24740 + Interview Questions in Mathematics Page 228 InterviewSolution

11351.	What are irrational numbers ?How they should be represented in decimal &in number line?
Answer» What are irrational numbers ?How they should be represented in decimal &in number line?

Discussion

11352.	The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent is added, the mean will increase by Rs.750. Find the salary of the office superintendent.
Answer» The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent is added, the mean will increase by Rs.750. Find the salary of the office superintendent.

Discussion

11353.	In rectangle ABCD, G and H are trisection points of AD, and E and F are trisection points of BC. If AB360 and BC450, compute the area of PORS
Answer» In rectangle ABCD, G and H are trisection points of AD, and E and F are trisection points of BC. If AB360 and BC450, compute the area of PORS

Discussion

11354.	Two equal chords, AB and CD are at a distance of 10 cm from each other. The distance of chord AB from the centre .
Answer» Two equal chords, $A B$ and $C D$ are at a distance of 10 cm from each other. The distance of chord $A B$ from the centre .

Discussion

11355.	Classify the following as constant, linear, quadratic and cubic polynomials.(i) 2–x2+x3(ii) 3x3(iii) 5t−√7(iv) 4–5y2
Answer» Classify the following as constant, linear, quadratic and cubic polynomials. (i) $2 - x^{2} + x^{3}$ (ii) $3 x^{3}$ (iii) $5 t - \sqrt{7}$ (iv) $4 - 5 y^{2}$

Discussion

11356.	What is the combined fraction of sweets eaten by John and Alex?
Answer» What is the combined fraction of sweets eaten by John and Alex?

Discussion

11357.	If the equations 3x – y + 8 = 0 and 6x – ky = - 16 represent coincident lines. Find the value of 'k'.
Answer» If the equations 3x – y + 8 = 0 and 6x – ky = - 16 represent coincident lines. Find the value of 'k'.

Discussion

11358.	In the given figure, O is the centre of a circle such that diameter AB = 17 cm and AC = 15 cm. BC is joined. Find the area of the unshaded part. (Take π=3.14
Answer» In the given figure, O is the centre of a circle such that diameter AB = 17 cm and AC = 15 cm. BC is joined. Find the area of the unshaded part. $(T a k e π = 3.14$

Discussion

11359.	Find the hypotenuse of a right angled triangle whose perpendicular sides are √6 cm and √3 cm.
Answer» Find the hypotenuse of a right angled triangle whose perpendicular sides are $\sqrt{6}$ cm and $\sqrt{3}$ cm.

Discussion

11360.	When theta is small why is it equal to sin theta?
Answer» When theta is small why is it equal to sin theta?

Discussion

11361.	The factors of (2a - b)3 + (b - 2c)3 + 8(c - a)3 are:
Answer» The factors of (2a - b)³ + (b - 2c)³ + 8(c - a)³ are:

Discussion

11362.	Evaluate:(i) (-1) × (-1) × (-1) × ……… 60 times.(ii) (-1) × (-1) × (-1) × (-1) × …….. 75 times.
Answer» Evaluate: (i) (-1) × (-1) × (-1) × ……… 60 times. (ii) (-1) × (-1) × (-1) × (-1) × …….. 75 times.

11362.

Evaluate:(i) (-1) × (-1) × (-1) × ……… 60 times.(ii) (-1) × (-1) × (-1) × (-1) × …….. 75 times.

Answer»

Evaluate:

(i) (-1) × (-1) × (-1) × ……… 60 times.

(ii) (-1) × (-1) × (-1) × (-1) × …….. 75 times.

Discussion

11363.	Question 40A trapezium with 3 equal sides and one side double the equal side, can be divided into ___ equilateral triangles of ___ area.
Answer» Question 40 A trapezium with 3 equal sides and one side double the equal side, can be divided into ___ equilateral triangles of ___ area.

11363.

