24740 + Interview Questions in Mathematics

1.	In the given figure, seg AD ⊥ side BC, seg BE ⊥ side AC, seg CF ⊥ side AB. Ponit O is the orthocentre. Prove that , point O is the incentre of ∆DEF.
Answer» In the given figure, seg AD ⊥ side BC, seg BE ⊥ side AC, seg CF ⊥ side AB. Ponit O is the orthocentre. Prove that , point O is the incentre of ∆DEF.

Discussion

2.	Find the length of PQ (in yd) in the given figure:25
Answer» Find the length of PQ (in yd) in the given figure: 25

Discussion

3.	Question 35Match the ordinates of the points given in Column A with the items mentioned in Column B. Column A Column Ba (0,5)(i)Y-coordinate is 2×(X-coordinate)+1.b (2,3)(ii)Coordinates of origin.c (4,8)(iii) Only Y-coordinate is zero.d (3,7)(iv) The distance from X-axis is 5.e (0,0)(v) Y-coordinate is double of X-coordinate.f (5,0)(vi) The distance from Y-axis is 2
Answer» Question 35 Match the ordinates of the points given in Column A with the items mentioned in Column B. $\begin{matrix} C o l u m n A & C o l u m n B a & (0,5) & (i)Y-coordinate is 2 \times (X-coordinate) + 1. b & (2,3) & (ii)Coordinates of origin. c & (4,8) & (iii) Only Y-coordinate is zero. d & (3,7) & (iv) The distance from X-axis is 5. e & (0,0) & (v) Y-coordinate is double of X-coordinate. f & (5,0) & (vi) The distance from Y-axis is 2 \end{matrix}$

Discussion

4.	Calculate the circumference of the circle if the diameter is 14 cm.
Answer» Calculate the circumference of the circle if the diameter is 14 cm.

Discussion

5.	Q. Represent 5/3 and -5/3 on a number line
Answer» Q. Represent 5/3 and -5/3 on a number line

Discussion

6.	If m=13−2√2 then,m2= _______.
Answer» $If m = \frac{1}{3 - 2 \sqrt{2}} then, m^{2} =$ _______.

Discussion

7.	Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
Answer» Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Discussion

8.	If x + 1 is a factor of the polynomial 2x2 + kx, then k =(a) −2(b) −3(c) 4(d) 2
Answer» If x + 1 is a factor of the polynomial 2x² + kx, then k = (a) −2 (b) −3 (c) 4 (d) 2

Discussion

9.	Draw lines parallel to the X - axis and Y-axis and pass through (2,3)
Answer» Draw lines parallel to the X - axis and Y-axis and pass through (2,3)

Discussion

10.	What is the mean of the data set 12, 14, 21, 27?18.5
Answer» What is the mean of the data set 12, 14, 21, 27? 18.5

Discussion

11.	if a point (x,y) is at equal distance from x-axis and y - axis. find relationship between x and y can be
Answer» if a point (x,y) is at equal distance from x-axis and y - axis. find relationship between x and y can be

Discussion

12.	Question 10 (i)ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD( See the given figure). Show thatΔAPB≅ΔCQD
Answer» Question 10 (i) ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD( See the given figure). Show that $Δ A P B ≅ Δ C Q D$

Discussion

13.	Find three different irrational numbers between the rational numbers 57 and 911.
Answer» Find three different irrational numbers between the rational numbers $\frac{5}{7} and \frac{9}{11}$ .

Discussion

14.	If A={1,2,3,4,5,6}, B={1,2}, then A−B=C . What of the following is true about C?
Answer» If A={1,2,3,4,5,6}, B={1,2}, then $A - B = C$ . What of the following is true about C?

Discussion

15.	The statement that 'the lines are parallel if they do not intersect' is in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof
Answer» The statement that 'the lines are parallel if they do not intersect' is in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

15.

The statement that 'the lines are parallel if they do not intersect' is in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

Answer»

The statement that 'the lines are parallel if they do not intersect' is in the form of

(a) a definition

(b) an axiom

(c) a postulate

(d) a proof

Discussion

16.	Question 79Fill in the blanks to make the statements true.A diagonal of a quadrilateral is a line segment that joins two ___ vertices of the quadrilateral.
Answer» Question 79 Fill in the blanks to make the statements true. A diagonal of a quadrilateral is a line segment that joins two ___ vertices of the quadrilateral.

