1 Marks Question

Question 11 Mark

Which of the following form an AP? Justify your answer.
1, 1, 2, 2, 3, 3, .....

Answer

Given form of numbers will form an A.P. If $d_1 = d_2 = d_3....$
$So, d_1 = 1 - 1$
$d_1 = 0$
$d_2 = 2 - 1$
$d_2 = 1$
$\therefore\text{d}_{1}\neq\text{d}_{2}$
Hence, the given form of numbers will form an A.P.

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Question 21 Mark

Which of the following form an AP? Justify your answer.
11, 22, 33, .......

Answer

Given form of numbers will form an A.P. If $d_1 = d_2 = d_3 =......$
$So, d_1 = 22 - 11$
$d_1 = 11$
$d_2 = 33 - 22$
$d_2 = 11$
$d_1 = d_2 = 11$
Hence, the given form of numbers will form an A.P.

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Question 31 Mark

Which of the following form an AP? Justify your answer.
$\frac{1}{2},\frac{1}{3},\frac{1}{4},... $

Answer

Given form of numbers will form an A.P. If $d_1 = d_2 = d_3 =.....$
$\text{So},\text{ d}_{1}=\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=\frac{-1}{6}$
$\text{d}_{2}=\frac{1}{4}-\frac{1}{3}=\frac{3-2}{12}=\frac{-1}{12}$
$\therefore\text{d}_{1}\neq\text{d}_{2}$

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Question 41 Mark

Which of the following form an AP? Justify your answer.
-1, -1, -1, -1 ...

Answer

A series of numbers will be in A.P. If $d_1 = d_2 = d_3......$
$So, d_1 = -1 - 1(-1) = 0$
$d_2 = -1 - (-1) = 0$
$d_3 = -1 - (-1) = 0$
$\therefore$ $d_1 = d_2 = d_3.....$
So, the given series form an A.P.

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Question 51 Mark

Which of the following form an AP? Justify your answer.
$2, 2^2, 2^3, 2^4, .......$

Answer

Given form of numbers will form an A.P. If $d_1 = d_2 = d_3....$
$So, d_1 = 2^2 - 2 = 4 - 2$
$d_2 = 2^3 - 2^2 = 8 - 4 = 4$
$d_3 = 2^4 - 2^3 = 16 - 8 = 8$
$\therefore\text{d}_{1}\neq\text{d}_{2}\neq\text{d}_{3}$

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Question 61 Mark

Which of the following form an AP? Justify your answer.
0, 2, 0, 2, .....

Answer

Given form of numbers will be in A.P. If $d_1 = d_2 = d_3......$
$So, d_1= 2 - 0$
$d_1 = 2$
$d_2 = 0 - 2$
$d_2 = -2$
$\therefore\text{d}_{1}\neq\text{d}_{2}$
So, the given of numbers is not an A.P.

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Question 71 Mark

Which of the following form an AP? Justify your answer.
$\sqrt{3},\sqrt{12},\sqrt{27},\sqrt{48},....$

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