Question 40A trapezium with 3 equal sides and one side double the equal side, can be divided into _ equilateral triangles of _ area.

Answer»

Question 40

A trapezium with 3 equal sides and one side double the equal side, can be divided into ___ equilateral triangles of ___ area.

Discussion

11364.	Write each of the following as an equation in two variables:(i) 2x =−3(ii) y = 3(iii) 5x = 72(iv) y = 32x
Answer» Write each of the following as an equation in two variables: (i) 2x =−3 (ii) y = 3 (iii) 5x = $\frac{7}{2}$ (iv) y = $\frac{3}{2} x$

Discussion

11365.	In a right angle triangle ABC (right angle at B) The value of tan A.tan C=___
Answer» In a right angle triangle ABC (right angle at B) The value of tan A.tan C=___

11365.

In a right angle triangle ABC (right angle at B) The value of tan A.tan C=___

Answer»

In a right angle triangle ABC (right angle at B)

The value of tan A.tan C=___

Discussion

11366.	9. Find the equation of circle which passes through the points (7,0) ,(0,7) and has its centre on x-axis
Answer» 9. Find the equation of circle which passes through the points (7,0) ,(0,7) and has its centre on x-axis

Discussion

11367.	If (x-1, y +3) = (7, -7), then find the values of x and y, respectively.
Answer» If (x-1, y +3) = (7, -7), then find the values of x and y, respectively.

Discussion

11368.	Centre of a circle lies in ____ of the circle.
Answer» Centre of a circle lies in ____ of the circle.

Discussion

11369.	If x=2+√3 then (x+1x) equals (a) −2√3 (b) 2 (c) 4 (d) 4−2√3
Answer» If $x = 2 + \sqrt{3}$ then $(x + \frac{1}{x})$ equals (a) $- 2 \sqrt{3}$ (b) 2 (c) 4 (d) $4 - 2 \sqrt{3}$

11369.

If x=2+√3 then (x+1x) equals (a) −2√3 (b) 2 (c) 4 (d) 4−2√3

Answer»

If $x = 2 + \sqrt{3}$ then $(x + \frac{1}{x})$ equals

(a) $- 2 \sqrt{3}$ (b) 2 (c) 4 (d) $4 - 2 \sqrt{3}$

Discussion

11370.	In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB. Then, AP is–
Answer» In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP $>$ PB. Then, AP is–

11370.

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB. Then, AP is–

Answer»

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP $>$ PB. Then, AP is–

Discussion

11371.	Coordination number of Co in [CoF6]^-3 is- (1) 4 (2) 5 (3) 6 (4) 8
Answer» Coordination number of Co in [CoF6]^-3 is- (1) 4 (2) 5 (3) 6 (4) 8

Discussion

11372.	What is the value of (a + b) (a – b)?
Answer» What is the value of (a + b) (a – b)?

Discussion

11373.	If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is
Answer» If A and B are two square matrices of order 3 $\times$ 3 which satisfy AB = A and BA = B then $(A + B)^{7}$ is

Discussion

11374.	A point O in the interior of rectangle ABCD is joined with each other of vertices A,B,C and D. Prove that- OB^2+OD^2=OC^2+OA^2.
Answer» A point O in the interior of rectangle ABCD is joined with each other of vertices A,B,C and D. Prove that- OB^2+OD^2=OC^2+OA^2.

Discussion

11375.	Write the number of surfaces of a right circular cylinder.
Answer» Write the number of surfaces of a right circular cylinder.

Discussion

11376.	Find the total amount of rainfall of the Jan, Feb and Apr month.
Answer» Find the total amount of rainfall of the Jan, Feb and Apr month.

Discussion

11377.	If x + 1 is a factor of x3 + a, then write the value of a.
Answer» If x + 1 is a factor of x³ + a, then write the value of a.

Discussion

11378.	How many onto (or surjective) functions are there from an n− element (n≥2) set to a 2-element set?
Answer» How many onto (or surjective) functions are there from an $n -$ element $(n \geq 2)$ set to a 2-element set?