Discussion

17.	State the Euclid’s Axiom used in X -15 is equal to 25
Answer» State the Euclid’s Axiom used in X -15 is equal to 25

Discussion

18.	Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.
Answer» Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

Discussion

19.	Question 59Choose a letter x, y, z, p etc ..., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The perimeter of an equilateral triangle, if side of the triangle is m.
Answer» Question 59 Choose a letter x, y, z, p etc ..., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement: The perimeter of an equilateral triangle, if side of the triangle is m.

19.

Question 59Choose a letter x, y, z, p etc ..., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The perimeter of an equilateral triangle, if side of the triangle is m.

Answer»

Question 59

Choose a letter x, y, z, p etc ..., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:

The perimeter of an equilateral triangle, if side of the triangle is m.

Discussion

20.

During a medical checkup, the number of heartbeats per minute of 40 patients were recorded and summarised as follows: Number of heartbeats per minute 64 − 68 68 − 72 72 − 76 76 − 80 80 − 84 84 – 88 Number of patients 6 8 10 12 3 1 Find the mean heartbeats per minute for these patients.

Answer» During a medical checkup, the number of heartbeats per minute of 40 patients were recorded and summarised as follows:

Number of heartbeats per minute	64 − 68	68 − 72	72 − 76	76 − 80	80 − 84	84 – 88
Number of patients	6	8	10	12	3	1

Find the mean heartbeats per minute for these patients.

Discussion

21.	Write two solutions for each of the following equations:(i) 3x + 4y = 7(ii) x = 6y(iii) x + xy = 4(iv) 23x-y=4
Answer» Write two solutions for each of the following equations: (i) 3x + 4y = 7 (ii) x = 6y (iii) x + xy = 4 (iv) $\frac{2}{3} x - y = 4$

Discussion

22.	If the dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 m2, then the volume of the cuboid is :
Answer» If the dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 $m^{2}$ , then the volume of the cuboid is :

Discussion

23.	The bisectors of ∠B and ∠C of an isosceles Δ ABC with AB = AC intersect each other at a point O. Show that the exterior angle adjacent to ∠ABC is equal to ∠BOC.
Answer» $The bisectors of ∠ B a n d ∠ C of an isosceles Δ ABC with AB = AC intersect each other at a point O. Show that the exterior angle adjacent to ∠ A B C is equal to ∠ B O C .$

Discussion

24.	An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
Answer» An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

Discussion

25.	x+y−82 = x+2y−148 = 3x+y−1211 Solve the given system of equations:
Answer» $\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$ Solve the given system of equations:

25.

x+y−82 = x+2y−148 = 3x+y−1211 Solve the given system of equations:

Answer»

$\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$
Solve the given system of equations:

Discussion

26.	In triangles ABC and PQR three equality relations between some parts are as follows:AB = QP, ∠B = ∠P and BC = PRState which of the congruence conditions applies:(a) SAS(b) ASA(c) SSS(d) RHS
Answer» In triangles ABC and PQR three equality relations between some parts are as follows: AB = QP, ∠B = ∠P and BC = PR State which of the congruence conditions applies: (a) SAS (b) ASA (c) SSS (d) RHS

Discussion

27.	In the trapezium ABCD, AB vector =6i, AD=3i +4j, DC=3i .Determine BC,BD,AC .What is the value of
Answer» In the trapezium ABCD, AB vector =6i, AD=3i +4j, DC=3i .Determine BC,BD,AC .What is the value of

Discussion

28.	In an infinite sequence of regular hexagons, each hexagon except the first is formed by connecting the midpoints of the sides of the previous hexagon. If the perimeter of the first hexagon is 12 and the sum of the perimeters of all the hexagons is a , then find (a + b).
Answer» In an infinite sequence of regular hexagons, each hexagon except the first is formed by connecting the midpoints of the sides of the previous hexagon. If the perimeter of the first hexagon is 12 and the sum of the perimeters of all the hexagons is a , then find (a + b).

Discussion

29.	Question 6ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD+∠CDB=12∠BAD.
Answer» Question 6 ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that $∠ C B D + ∠ C D B = \frac{1}{2} ∠ B A D$ .

