[2 Mark Question Answer]

Question 12 Marks

Two complementary angles differ by $14^\circ .$ Find the angles.

Answer

Let the complementary angles be
$\angle 1 + \angle 2 = 90^\circ $
Then, as per questions,
Also, $\angle 1 - \angle 2 = 14^\circ $
Solving, the equation:
$\angle 1 = 52^\circ $ and $\angle 2 = 38^\circ .$

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Question 22 Marks

Find two consecutive even numbers, whose sum is $38.$

Answer

Let the two consecutive even numbers be $2n$ and $2n + 1.$
Then As per the question,
$2n + (2n + 2) = 38$
$\Rightarrow 4n = 36$ or $n = 9$
Thus, numbers are $2n = 18$ and $2n + 1 = 20.$

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Question 32 Marks

A number is as much greater than $21$ as it is less than $71.$ Find the number.

Answer

Let the two nos be $x$ and $y$
Then, as per the question,
$x - 21 = 71 -x$
$\Rightarrow 2x = 92$
$\Rightarrow x = 46.$

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Question 42 Marks

Solve the following equations for the unknown$: \sqrt{x-5}=3$

Answer

$\sqrt{x-5}=3$
Squaring both sides
$\Rightarrow x-5=(3)^2 $
$\Rightarrow x-5=9 $
$\Rightarrow x=9+5 $
$\Rightarrow x=14 .$

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Question 52 Marks

Solve the following equations for the unknown$: 3(3x - 4) -2(4x - 5) = 6$

Answer

$3(3x - 4) -2(4x - 5) = 6$
Simplifying by Collecting like terms,
$9x - 8x = 6 + 12 - 10$
$\Rightarrow x = 8.$

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Question 62 Marks

In the following equations, verify if the given value is a solution of the equation$: 2x - 5 = 3x; x = 3$

Answer

$2x - 5 = 3x; x = 3$
Can be written as $: x = -5,$
which is not satisfied by $x = 3.$
Thus,$ x = 3$ is not a solution of $2x - 5 = 3x.$

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MATHEMATICS [2 Mark Question Answer]

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