Discussion

11379.	The midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD are joined to form a quadrilateral. If AC = BD and AC ⊥ BD then prove that the quadrilateral formed is a square.
Answer» The midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD are joined to form a quadrilateral. If AC = BD and AC ⊥ BD then prove that the quadrilateral formed is a square.

Discussion

11380.	Determine the measure of each of the equal angles of a right-angled isosceles triangle.ORABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.
Answer» Determine the measure of each of the equal angles of a right-angled isosceles triangle. OR ABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

Discussion

11381.	44. In a triangle ABC, prove that acos(A)+b cos (B)+ c cos (C)= 2a sin(B)sin ©
Answer» 44. In a triangle ABC, prove that acos(A)+b cos (B)+ c cos (C)= 2a sin(B)sin ©

Discussion

11382.	Question 4The number of teeth and the age of a person vary(a) directly with each other(b) inversely with each other(c) neither directly nor inversely with each other(d) sometimes directly and sometimes inversely with each other
Answer» Question 4 The number of teeth and the age of a person vary (a) directly with each other (b) inversely with each other (c) neither directly nor inversely with each other (d) sometimes directly and sometimes inversely with each other

11382.

Question 4The number of teeth and the age of a person vary(a) directly with each other(b) inversely with each other(c) neither directly nor inversely with each other(d) sometimes directly and sometimes inversely with each other

Answer»

Question 4

The number of teeth and the age of a person vary

(a) directly with each other

(b) inversely with each other

(c) neither directly nor inversely with each other

(d) sometimes directly and sometimes inversely with each other

Discussion

11383.	Récrivez ce texte au passé composé.Aujourd'hui, il fait agréable. Julienne va au pique-nique avec ses amies. Elle prend sa voiture. Là, elles rencontrent Julia Roberts, une actrice bien connue. Elles mangent des plats délicieux et elles bavardent beaucoup. Ensuite elles jouent aux cartes et au badminton. Le soir, elles montent dans la voiture et elles rentrent à la maison. Elles arrivent à 8h du soir. À 9h30, Julienne prend son dîner avec sa famille. Puis, elle regarde un bon film sur la télé.
Answer» Récrivez ce texte au passé composé. Aujourd'hui, il fait agréable. Julienne va au pique-nique avec ses amies. Elle prend sa voiture. Là, elles rencontrent Julia Roberts, une actrice bien connue. Elles mangent des plats délicieux et elles bavardent beaucoup. Ensuite elles jouent aux cartes et au badminton. Le soir, elles montent dans la voiture et elles rentrent à la maison. Elles arrivent à 8h du soir. À 9h30, Julienne prend son dîner avec sa famille. Puis, elle regarde un bon film sur la télé.

Discussion

11384.	A line that intersects two lines at distinct points is called as ___.
Answer» A line that intersects two lines at distinct points is called as ___.

Discussion

11385.	Prepare Bank Reconciliation Statement from the following particulars as on 31st March, 2018, when Pass Book shows a debit balance of ₹ 2,500:(i) Cheque issued for ₹ 5,000 but up to 31st March, 2018 only ₹ 3,000 could be cleared.(ii) Cheques issued for ₹ 1,000 but omitted to be recorded in the Cash Book.(iii) Cheques deposited for ₹ 5,500 but cheques for ₹ 500 were collected on 4th April 2018.(iv) A discounted Bill of Exchange dishonoured ₹ 1,000.(v) A cheque of ₹ 500 debited in Cash Book but omitted to be banked.(vi) Interest allowed by bank ₹ 200 but no entry was passed in the Cash Book.
Answer» Prepare Bank Reconciliation Statement from the following particulars as on 31st March, 2018, when Pass Book shows a debit balance of ₹ 2,500: (i) Cheque issued for ₹ 5,000 but up to 31st March, 2018 only ₹ 3,000 could be cleared. (ii) Cheques issued for ₹ 1,000 but omitted to be recorded in the Cash Book. (iii) Cheques deposited for ₹ 5,500 but cheques for ₹ 500 were collected on 4th April 2018. (iv) A discounted Bill of Exchange dishonoured ₹ 1,000. (v) A cheque of ₹ 500 debited in Cash Book but omitted to be banked. (vi) Interest allowed by bank ₹ 200 but no entry was passed in the Cash Book.