Discussion

30.	Simplify 4√81x8y4z16
Answer» Simplify $\sqrt[4]{81 x^{8} y^{4} z^{16}}$

Discussion

31.	In each of the following, determine whether the statements is true or false. If it is true, prove it. If it is false, give an example.(i) If x∈A and A∈B, then x∈B(ii) A⊂B and B∈C, then A∈C(iii) A⊂B and B⊂C, then A⊂C(iv) If A⊄B and B⊄C, then A⊄C(v) If x∈A and A⊄B, then x∈B(vi) If A⊂B and x∉B, then x∉A
Answer» In each of the following, determine whether the statements is true or false. If it is true, prove it. If it is false, give an example. $(i)$ If $x \in A$ and $A \in B$ , then $x \in B$ $(i i)$ $A \subset B$ and $B \in C$ , then $A \in C$ $(i i i)$ $A \subset B$ and $B \subset C$ , then $A \subset C$ $(i v)$ If $A \subset̸ B$ and $B \subset̸ C$ , then $A \subset̸ C$ $(v)$ If $x \in A$ and $A \subset̸ B$ , then $x \in B$ $(v i)$ If $A \subset B$ and $x \notin B$ , then $x \notin A$

Discussion

32.	Check which of the following are solutions of the equation x − 2y = 4 and which are not:(i) (0, 2 (ii) (2, 0) (iii) (4, 0)(iv) (v) (1, 1)
Answer» Check which of the following are solutions of the equation x − 2y = 4 and which are not: (i) (0, 2 (ii) (2, 0) (iii) (4, 0) (iv) (v) (1, 1)

32.

Check which of the following are solutions of the equation x − 2y = 4 and which are not:(i) (0, 2 (ii) (2, 0) (iii) (4, 0)(iv) (v) (1, 1)

Answer»

Check which of the following are solutions of the equation x − 2y = 4 and which are not:

(i) (0, 2 (ii) (2, 0) (iii) (4, 0)

(iv) (v) (1, 1)

Discussion

33.	Which of the following is not a quadrilateral?
Answer» Which of the following is not a quadrilateral?

Discussion

34.	Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per seconds into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes ?
Answer» Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per seconds into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes ?

Discussion

35.	Question 6Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Answer» Question 6 Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Discussion

36.	Find the value of 1 + sin30∘cos30∘+cos30∘1 + sin30∘.
Answer» Find the value of $\frac{1 + s i n 30^{\circ}}{c o s 30^{\circ}} + \frac{c o s 30^{\circ}}{1 + s i n 30^{\circ}} .$

Discussion

37.	Question 1 (iv)ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show thatAP is the perpendicular bisector of BC.
Answer» Question 1 (iv) $Δ$ ABC and $Δ$ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that AP is the perpendicular bisector of BC.

Discussion

38.	In the given figure, if AB \|\| CD \|\| EF, PQ \|\| RS, ∠RQD=25∘ and ∠CQP=60∘, then ∠ARS is equal to
Answer» In the given figure, if AB \|\| CD \|\| EF, PQ \|\| RS, $∠ R Q D = 25^{\circ}$ and $∠ C Q P = 60^{\circ}$ , then $∠ A R S$ is equal to

Discussion

39.

Surya does not keep a systematic record of his transactions. He is able to give you the following information regarding his assets and liabilities: 31st March 2018 (₹) 31st March, 2019 (₹) Creditors for goods 21,000 19,000 Creditors for expenses 1,500 1,800 Bills Payable 8,700 11,500 Sundry Debtors 35,000 34,000 Stock (At cost) 28,000 25,000 Furniture and Fittings 10,000 12,000 Cash 5,100 Following additional information is also available for the year ended 31st March, 2019: ₹ Bills Payable Issued 20,800 Cash Sales 15,000 Payment to Sundry Creditors 31,000 Expenses paid 6,600 Drawings 8,000 Bad Debts during the year were ₹ 900. As regards sale, Surya tells you that he always sells goods at Cost plus 25%. Furniture and Fittings are to be depreciated at 10% of the value in the beginning of the year.Prepare Surya's Trading and Profit and Loss Account for the year ended 31st March, 2019 and his Balance Sheet on that date.

