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Question 1
1 / -0
Which number comes next?
$$5, 9, 13, 17, 21, 25, 29,...$$
Solution
The series adds $$4$$ to each number to get the next number.
So, the next number is $$29 + 4 = 33$$
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Question 2
1 / -0
Find the next number of the series.
$$7, 10, 8, 11, 9, 12,....$$
Solution
The next number is $$10$$.
The first $$2$$ numbers difference is $$3$$.
The second $$2$$ numbers difference is $$2$$.
So, this is simple alternating addition of $$ 3$$ and subtraction of $$2$$.
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Question 3
1 / -0
$$2, 3,$$ __$$, 4, 4, 5, 6, 6, 6, 7, 7, 7...$$ What number should fill the blank?
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Question 4
1 / -0
Which pair of numbers comes next?
$$10, 18, 12, 21, 15 ,25, ,....$$
Solution
This is an alternating addition series First series = $$10, 10+2=12, 12+3=15$$. $$\therefore$$ next number= $$15+4=19$$
Second series = $$18, 18+3=21, 21+4=25$$ $$\therefore$$ next number = $$25+5=30$$
The next pair of numbers are $$19, 30$$.
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Question 5
1 / -0
Fill in the blank: $$62, 66, 63, 66, 64,$$ __$$, 65,....$$
Solution
The series alternates the addition of $$4$$ with the subtraction of $$3$$.
So, the missing number is $$61$$.
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Question 6
1 / -0
Look at this series: $$32, 31, 33, 32, 34, 33,...$$. What is the next number?
Solution
The next number is $$35$$.
Here first $$1$$ is subtracted and then $$2$$ is added, and so on.
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Question 7
1 / -0
Find the value of $$'?'$$ in the series: $$12, 17, 15, ?, 18, 23, 21,....$$
Solution
The series alternates the addition of $$5$$ with the subtraction of $$2$$.
So, the number is $$20$$.
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Question 8
1 / -0
The area of the triangle formed from points $$(1, 2), (2, 4)$$ and $$(3, 1)$$ is ____ square units.
Solution
Formula for area of triangle is $$\left|\dfrac{1}{2}[x_{1}(y_{2}-y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})] \right|$$
where $$x_{1} = 1$$, $$y_{1} = 2$$, $$x_{2} = 2$$, $$y_{2} = 4$$, $$x_{3} = 3$$ and $$y_{3} = 1$$
Substitute the values, we get,
Area of triangle $$=$$ $$\left|\dfrac{1}{2}\times[1(4 - 1) + 2(1 - 2) + 3(2 - 4)]\right|$$
$$=$$ $$\left|\dfrac{1}{2}\times[3 - 2 - 6]\right|$$
$$=$$ $$\left|\dfrac{1}{2}\times -5\right|$$
$$=$$ $$\left|-\frac{5}{2} \right|$$
Area always in absolute value.
So, area of the triangle $$= \dfrac{5}{2}$$ square units.
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Question 9
1 / -0
Choose the missing number in the series: $$2, 2, 3, 4, 4,$$__$$, 6, 6, 7, 8, 8, 9....$$
Solution
This is a continuous series of adding $$1$$ to the previous number, in which every third number is not repeated.
So, the missing number is $$5$$.
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Question 10
1 / -0
Find the value of $$'x'$$ in the series: $$144, 169, x, 225, 256, 289$$.
Solution
The series is a perfect square in increasing order of $$12, 13, 14, 15...$$
So, the value of $$x$$ is $$196$$.
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