Discussion

11386.	Which of the following statements are true and which are false? Give reasons for your answers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A terminated line can be produced indefinitely on both the sides.(iv) If two circles are equal, then their radii are equal.(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.
Answer» Which of the following statements are true and which are false? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are an infinite number of lines which pass through two distinct points. (iii) A terminated line can be produced indefinitely on both the sides. (iv) If two circles are equal, then their radii are equal. (v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

11386.

Which of the following statements are true and which are false? Give reasons for your answers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A terminated line can be produced indefinitely on both the sides.(iv) If two circles are equal, then their radii are equal.(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

Answer»

Which of the following statements are true and which are false? Give reasons for your answers.

(i) Only one line can pass through a single point.

(ii) There are an infinite number of lines which pass through two distinct points.

(iii) A terminated line can be produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

Discussion

11387.	Which side of the Y axis will x + 5 = 0 lie on? __
Answer» Which side of the Y axis will x + 5 = 0 lie on? __

Discussion

11388.	Consider the following statements and answer the question carefully. (i) ′A×D′ means 'A is the sister of D'. (ii) ′A+D′ means 'D is the daughter of A' . (iii) ′A÷D′ means 'A is the mother of D'. How will 'N is the aunt of M' be denoted?
Answer» Consider the following statements and answer the question carefully. (i) $^{'} A \times D^{'}$ means 'A is the sister of D'. (ii) $^{'} A + D^{'}$ means 'D is the daughter of A' . (iii) $^{'} A \div D^{'}$ means 'A is the mother of D'. How will 'N is the aunt of M' be denoted?

Discussion

11389.	If ABCD is a quadrilateral such that diagonal AC bisects the angles A and C,then prove that AB=AD and CB=CD.
Answer» If $A B C D$ is a quadrilateral such that diagonal $A C$ bisects the angles $A$ and $C$ ,then prove that $A B = A D$ and $C B = C D$ .

11389.

If ABCD is a quadrilateral such that diagonal AC bisects the angles A and C,then prove that AB=AD and CB=CD.

Answer»

If $A B C D$ is a quadrilateral such that diagonal $A C$ bisects the angles $A$ and $C$ ,then prove that $A B = A D$ and $C B = C D$ .

Discussion

11390.	For the given reaction A---D ;△ H=x. Steps involved are:A---B;△ H1=x ,B--C△ H2=?,C--D;△ H3=x
Answer» For the given reaction A---D ;△ H=x. Steps involved are:A---B;△ H1=x ,B--C△ H2=?,C--D;△ H3=x

Discussion

11391.	If 2p3p=4k6k=2p+8q3p+12q , then the value of k is .
Answer» If $\frac{2 p}{3 p} = \frac{4 k}{6 k} = \frac{2 p + 8 q}{3 p + 12 q}$ , then the value of k is .

Discussion

11392.	Find the number of numbers between 1 and 10^{10} which contains the digit 1.
Answer» Find the number of numbers between 1 and 10^{10} which contains the digit 1.

Discussion

11393.	the number of ways in which 10 identical objects of one kind 10 of another kind and 10 of third kind can be divided between two persons so that each person has 15 objects is
Answer» the number of ways in which 10 identical objects of one kind 10 of another kind and 10 of third kind can be divided between two persons so that each person has 15 objects is

Discussion

11394.	ABC is a right angled triangle in which ∠A = 90º and AB = AC. Find ∠B and ∠C.
Answer» ABC is a right angled triangle in which ∠A = 90º and AB = AC. Find ∠B and ∠C.

