Axioms

Q.

In the following figure, if AC = BD, then prove that AB = CD.

Q.

If $A$ and $B$ are two sets, then $A\cap (A\cup B)$ is equal to

1. $A$

2. $B$

3. $\varphi$

4. None of these

Q. Statements which are assumed to be true without mathematical proof are said to be axioms. State whether true or false

1. true
2. false

Q.

The solution of $\left(x+y+1\right)\frac{dy}{dx}=1$ is

1. $y=\left(x+2\right)+c{e}^x$

2. $y=-\left(x+2\right)+c{e}^x$

3. $x=-\left(y+2\right)+c{e}^y$

4. $x={\left(y+2\right)}^2+c{e}^y$

Q.

What is the difference between a theorem and an axiom?

Q.

Q. There are four prime numbers written in ascending order. The product of the first three is 385 and of the last three is 1001. Find the last number.

Thank you..

Q.

Which of the following needs a proof ?

(a) axiom

(b) postulate

(c) definition

(d) theorem

Q.

What are joint and disjoint sets

Q. In the given figure, AB = BC, M is the midpoint of AB and N is the midpoint of BC. Which one of the following options is correct ?

1. BN = NC
2. AM = NC
3. AM = MB
4. All of the above

Q.

a man has 8 children to take them zoo. he takes three of them at a time to the zoo as often as he can without taking the same 3 children together more than once. how many times will he have to go to the zoo? how many times a particular child will go to the zoo

Q.

'Lines are parallel if they do not intersect' - is stated in the form of:

1. A postulate

2. An axiom

3. A proof

4. A definition

Q. Which of the following statements is not a Euclid’s axiom?

1. If equals are added to equals, then the wholes are equal
2. The whole is greater than the part
3. All right angles are equal to one another
4. Things which are double of the same thing are equal to one another

Q.

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are _______(in degrees).

Q. If P, Q, R are three points on a line and Q lies between P and R, then which of the following is equal to PR - PQ?

1. PQR
2. QR
3. PR
4. PQ

Q.

In figure, AD = BC, then prove that AC = BD

Q. Euclid's which axiom illustrates the statement that when x + y = 15, then x + y + z = 15 + z ?

1. Euclid's second axiom states that if equals be added to equals, the wholes are equal.
2. Euclid's sixth axiom states that, the things which are double of the same things are equal to one another
3. Euclid's fourth axiom states that, the things which coincide with one another are equal to one another.
4. Euclid's third axiom states that if equals are subtracted from equals, the remainders are equal.

Q. 'Things which are equal to same thing are equal to one another' this statement is

1. An axiom
2. a conjecture
3. a theorem
4. not a mathematical statement

Q.

The edges of a surface are

1. Points

2. Lines

3. Rays

4. Plans

Q. Rahul added 5 chocolates to his box of 100 chocolates. His friend Ramu also added 5 chocolates to his own box to get a total of 105 chocolates. How many chocolates did Ramu have in his box before adding 5 chocolates?

1. 90
2. 110
3. 95
4. 100

Q.

What is a theorem?

Q.

Things which are double of the same things are _____ to one another.

1. Perpendicular

2. Equal

3. Not Equal

4. Parallel

Q. What is the difference between an axiom and a postulate?

Q. Classroom activity(Constructing the 'square root spiral'): Take a large sheet of paper and construct the 'square root spiral' in the following fashion. Start with a point O and draw a line segment $O{P}_1$ of unit length. Draw a line segment $P_1{P}_2$ perpendicular to $O{P}_1$ of unit length. Now draw a line segment $P_2{P}_3$ perpendicular to $O{P}_2$. Then draw a line segment $P_3{P}_4$ perpendicular to $O{P}_3$. Continuing in this manner, you can get the line segment $P_{n-1}{P}_n$ by drawing a line segment of unit length perpendicular to $O{P}_{n-1}$. In this manner, you will have created the points $P_2,P_3,.......,P_n,.....,$ and joined them to create a beautiful spiral depicting $\sqrt{2},\sqrt{3},\sqrt{4},.......$

Q. If equals are subtracted from equals, the remainders are .

1. also equal
2. greater
3. equal/greater
4. less

Q.

If a transversal intersects two parallel lines, then the consecutive interior angles are

1. Supplementary

2. Complementary

3. Congruent

4. Equal

Q. Question 2 (i)
Give two different examples of pair of

(i) Similar figures

Q.

Axioms are assumed

(a) definitions

(b) theorems

(c) universal truths specific to geometry

(d) universal truths in all branches of mathematics

Q.

Write five distinct integers whose sum is $4$.

Q. In the given figure, points X, Y, Z are the midpoints of side AB, side BC and side AC of $∆$ABC respectively. AB = 5 cm, AC = 9 cm and BC = 11 cm. Find the length of XY, YZ, XZ.

Q. If equals are added to equals, the wholes

1. are equal
2. are greater
3. are equal or greater
4. may or may not be equal.