MATHEMATICAL REASONING - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 Mark

If the truth value of the statement p → (~q ∨ r) is false (F), then the truth values of the statements p, q, r are respectively.

✓
T, T, F
B
T, F, F
C
T, F, T
D
F, T, T

Answer: A.

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Q 2MCQ1 Mark

Choose the correct answer: The negation of the statement “The product of 3 and 4 is 9” is.

✓
It is false that the product of 3 and 4 is 9.
B
The product of 3 and 4 is 12.
C
The product of 3 and 4 is not 12.
D
It is false that the product of 3 and 4 is not 9.

Answer: A.

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Q 3MCQ1 Mark

Write the inverse of the statement: If you do not drink your milk, you will not be strong.

A
If you are strong, then you drink your milk,
B
If you do not drink your milk, then you are strong.
✓
If you drink your milk, then you are strong.
D
None of the above.

Answer: C.

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Q 4MCQ1 Mark

The converse of: "If two triangles are congruent then they are similar" is:

✓
If two triangles are similar then they are congruent.
B
If two triangles are not congruent then they are not similar.
C
If two triangles are not similar then they are not congruent.
D
None.

Answer: A.

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Q 5MCQ1 Mark

If statement $p \rightarrow (q∨r)$ is true then the truth values of statements $p, q, r$ respectively:

✓
$\text{T, F, T}$
B
$\text{F, T, F}$
C
$\text{F, F, F}$
D
all of these

Answer: A.

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Q 6(Each question 1 marks)1 Mark

Write each of the following statements in the form “if-then” The Bannana trees will bloom if it stays warm for a month.

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Q 7(Each question 1 marks)1 Mark

Which of the following sentences are statements? Give reasons for your answer. Today is a windy day.

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Q 8(Each question 1 marks)1 Mark

Which of the following sentences are statements? Give reasons for your answer. Mathematics is difficult.

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Q 9(Each question 1 marks)1 Mark

Write each of the following statements in the form “if-then” You get a job implies that your credentials are good.

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Q 10(Each question 1 marks)1 Mark

Check whether the following pair of statements are negation of each other. Give reasons for your answer. There exists real numbers x and y for which x + y = y + x.

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Q 11(Each question 2 marks)2 Marks

Find the component statements of the following compound statements and check whether they are true or false. Number 3 is prime or it is odd.

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Q 12(Each question 2 marks)2 Marks

State the converse and contrapositive of each of the following statements: p: A positive integer is prime only if it has no divisors other than 1 and itself.

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Q 13(Each question 2 marks)2 Marks

Find the component statements of the following compound statements and check whether they are true or false. All integers are positive or negative.

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Q 14(Each question 2 marks)2 Marks

Given below are two statements p : 25 is a multiple of 5. q : 25 is a multiple of 8. Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.

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Q 15(Each question 2 marks)2 Marks

Which of the following statements are true and which are false? In each case give a valid reason for saying so. r: Circle is a particular case of an ellipse.

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Q 16(Each question 3 marks)3 Marks

Check the validity of the statements given below by the method given against it. q: If n is a real number with n > 3, then n2 > 9 (by contradiction method).

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Q 17(Each question 3 marks)3 Marks

Give three examples of sentences which are not statements. Give reasons for the answers.

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Q 18(Each question 3 marks)3 Marks

Show that the following statement is true by the method of contrapositive. p: If x is an integer and $x^2$ is even, then x is also even.

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Q 19(Each question 3 marks)3 Marks

Check the validity of the statements given below by the method given against it. p: The sum of an irrational number and a rational number is irrational (by contradiction method).

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Q 20(Each question 3 marks)3 Marks

Show that the statement “For any real numbers a and b, $\text{a}^2=\text{b}^2$ implies that $\text{a = b}$” is not true by giving a counter-example.

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Q 21(Each question 4 marks)4 Marks

Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

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