Answer» Surya does not keep a systematic record of his transactions. He is able to give you the following information regarding his assets and liabilities:

	31st March 2018 (₹)	31st March, 2019 (₹)
Creditors for goods	21,000	19,000
Creditors for expenses	1,500	1,800
Bills Payable	8,700	11,500
Sundry Debtors	35,000	34,000
Stock (At cost)	28,000	25,000
Furniture and Fittings	10,000	12,000
Cash	5,100

Following additional information is also available for the year ended 31st March, 2019:

	₹
Bills Payable Issued	20,800
Cash Sales	15,000
Payment to Sundry Creditors	31,000
Expenses paid	6,600
Drawings	8,000

Bad Debts during the year were ₹ 900. As regards sale, Surya tells you that he always sells goods at Cost plus 25%. Furniture and Fittings are to be depreciated at 10% of the value in the beginning of the year.

Prepare Surya's Trading and Profit and Loss Account for the year ended 31st March, 2019 and his Balance Sheet on that date.

Discussion

40.	A water container can hold 40 litres of water. Then find the total number of ice cubes of side 5 cm which the container can hold.
Answer» A water container can hold 40 litres of water. Then find the total number of ice cubes of side 5 cm which the container can hold.

Discussion

41.	Prove X is a rational number, non termination and repeating. If its prime factors are p & q, written in from p/q where q not= 2n(5m) form.
Answer» Prove X is a rational number, non termination and repeating. If its prime factors are p & q, written in from p/q where q not= 2n(5m) form.

Discussion

42.	Let z be a complex number such that the imaginary part of t is non zero and a = z2+z +1 is real.Then a cannot take the value
Answer» Let z be a complex number such that the imaginary part of t is non zero and a = z²+z +1 is real.Then a cannot take the value

Discussion

43.	Factorize- x^2-2x+5
Answer» Factorize- x^2-2x+5

Discussion

44.	Find the areas of the rectangles whose sides are: (a) 3 cm and 4 cm (b) 12 m and 21 m (c) 2 km and 3 km (d) 2 m and 70 cm
Answer» Find the areas of the rectangles whose sides are: (a) 3 cm and 4 cm (b) 12 m and 21 m (c) 2 km and 3 km (d) 2 m and 70 cm

44.

Find the areas of the rectangles whose sides are: (a) 3 cm and 4 cm (b) 12 m and 21 m (c) 2 km and 3 km (d) 2 m and 70 cm

Answer»

Find the
areas of the rectangles whose sides are:

(a) 3 cm
and 4 cm (b) 12 m and 21 m

(c) 2 km
and 3 km (d) 2 m and 70 cm

Discussion

45.	A paper file costs Rs0.80 and a plastic file Rs1.50. Suman bought x paper files and y plastic files. How many rupees should she pay the shopkeeper?
Answer» A paper file costs Rs0.80 and a plastic file Rs1.50. Suman bought $x$ paper files and $y$ plastic files. How many rupees should she pay the shopkeeper?

Discussion

46.	ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.
Answer» ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Discussion

47.	Construct a △ ABC in which AC = 5 cm, and ∠BAC = 600 and AB – BC = 1.2 cm.
Answer» Construct a △ ABC in which AC = 5 cm, and ∠BAC = 60⁰ and AB – BC = 1.2 cm.

Discussion

48.	Using trapezoidal method find ∫30ex2dx with step size h = 0.52319.07
Answer» Using trapezoidal method find $\int_{0}^{3} e^{x^{2}}$ dx with step size h = 0.5 2319.07

Discussion

49.	ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of ΔABC.
Answer» ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of ΔABC.

Discussion

50.	Question 18 Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A (or B) intersecting the circles at P and Q. prove that PQ = 2 OO'.
Answer» Question 18 Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A (or B) intersecting the circles at P and Q. prove that PQ = 2 OO'.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the given figure, seg AD ⊥ side BC, seg BE ⊥ side AC, seg CF ⊥ side AB. Ponit O is the orthocentre. Prove that , point O is the incentre of ∆DEF.

Find the length of PQ (in yd) in the given figure:25

Calculate the circumference of the circle if the diameter is 14 cm.

Q. Represent 5/3 and -5/3 on a number line

If m=13−2√2 then,m2= _______.

