25}{6}$ gives:

x = 3
x = 4
x = 5
x = 2

Answer

x = 4

Solution:

$\frac{\text{x}+5}{2}+\frac{\text{x}-5}{3}=\frac{25}{6}$(because L.C.M. of 2 and 3 is 6)

$\Rightarrow\frac{3(\text{x}+5)+2(\text{x}-5)}{6}=\frac{25}{6}$

$\Rightarrow\frac{3\text{x}+15+2\text{x}-10}{6}=\frac{25}{6}$

$\Rightarrow\frac{5\text{x}+5}{6}=\frac{25}{6}$

$\Rightarrow5\text{x}+5=25$ (cancelling 6 from the denominator on both the sides)

$\Rightarrow5\text{x}=25-5$

$\Rightarrow\text{5x}=20$

$\Rightarrow\text{x}=\frac{20}{5}$

$\Rightarrow\text{x}=4$

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Question 121 Mark

Fill in the blanks.
$9 z^2-x^2-4 y^2+4 x y=$(_____)(_____)

Answer

$(3z + x - 2y)(3z - x + 2y)$
Solution:
$9 z^2-x^2-4 y^2+4 x y$
$=9 z^2-\left(x^2-4 x y+4 y^2\right)$
$=9 z^2-\left(x^2-2 x x \times 2 y+(2 y)^2\right)$
$=9 z^2-(x-2 y)^2$
$=(3 z)^2-(x-2 y)^2$
$=(3 z+(x-2 y)(3 z-(x-2 y))$
$=(3 z+x-2 y)(3 z-x+2 y)$

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Question 131 Mark

Write 'T' for true and 'F' for false of the following:
When x = 2 and y = 1, the value of $\frac{-8}{7}\text{x}^3\text{y}^4\text{ is }\frac{-64}{7}$

Answer

True
Solution:
x = 2
y = 2
Give expression $=\frac{-8}{7}(2)^3(1)^4$
$=\frac{-8}{7}\times8\times1$
$=\frac{-64}{7}$

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Question 141 Mark

Write 'T' for true and 'F' for false for the following:
$(5 - 3x^2)$ is a binomial.

Answer

True
Solution:
Binomial expression is an expression that shows the sum or the difference of two unlike terms. The above expression has two unlike terms, i.e. 5 and $3x^2.$

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Maths Solve The Following Question.1MARKS

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