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Published on: 18/09/2019
Mathematical Reasoning
Download CBSE Class 11th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 11th Standard CBSE Mathematics
Questions + Answers key
Take MCQ Mathematics Test
1.
Write the negation of the following statements
Sets A and B are equal if and only if A \(\subseteq\) B and B \(\subseteq\) A.
2.
Write down the contrapositive of the following statements.
If PT Usha stands first in 200 m race, then she will be awarded.
3.
Write down the contrapositive of the following statements.
If Lara Dutta is Miss Universe, then she is beautiful.
4.
For the following compound statement, first identify the connecting words and then break into component statement.
x=2 and x=3 are the roots of the equation 3x2 - x -10=0.
5.
For the following compound statement, first identify the connecting words and then break into component statement.
The sand heats up quickly in the Sun and does not cool down fast at night.
6.
Write down the converse of the following statements.
If you go to Agra, then you must visit Taj Mahal.
7.
Write down the converse of the following statements.
If a rectangle R is a square, then R is a rhombus.
8.
Write negation
Mridul is cruel or he is strict.
9.
Write negation
Ramesh is smart and healthy.
10.
Write down the converse of the following statements.
If today is Monday, then tomorrow is Tuesday.
11.
Find the component statement of the following compound statements and check whether they are true or false.
100 is divisible by 3,11 and 5.
12.
Using contrapositive method, prove that if n2 is an even integer, then n is also an even integer.
13.
By giving a counter example, show that the following statement is false. If x is even integer, then x is a prime.
14.
Check the validity of the following statements
r :60 is a multiple of 3 or 5.
15.
Check the validity of the following statements
p :20 is a multiple of 4 and 5.
1.
Let p : Sets A and B are equal.
and q : A \(\subseteq\) B and B \(\subseteq\) A.
Then, the given statement is p \(\Leftrightarrow \) q.
the negation of the given statement is
\((p\wedge \sim q)\vee (q\wedge \sim p)\)
'Either A = B and (A \(\nsubseteq\) B or B\(\nsubseteq\) A) or (A \(\subseteq\) B and B \(\subseteq\) A) and A\(\neq \) B.'
2.
If PT Usha is not awarded, then she does not stand first in 200 m race.
3.
If Lara Dutta is not beautiful, then she is not Miss Universe.
4.
"And". The component statements are
p : x=2 is a root of the equation 3x2 - x - 10 =0.
q : x=3 is a root of the equation 3x2 - x - 10 =0.
5.
"And", The component statement are
20 p :The sand heats up quickly in the Sun.
q :The sand does not cool down fast at night.
6.
If you must visit Taj Mahal, then you go to Agra.
7.
If the rectangle R is rhombus, then R is a square.
8.
Mridul is neither cruel nor strict.
9.
Ramesh is either not smart or not healthy.
10.
If tomorrow is Tuesday, then today is Monday.
11.
The component statements are
p :100 is divisible by 3
q :100 is divisible by 11
r : 100 is divisible by 5
p,q are false and r is true. So \(p\vee q\) is true.
12.
Let p:n2 is an even integer
and q: n is also an even integer.
Let\(\sim \)p is true, i.e. n is not an even integer.
\(\Rightarrow \)n2 is not an integer.
\(\Rightarrow \) \(\sim \) p is true.
13.
Let p:x is even integer.
q:x is prime
We have to show that,p \(\Rightarrow \) q is false, i.e. p-> \(\sim \)q.
For this, we have to given an example.
Now, take a number greater than x which is even, but not a prime. So, x=10 is counter example.
Thus, we conclude that given statement is false.
14.
Valid
15.
Valid
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