32581 + Interview Questions in Mathematics Page 64 InterviewSolution

3151.	Decide whether 52.123456789 is a rational number or not. If rational (in the form pq), what can you say about the prime factors of q?
Answer» Decide whether 52.123456789 is a rational number or not. If rational (in the form $\frac{p}{q}$ ), what can you say about the prime factors of q?

Discussion

3152.	The same value of x satisfies the equations 4x + 5 = 0 and 4x2+ (5 + 3p)x + 3p2=0, then p is
Answer» The same value of x satisfies the equations 4x + 5 = 0 and 4x²+ (5 + 3p)x + 3p²=0, then p is

Discussion

3153.	14. If M and N are the mid points of the diagonals AC and BD respectively of a quadrilateral ABCD, then the value of ABvector + ADvector + CBvector + CDvector equals (1) 2MNvector) (2) 2NMvector (3) 4NMvector (4) 4MNvector
Answer» 14. If M and N are the mid points of the diagonals AC and BD respectively of a quadrilateral ABCD, then the value of ABvector + ADvector + CBvector + CDvector equals (1) 2MNvector) (2) 2NMvector (3) 4NMvector (4) 4MNvector

Discussion

3154.	Question 08.When we toss a coin, there are two possible outcomes - head or tail. Therefore, the probability of each outcome is 12. Justify your answer.
Answer» Question 08. When we toss a coin, there are two possible outcomes - head or tail. Therefore, the probability of each outcome is $\frac{1}{2} .$ Justify your answer.

Discussion

3155.	16.Figure shows a hollow cube of side a and volume V. There is a small chamber of volume V/4 in the cube. The chamber is completely filled by m kg of water . Water leaks through a hole Hall and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is 1) 1/2mga 2) 3/8mga 3) 5/8mga 4) 1/8 mga
Answer» 16.Figure shows a hollow cube of side a and volume V. There is a small chamber of volume V/4 in the cube. The chamber is completely filled by m kg of water . Water leaks through a hole Hall and spreads in the whole cube. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is 1) 1/2mga 2) 3/8mga 3) 5/8mga 4) 1/8 mga

Discussion

3156.	If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is(a) n(b) 3n(c) 3(d) none of these
Answer» If S_r denotes the sum of the first r terms of an A.P. Then , S_3n: (S_2n − S_n) is (a) n (b) 3n (c) 3 (d) none of these

Discussion

3157.	In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is
Answer» In a flag race, a pole is placed at the starting point, which is 10m from the first flag and the other flags are placed 6m apart in a straight line. There are 10 flags in the line. Each competitor starts from the pole, picks up the nearest flag, comes back up the next flag and continues the same way until all the flags are on the pole. The total distance covered is

Discussion

3158.	The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that 2n2=12n. Hence find n.
Answer» The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that $2 n^{2} = 12 n$ . Hence find n.

Discussion

3159.	A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?(i) that the sum of the two numbers that turn up is 7?(ii) of obtaining a total of 6?(iii) of obtaining a total of 10?(iv) of obtaining the same number on both dice?(v) of obtaining a total more than 9?(vi) that the sum of the two numbers appearing on the top of the dice is 13?(vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12?(viii) that the product of numbers appearing on the top of the dice is less than 9. [CBSE 2014](ix) that the difference of the numbers appearing on the top of two dice is 2. [CBSE 2014]
Answer» A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability? (i) that the sum of the two numbers that turn up is 7? (ii) of obtaining a total of 6? (iii) of obtaining a total of 10? (iv) of obtaining the same number on both dice? (v) of obtaining a total more than 9? (vi) that the sum of the two numbers appearing on the top of the dice is 13? (vii) that the sum of the numbers appearing on the top of the dice is less than or equal to 12? (viii) that the product of numbers appearing on the top of the dice is less than 9. [CBSE 2014] (ix) that the difference of the numbers appearing on the top of two dice is 2. [CBSE 2014]

Discussion

3160.	11. If A(9,-9), (1,-3) are the vertices of a right angled isosceles triangle, then find the third vertex.
Answer» 11. If A(9,-9), (1,-3) are the vertices of a right angled isosceles triangle, then find the third vertex.