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

If x + 1 is a factor of the polynomial 2x2 + kx, then k =(a) −2(b) −3(c) 4(d) 2

Draw lines parallel to the X - axis and Y-axis and pass through (2,3)

What is the mean of the data set 12, 14, 21, 27?18.5

if a point (x,y) is at equal distance from x-axis and y - axis. find relationship between x and y can be

Question 10 (i)ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD( See the given figure). Show thatΔAPB≅ΔCQD

Find three different irrational numbers between the rational numbers 57 and 911.

If A={1,2,3,4,5,6}, B={1,2}, then A−B=C . What of the following is true about C?

The statement that 'the lines are parallel if they do not intersect' is in the form of (a) a definition (b) an axiom (c) a postulate (d) a proof

Question 79Fill in the blanks to make the statements true.A diagonal of a quadrilateral is a line segment that joins two ___ vertices of the quadrilateral.

State the Euclid’s Axiom used in X -15 is equal to 25

Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

Question 59Choose a letter x, y, z, p etc ..., wherever necessary, for the unknown (variable) and write the corresponding expressions for the given statement:The perimeter of an equilateral triangle, if side of the triangle is m.

During a medical checkup, the number of heartbeats per minute of 40 patients were recorded and summarised as follows: Number of heartbeats per minute 64 − 68 68 − 72 72 − 76 76 − 80 80 − 84 84 – 88 Number of patients 6 8 10 12 3 1 Find the mean heartbeats per minute for these patients.

Write two solutions for each of the following equations:(i) 3x + 4y = 7(ii) x = 6y(iii) x + xy = 4(iv) 23x-y=4

If the dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 m2, then the volume of the cuboid is :

The bisectors of ∠B and ∠C of an isosceles Δ ABC with AB = AC intersect each other at a point O. Show that the exterior angle adjacent to ∠ABC is equal to ∠BOC.

An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

x+y−82 = x+2y−148 = 3x+y−1211 Solve the given system of equations:

In triangles ABC and PQR three equality relations between some parts are as follows:AB = QP, ∠B = ∠P and BC = PRState which of the congruence conditions applies:(a) SAS(b) ASA(c) SSS(d) RHS

In the trapezium ABCD, AB vector =6i, AD=3i +4j, DC=3i .Determine BC,BD,AC .What is the value of

In an infinite sequence of regular hexagons, each hexagon except the first is formed by connecting the midpoints of the sides of the previous hexagon. If the perimeter of the first hexagon is 12 and the sum of the perimeters of all the hexagons is a ￼, then find (a + b).

Question 6ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD+∠CDB=12∠BAD.

Simplify 4√81x8y4z16

Check which of the following are solutions of the equation x − 2y = 4 and which are not:(i) (0, 2 (ii) (2, 0) (iii) (4, 0)(iv) (v) (1, 1)

Which of the following is not a quadrilateral?

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per seconds into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes ?

Question 6Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

Find the value of 1 + sin30∘cos30∘+cos30∘1 + sin30∘.

Question 1 (iv)ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show thatAP is the perpendicular bisector of BC.

In the given figure, if AB || CD || EF, PQ || RS, ∠RQD=25∘ and ∠CQP=60∘, then ∠ARS is equal to

A water container can hold 40 litres of water. Then find the total number of ice cubes of side 5 cm which the container can hold.

Prove X is a rational number, non termination and repeating. If its prime factors are p & q, written in from p/q where q not= 2n(5m) form.

Let z be a complex number such that the imaginary part of t is non zero and a = z2+z +1 is real.Then a cannot take the value

Factorize- x^2-2x+5

Find the areas of the rectangles whose sides are: (a) 3 cm and 4 cm (b) 12 m and 21 m (c) 2 km and 3 km (d) 2 m and 70 cm

A paper file costs Rs0.80 and a plastic file Rs1.50. Suman bought x paper files and y plastic files. How many rupees should she pay the shopkeeper?

ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

Construct a △ ABC in which AC = 5 cm, and ∠BAC = 600 and AB – BC = 1.2 cm.

Using trapezoidal method find ∫30ex2dx with step size h = 0.52319.07

ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that the perimeter of ΔPQR is double the perimeter of ΔABC.

Question 18 Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A (or B) intersecting the circles at P and Q. prove that PQ = 2 OO'.

In an infinite sequence of regular hexagons, each hexagon except the first is formed by connecting the midpoints of the sides of the previous hexagon. If the perimeter of the first hexagon is 12 and the sum of the perimeters of all the hexagons is a , then find (a + b).