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Best wishes for your exam. Here is the step-by-step solution for all questions in .1:

1. Identify positive and negative integers:

Integers are numbers that can be positive, negative, or zero, but they do not have any fractional or decimal parts.

• 1(a) $4, \frac{3}{2}, (+2), +7, 0, -5$

  • Step 1: Identify the integers from the given numbers. $\frac{3}{2}$ is a fraction and not an integer.
  • Step 2: Classify the integers based on their sign.
    • Positive integers: Integers greater than zero.
    • Negative integers: Integers less than zero.
    • Zero: It is neither positive nor negative.
  • Answer:
    • Positive integers: $4, (+2), +7$
    • Negative integers: $-5$
    • Neither positive nor negative: 0

• 1(b) $-11, 51, 4.5, \frac{6}{7}, -7, \frac{5}{8}$

  • Step 1: Identify the integers from the given numbers. $4.5, \frac{6}{7}, \frac{5}{8}$ are fractions or decimals and not integers.
  • Step 2: Classify the integers based on their sign.
  • Answer:
    • Positive integers: 51
    • Negative integers: $-11, -7$

2. Write the opposite of the following:

The opposite of any statement means its inverse meaning.

• 2(a) Increase in weight by 10 kg

  • Step 1: The opposite of "increase" is "decrease".
  • Answer: Decrease in weight by 10 kg

• 2(b) Going towards West

  • Step 1: The opposite of "West" is "East".
  • Answer: Going towards East

• 2(c) $-80$

  • Step 1: The opposite of a number is the same value but with the opposite sign.
  • Answer: $*+80*$

• 2(d) 100 m above sea level

  • Step 1: The opposite of "above" is "below".
  • Answer: 100 m below sea level

• 2(e) Loss of ₹500

  • Step 1: The opposite of "loss" is "gain" or "profit".
  • Answer: Profit of ₹500

• 2(f) Violence in the country

  • Step 1: The opposite of "violence" is "peace".
  • Answer: Peace in the country

3. Write the numbers used in the following using the sign (+ or -):

• 3(a) An aeroplane is flying at a height of two thousand five hundred meters above the ground.

  • Step 1: Being "at a height" or "above" is represented by a positive sign (+).
  • Answer: $\boxed{+2500 \text{ m}}$

• 3(b) A submarine is moving at a depth of 800 m below sea level.

  • Step 1: Being "at a depth" or "below" is represented by a negative sign (-).
  • Answer: $\boxed{-800 \text{ m}}$

• 3(c) Temperature $10^\circ C$ above $0^\circ C$.

  • Step 1: Being "above" is represented by a positive sign (+).
  • Answer: $\boxed{+10^\circ C}$

• 3(d) Depositing ₹100 in the bank.

  • Step 1: "Depositing" (i.e., an increase in the account) is represented by a positive sign (+).
  • Answer: $\boxed{+₹100}$

• 3(e) Loss of ₹100.

  • Step 1: "Loss" is represented by a negative sign (-).
  • Answer: $\boxed{-₹100}$

4. What is represented by the following?

• 4(a) $+10^\circ C$ (if $-10^\circ C$ represents temperature below $0^\circ C$)
  • Step 1: If a negative sign (-) represents "below", then a positive sign (+) will represent its opposite, which is "above".
  • Answer: This represents a temperature of $10^\circ C$ above $0^\circ C$.