Axioms

Q.

The length of a rectangle exceeds the breadth by 6cm.If the length is increased by 3cm and breadth decreased by 2cm the area is the same.Find length and breadth of the rectangle.

Q.

On the set $N$ of all natural numbers define the relation $R$ by $aRb$, if and only if the GCD of $a$ and $b$ is $2$, then $R$ is

1. reflexive but not symmetric

2. only symmetric

3. reflexive and transitive

4. reflexive, symmetric and transitive

Q.

What is the difference between an axiom and a postulate?

Q.

Find two numbers whose product is a 1 digit number and the sum is a two digit number

Q.

By joining the points (0, 0), (1, 1), (2, 2) and (3, 3) we get

1. A square

2. A parallelogram

3. A curved line

4. A straight line

Q. The point in AB through which the perpendicular bisector of the segment joining the point A(7 1) B(3 -3)passes is

Q. 15. A man has 50 paise and 25 paise coins worth rupee 5 . The value of the 50 paise coins is equal to that of the 25 paise coins . How many coins of each has he

Q.

In the given pentagon ABCDE, prove that 2CD < Perimeter (ABCDE). [4 MARKS]

Q.

1L = 100 cm³ .State with True or False.

1. True

2. False

Q.

If the numbers $x,6\&9$are in continued proportion, find the value of $x.$

Q. Im(iz-2/z-1)+1=0, z belongs to C, z not equals to i represents a part of circle having radius equal to:

Q.

Let ABCD be a square. Locate points P, Q, R, S on the sides AB, BC, CD, DA respectively such that AP = BQ = CR = DS. Prove that PQRS is a square.

Q. In the adjoining figure. line $p||$ line $q$. line $l||$ line $m$. Find measures of $\angle a,\angle b$, and $\angle c$, using the measures of given angles. Justify your answers.

Q.

In ΔABC, we have AB : BC = 2 : 3 and BC : CA = 4 : 5. What is AB : BC : CA?

Q. In the language of Math, the fact that Earth revolves around Sun is a/an:

1. assumption
2. rule
3. axiom
4. theorem

Q. A, B, C are three points on a straight line. If AB = BC and AC = 4 units then

1. BC = 4
2. AB = 2
3. BC = 8
4. AB =4

Q. Which of these represents borrowing 10 rupees?

1. 10
2. -10
3. 10
4. $$\pm 10$$

Q.

Let ABCD be a quadrilateral in which AB is the smallest side and CD is the largest side. Prove that ∠A > ∠C and ∠B > ∠D. (Hint: Join AC and BD.)

Q.

In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of $\angle$POS and $\angle$SOQ, respectively. If $\angle$POS = $x$, find $\angle$ROT.

1. ${180}^{\circ }$

2. ${75}^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$

Q. ntO is the centre of an ellipse whose semi major axis is b.the ordinate of the point P of the ellipse intersects its auxillary circle at Q(when produced) . The straight through P drawn parallel to OQ cuts the major axis at G .prove then PG=b.n

Q.

Let a*b denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (12*16)*k=25 then find the value of k2.

Q.

Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

(a) AB + BC + CD > AD;

(b) AB + BC + CD + DA > 2AC;

(c) AB + BC + CD + DA > 2BD;

(d) AB + BC + CD + DA > AC + BD.

Q. Q-1700 rupees are to be distributed among three people A, B and C. A has got double of B and five times of C. Then how much money does B get? 1)rs 300 2)rs.400 3)rs.500 4)rs.70

Q.

Find the value of ‘a’, given that 3, a, 5, 20 are in proportion.

Q. In the figure below, M is the midpoint of the line AB. Compute the other two angles of ∆ABC

Q. In the given figure, AB||CD then the value of x is

1. ${285}^{\circ }$
2. ${75}^{\circ }$
3. ${235}^{\circ }$
4. ${220}^{\circ }$

Q.

Which of the following are the sides of right angled triangle?

1. 8, 6, 10

2. 7, 6, 10

3. 8, 6, 11

4. 8, 7, 10

Q.

Find the value of $\mathrm{y}$ when $\mathrm{x}=5$.

$\mathrm{y}=10\mathrm{x}$

Q.

Choose the correct option:

If a = 60 and b = a, then b = 60 by ____________

A. Axiom 1

B. Axiom 2

C. Axiom 3

D. Axiom 4

Q. The diagonals AC and BD of rectangle ABCD intersect at point K. If l(AK) = 3.5 cm, find l(KC) and l(AC).