Discussion

3161.	Simplify 6x2+13x−59x2+3x−2×3x2−10x−816x2−1.
Answer» Simplify $\frac{6 x^{2} + 13 x - 5}{9 x^{2} + 3 x - 2} \times \frac{3 x^{2} - 10 x - 8}{16 x^{2} - 1} .$

Discussion

3162.	Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents
Answer» Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

3162.

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

Answer»

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

Discussion

3163.	Divya recorded the shoe sizes of girls in her class : Calculate the Median shoe size from the given data?
Answer» Divya recorded the shoe sizes of girls in her class : Calculate the Median shoe size from the given data?

3163.

Divya recorded the shoe sizes of girls in her class : Calculate the Median shoe size from the given data?

Answer»

Divya recorded the shoe sizes of girls in her class :

Calculate the Median shoe size from the given data?

Discussion

3164.	Draw an angle ABC=75o.Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.
Answer» Draw an angle ABC= $75^{o}$ .Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.

Discussion

3165.	Question 1The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm.How many litres of water can it hold? (1000cm3=1l)[Assume π=227]
Answer» Question 1 The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? $(1000 c m^{3} = 1 l) [A s s u m e π = \frac{22}{7}]$

3165.

Question 1The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm.How many litres of water can it hold? (1000cm3=1l)[Assume π=227]

Answer»

Question 1

The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm.

How many litres of water can it hold? $(1000 c m^{3} = 1 l) [A s s u m e π = \frac{22}{7}]$

Discussion

3166.	Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....
Answer» Write the value of a₃₀ − a₁₀ for the A.P. 4, 9, 14, 19, ....

Discussion

3167.	During a 360∘ rotation of a regular triangle, the figure identical to the original figure is at and 240∘ angles of rotation.
Answer» During a $360^{\circ}$ rotation of a regular triangle, the figure identical to the original figure is at and $240^{\circ}$ angles of rotation.

Discussion

3168.	In the 'less than ' type of ogive the cumulative frequency is plotted against (a) the lower limit of the concerned class interval (b) the upper limit of the concerned class interval (c) the mid-value of the concerned class interval (d) any value of the concernd class interval
Answer» In the 'less than ' type of ogive the cumulative frequency is plotted against (a) the lower limit of the concerned class interval (b) the upper limit of the concerned class interval (c) the mid-value of the concerned class interval (d) any value of the concernd class interval

3168.

In the 'less than ' type of ogive the cumulative frequency is plotted against (a) the lower limit of the concerned class interval (b) the upper limit of the concerned class interval (c) the mid-value of the concerned class interval (d) any value of the concernd class interval

Answer»

In the 'less than ' type of ogive the cumulative frequency is plotted against

(a) the lower limit of the concerned class interval

(b) the upper limit of the concerned class interval

(c) the mid-value of the concerned class interval

(d) any value of the concernd class interval

Discussion

3169.	The HCF to two numbers is 16 and their product is 3072. Find their LCM.
Answer» The HCF to two numbers is 16 and their product is 3072. Find their LCM.

Discussion

3170.	In ∆ ABC, right angled at B, if tan A = 1/√3 then the value of sin A + cos A is
Answer» In ∆ ABC, right angled at B, if tan A = ¹/_√3 then the value of sin A + cos A is

Discussion

3171.	find the value of k for which the quadratic polynomial kx^2+x+k has equal zeros as 1/2.
Answer» find the value of k for which the quadratic polynomial kx^2+x+k has equal zeros as 1/2.

Discussion

3172.

The following balances were extracted from the books of Harish Chandra on 31st March, 2019: ₹ ₹ Drawings 15,000 Capital 2,45,000 Life Insurance Premium 5,000 Loan 78,800 General Expenses 25,000 Sales 6,53,600 Building 1,10,000 Purchases 4,70,000 Machinery 93,400 Motor Car 20,000 Stock on 1st April, 2018 1,62,000 Reserve Fund (Cr.) 9,000 Power 22,400 Commission (Cr.) 13,200 Insurance 13,150 Car Expenses 18,000 Wages 72,000 Bills Payable 38,500 Debtors 62,800 Cash 800 Creditors 25,000 Bank Overdraft 33,000 Input CGST A/c 15,000 Charity 1,050 Input SGST A/c 15,000 Bad Debts 5,500 Output IGST A/c 30,000 Stock on 31st March, 2019 was valued at ₹ 2,35,000.Prepare final accounts for the year ended 31st March, 2019.

