Mathematical Proof

Q.

What is the unit digit in the product of the first 50 odd natural numbers? Explain how.

Q.

If we add 1 to a natural number, we get the next natural number.

1. True

2. False

Q. Assume any number $x$, add 7 to it, multiply by 2, add 2, divide by 2, finally subtract $x$.

The number we get after all the operations is ___.

1. 6
2. 7
3. 8
4. 9

Q.

State whether the following statements are True or False:

The product of two even numbers is always even.

1. True
2. False

Q. Of which of the following is the set of natural numbers a subset?

1. The set of odd numbers
2. The set of even numbers
3. The set of composite numbers
4. The set of real numbers

Q.

The expression for “$7$ added to the quotient of $\text{x by}3$”

1. $\frac{x}{3}+7$

2. $7x+3$

3. $7+3x$

4. $\frac{7+x}{3}$

Q.

Rationalize the denominator of 4√3+3√2/√48+√18

Q. The sum of three consecutive even numbers is divisible by _________

1. 6
2. 17
3. 13
4. 7

Q. The Statement - "Product of 38 and 72 is a multiple of 4." can be proved with the help of which of the following statements?

1. Product of two odd natural numbers is always odd.
2. Product of two even natural numbers is always divisible by 4.
3. Product of an even and an odd natural number is always divisible by 2.
4. Product of two even natural numbers is always divisible by 2.

Q.

What isthe sum of any two (a) Odd numbers? (b) Even numbers?

Q. Product of two even number is divisible by

1. 4
2. 5
3. 3
4. 7

Q. Assertion: If the side BC of ∆ABC is produced to D, then ∠ACD = ∠A + ∠B.
Reason: The sum of the angles of a triangle is 180°.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q.

Which of the following pairs of sets are disjoint?

1. {3, 4, 5, 6, 7} and {x: x is a natural number and 7≤ x ≤ 10}

2. {x: x is a prime number} and {x: x is an even number}

3. {x: x is an odd number} and {x: x is an even number}

4. None of these

Q. If a, b, c are positive real numbers, then $\sqrt[5]{3125a^{10}{b}^5{c}^{10}}$ is equal to

(a) 5a²bc²

(b) 25ab²c

(c) 5a³bc³

(d) 125a²bc²

Q. Choose the correct option(s).

1. An Axiom is a mathematical statement that is assumed to be true without a proof.
2. A mathematical statement whose truth has been estabilished proved is called a theorem.
3. A conjecture is statement we believe is true based on our mathematical intuition, but which we are yet to prove.
4. A process which can establish the truth of a mathematical statement based purely on logical arguments is called a mathematical proof.

Q. Aruna drew 3 lines CD, KA, TP such that:
CD = KA
CD = TP
What is the relation between KA and TP?

1. KA > TP
2. TP + KA = 2 CD
3. TP = KA
4. Data insufficient

Q. If y is odd, then ($y^2$ + 3) is a

1. odd number
2. even number
3. perfect square
4. negative number

Q. Sum of two odd numbers is a

1. Average of both number
2. perfect square
3. even number
4. Half of the product of those numbers

Q. If A, B and C are three points on the line (in the same order), then which of the following is true?

1. AB+BC > AC.
2. AB+BC < AC.
3. AB=BC=AC
4. AB+BC = AC.

Q.

State whether the following statement is True or False

The sum of three odd numbers is even.

1. True
2. False

Q. 5t + 25t²

Q. Akhil and Sanjeev were given two baskets of mangoes of equal number. Akhil added 2 mangoes to his basket while Sanjeev also added 2 mangoes to his basket. After some time their friend Sarath counted the number of mangoes in the two boxes. Which of the following will be true, in terms of the number of mangoes?

1. The number of mangoes in Akhil's basket is more than that of Sanjeev.
2. The number of mangoes in Sanjeev's basket is more than that of Akhil.
3. The number of mangoes in both the baskets are equal.
4. The number of mangoes in Sarath's basket is more than that of Akhil.

Q. Assertion: It is always possible to draw a triangle whose sides measure 4 cm, 5 cm and 10 cm respectively.
Reason: In an isosceles ∆ABC with AB = AC, if BD and CE are bisectors of ∠B and ∠C respectively, then BD = CE.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.