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Mathematical Reasoning MATHS - Mathematical Reasoning

UP Board (UPMSP) - STD 11 Science - MATHS (UPMSP - English Medium). 443 questions in this chapter.

Question types

Mathematical Reasoning question types

443 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

443
Questions
6
Question groups
5
Question types
Sample Questions

Mathematical Reasoning questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
If the truth value of the statement $p \rightarrow (\sim q ∨ r)$ is false $(F),$ then the truth values of the statements $p, q, r$ are respectively.
  • ✓
    $\text{T, T, F}$
  • B
    $\text{T, F, F}$
  • C
    $\text{T, F, T}$
  • D
    $\text{F, T, T}$

Answer: A.

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Q 2M.C.Q (1 Marks)1 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 3M.C.Q (1 Marks)1 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 4M.C.Q (1 Marks)1 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 5M.C.Q (1 Marks)1 Mark
If statement p → (q∨r) is true then the truth values of statements p, q, r respectively:
  • A
    T, F, T
  • B
    F, T, F
  • C
    F, F, F
  • ✓
    all of these

Answer: D.

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Q 141 Marks Question1 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 162 Marks Questions2 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 172 Marks Questions2 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 182 Marks Questions2 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 192 Marks Questions2 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 203 Marks Question3 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 233 Marks Question3 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 243 Marks Question3 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 255 Marks Questions5 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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Q 265 Marks Questions5 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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