Discussion

11395.	Identify polynomials in the following:(i) f(x) = 4x3 − x2 − 3x + 7(ii) g(x) = 2x3 − 3x2 + x − 1(iii) p(x) = 23x2-74x+9(iv) q(x) = 2x2 − 3x + 4x+ 2(v) h(x) = x4-x32+x-1(vi) f(x) = 2 +3x+4x
Answer» Identify polynomials in the following: (i) f(x) = 4x³ − x² − 3x + 7 (ii) g(x) = 2x³ − 3x²+ $\sqrt{x}$ − 1 (iii) p(x) = $\frac{2}{3} x^{2} - \frac{7}{4} x + 9$ (iv) q(x) = 2x² − 3x + $\frac{4}{x}$ + 2 (v) h(x) = $x^{4} - x^{\frac{3}{2}} + x - 1$ (vi) f(x) = $2 + \frac{3}{x} + 4 x$

Discussion

11396.	Find the perimeters of(i) Triangle ABE(ii) The rectangle BCDE in this figure. Whose perimeter is greater?
Answer» Find the perimeters of (i) Triangle ABE (ii) The rectangle BCDE in this figure. Whose perimeter is greater?

Discussion

11397.	If AB \|\| CD and T is a transversal then the measurement of ∠n is:
Answer» If AB \|\| CD and T is a transversal then the measurement of $∠ n$ is:

Discussion

11398.	Question 3Can the angles 110∘,80∘,70∘and 95∘ be the angles of a quadrilateral? Why or why not?
Answer» Question 3 Can the angles $110^{\circ}, 80^{\circ}, 70^{\circ} a n d 95^{\circ}$ be the angles of a quadrilateral? Why or why not?

Discussion

11399.	One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?
Answer» One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

11399.

One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

Answer»

One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

Discussion

11400.	If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is(a) 13πr3(b) 23πr3(c) 3πr3(d) 9πr3
Answer» If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is (a) $\frac{1}{3} {πr}^{3}$ (b) $\frac{2}{3} {πr}^{3}$ (c) $3 {πr}^{3}$ (d) 9 ${πr}^{3}$

Discussion

Explore topic-wise InterviewSolutions in .

What are irrational numbers ?How they should be represented in decimal &in number line?

The mean salary of 20 workers is Rs.10,250. If the salary of office superintendent is added, the mean will increase by Rs.750. Find the salary of the office superintendent.

In rectangle ABCD, G and H are trisection points of AD, and E and F are trisection points of BC. If AB360 and BC450, compute the area of PORS

Two equal chords, AB and CD are at a distance of 10 cm from each other. The distance of chord AB from the centre .

Classify the following as constant, linear, quadratic and cubic polynomials.(i) 2–x2+x3(ii) 3x3(iii) 5t−√7(iv) 4–5y2

What is the combined fraction of sweets eaten by John and Alex?

If the equations 3x – y + 8 = 0 and 6x – ky = - 16 represent coincident lines. Find the value of 'k'.

In the given figure, O is the centre of a circle such that diameter AB = 17 cm and AC = 15 cm. BC is joined. Find the area of the unshaded part. (Take π=3.14

Find the hypotenuse of a right angled triangle whose perpendicular sides are √6 cm and √3 cm.

When theta is small why is it equal to sin theta?

The factors of (2a - b)3 + (b - 2c)3 + 8(c - a)3 are:

Evaluate:(i) (-1) × (-1) × (-1) × ……… 60 times.(ii) (-1) × (-1) × (-1) × (-1) × …….. 75 times.

Question 40A trapezium with 3 equal sides and one side double the equal side, can be divided into ___ equilateral triangles of ___ area.

