MCQ Implications and Validating of Statements, Class 11 Mathematics

1. There will be total 10  MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying.

1. Two pairs of statement are:

p: If a quadrilateral is a rectangle, then its opposite sides are equal.

q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle.

The combined statement of these pairs using “If and only if” is:

A quadrilateral is a rectangle if and only if its all sides are equal.

A quadrilateral is a rectangle if and only if its opposite sides are equal.

A quadrilateral is a square if and only if its opposite sides are equal.

A quadrilateral is not a rectangle if and only if its opposite sides are equal.

Question 1 of 10

2. Write the contra positive of the given statement
If -7 < 0 then 7 > 0

 

A.  B.  C.  D.  

A

B

C

D

Question 2 of 10

3. The contra positive of a statement p ⇒ q, is the statement

~q ⇒ ~p

~ q ⇒ p

q ⇒ p

q⇒ ~ p

Question 3 of 10

4. Name the technique used in the first step of the soluntion of the problem below :
Verify that √5 is irrational
Solution ; Let us assume that √5 is rational

Counter example

Direct method

By Contradiction

Contrapositive method

Question 4 of 10

5. If p and q are mathematical statements, then in order to show that the statement “p and q” is true, we need to show that:

The statement p is true and the statement q is not true

The statement p is false and the statement q is true.

The statement p is true and the statement q is false

The statement p is true and the statement q is true

Question 5 of 10

6. In order to prove the statement “If p then q” we need to show that:

By assuming that p is true, prove that q must be true.

By assuming that p is true, prove that q must be false.

By assuming that p is false, prove that q must be true

By assuming that p is not true, prove that q must be true.

Question 6 of 10

7. In order to prove the statement “p if and only if q” we need to show:

If p is false, then q is false.

If p is true, then q is false

If p is false, then q is true

If p is true, then q is true

Question 7 of 10

8. The component statements are:

p: You are wet when it rains.

q: You are wet when you are in river.

The compound statement of these component statements using appropriate connective is:

You are not wet when you are in river or it rains.

You are wet when you are in river and it rains.

You are wet when it rains and you are in a river

You are wet when it rains or you are in a river.

Question 8 of 10

9. Which option is not same as “if p then q”?

~p implies q.

p is a sufficient condition for q.

~q implies ~p

p only if q.

Question 9 of 10

10. Name the technique used in the solution of the problems below :
Question: Show that the following statement is false: If n is an odd integer, then n is prime.
Solution: The given statement is in the form "if p then q" we have to show that this is false, If p then ~q.
n= 99 is odd integer which is not a prime number. Thus, we conclude that the given statement is false.

Counter example

Contrapositive method

Direct method

By Contradiction

Question 10 of 10

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