Write each of the following as an equation in two variables:(i) 2x =−3(ii) y = 3(iii) 5x = 72(iv) y = 32x

In a right angle triangle ABC (right angle at B) The value of tan A.tan C=___

9. Find the equation of circle which passes through the points (7,0) ,(0,7) and has its centre on x-axis

If (x-1, y +3) = (7, -7), then find the values of x and y, respectively.

Centre of a circle lies in ____ of the circle.

If x=2+√3 then (x+1x) equals (a) −2√3 (b) 2 (c) 4 (d) 4−2√3

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP &gt; PB. Then, AP is–

Coordination number of Co in [CoF6]^-3 is- (1) 4 (2) 5 (3) 6 (4) 8

What is the value of (a + b) (a – b)?

If A and B are two square matrices of order 3 × 3 which satisfy AB = A and BA = B then (A+B)7 is

A point O in the interior of rectangle ABCD is joined with each other of vertices A,B,C and D. Prove that- OB^2+OD^2=OC^2+OA^2.

Write the number of surfaces of a right circular cylinder.

Find the total amount of rainfall of the Jan, Feb and Apr month.

If x + 1 is a factor of x3 + a, then write the value of a.

How many onto (or surjective) functions are there from an n− element (n≥2) set to a 2-element set?

The midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD are joined to form a quadrilateral. If AC = BD and AC ⊥ BD then prove that the quadrilateral formed is a square.

Determine the measure of each of the equal angles of a right-angled isosceles triangle.ORABC is a right-angled triangle in which ∠A = 90° and AB = AC. Find ∠B and ∠C.

44. In a triangle ABC, prove that acos(A)+b cos (B)+ c cos (C)= 2a sin(B)sin ©

Question 4The number of teeth and the age of a person vary(a) directly with each other(b) inversely with each other(c) neither directly nor inversely with each other(d) sometimes directly and sometimes inversely with each other

A line that intersects two lines at distinct points is called as ___.

Which side of the Y axis will x + 5 = 0 lie on? __

Consider the following statements and answer the question carefully. (i) ′A×D′ means 'A is the sister of D'. (ii) ′A+D′ means 'D is the daughter of A' . (iii) ′A÷D′ means 'A is the mother of D'. How will 'N is the aunt of M' be denoted?

If ABCD is a quadrilateral such that diagonal AC bisects the angles A and C,then prove that AB=AD and CB=CD.

For the given reaction A---D ;△ H=x. Steps involved are:A---B;△ H1=x ,B--C△ H2=?,C--D;△ H3=x

If 2p3p=4k6k=2p+8q3p+12q , then the value of k is .

Find the number of numbers between 1 and 10^{10} which contains the digit 1.

the number of ways in which 10 identical objects of one kind 10 of another kind and 10 of third kind can be divided between two persons so that each person has 15 objects is

ABC is a right angled triangle in which ∠A = 90º and AB = AC. Find ∠B and ∠C.

Identify polynomials in the following:(i) f(x) = 4x3 − x2 − 3x + 7(ii) g(x) = 2x3 − 3x2 + x − 1(iii) p(x) = 23x2-74x+9(iv) q(x) = 2x2 − 3x + 4x+ 2(v) h(x) = x4-x32+x-1(vi) f(x) = 2 +3x+4x

Find the perimeters of(i) Triangle ABE(ii) The rectangle BCDE in this figure. Whose perimeter is greater?

If AB || CD and T is a transversal then the measurement of ∠n is:

Question 3Can the angles 110∘,80∘,70∘and 95∘ be the angles of a quadrilateral? Why or why not?

One angle of a parallelogram is twice the adjacent angle. What are the angles of the parallelogram?

If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is(a) 13πr3(b) 23πr3(c) 3πr3(d) 9πr3

Question 40A trapezium with 3 equal sides and one side double the equal side, can be divided into _ equilateral triangles of _ area.

In the adjoining figure, O is the centre of a circle. Chords AB and CD intersect at P. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB. Then, AP is–