Answer» The following balances were extracted from the books of Harish Chandra on 31st March, 2019:

	₹		₹
Drawings	15,000	Capital	2,45,000
Life Insurance Premium	5,000	Loan	78,800
General Expenses	25,000	Sales	6,53,600
Building	1,10,000	Purchases	4,70,000
Machinery	93,400	Motor Car	20,000
Stock on 1st April, 2018	1,62,000	Reserve Fund (Cr.)	9,000
Power	22,400	Commission (Cr.)	13,200
Insurance	13,150	Car Expenses	18,000
Wages	72,000	Bills Payable	38,500
Debtors	62,800	Cash	800
Creditors	25,000	Bank Overdraft	33,000
Input CGST A/c	15,000	Charity	1,050
Input SGST A/c	15,000	Bad Debts	5,500
Output IGST A/c	30,000

Stock on 31st March, 2019 was valued at ₹ 2,35,000.

Prepare final accounts for the year ended 31st March, 2019.

Discussion

3173.	What is the total number of factors of a prime number?
Answer» What is the total number of factors of a prime number?

Discussion

3174.	In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]
Answer» In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that $∠ A O C + ∠ B O D = 2 ∠ A E C$ . [4 MARKS]

3174.

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]

Answer»

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that $∠ A O C + ∠ B O D = 2 ∠ A E C$ .
[4 MARKS]

Discussion

3175.	If x, 2x + 2, 3x + 3, are in G.P., then the fourth term is _____.
Answer» If x, 2x + 2, 3x + 3, are in G.P., then the fourth term is _____.

Discussion

3176.	Which of the following is equal to cotθ?
Answer» Which of the following is equal to $cot θ$ ?

Discussion

3177.	Simplify x+4x+3+x−1x+2.
Answer» Simplify $\frac{x + 4}{x + 3} + \frac{x - 1}{x + 2} .$

Discussion

3178.	Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If ∠AOB = ∠AOC, then prove that AB = AC and ∠OAB = ∠OAC.
Answer» Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If ∠AOB = ∠AOC, then prove that AB = AC and ∠OAB = ∠OAC.

Discussion

3179.	In the following fig α is
Answer» In the following fig α is

3179.

In the following fig α is

Answer»

In the following fig α is

Discussion

3180.	At what point do the lines of equations 3x + 2y + 5 = 0 and 2x − 3y − 1 = 0 intersects each other? Find one more point on each of these lines. Prove that these lines are perpendicular.
Answer» At what point do the lines of equations 3x + 2y + 5 = 0 and 2x − 3y − 1 = 0 intersects each other? Find one more point on each of these lines. Prove that these lines are perpendicular.

Discussion

3181.	The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio(a) 1 : 3(b) 2 : 3(c) 3 : 1(d) 2 : 3
Answer» The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio (a) 1 : 3 (b) 2 : 3 (c) 3 : 1 (d) 2 : 3

Discussion

3182.	The probability of getting 2 heads, when two coins are tossed, is (a) 1 (b) 34 (c) 12 (d) 14
Answer» The probability of getting 2 heads, when two coins are tossed, is (a) 1 (b) $\frac{3}{4}$ (c) $\frac{1}{2}$ (d) $\frac{1}{4}$

Discussion

3183.	If sin x= cos 11x then the value of tan9x+cot 9x is equal to
Answer» If sin x= cos 11x then the value of tan9x+cot 9x is equal to

Discussion

3184.	If A=diag [3 5] and B=diag[2 −3], find A + 2B :
Answer» If $A = d i a g [35] a n d B = d i a g [2 - 3]$ , find A + 2B :

Discussion

3185.	The mean of the following distribution is ____.xi10131619fi2576
Answer» The mean of the following distribution is ____. $\begin{matrix} x_{i} & 10 & 13 & 16 & 19 f_{i} & 2 & 5 & 7 & 6 \end{matrix}$

Discussion

3186.	Solve 2x + 3y = 11 and 2x − 4y = − 24 and hence find the value of ‘m’ for which y = mx + 3.
Answer» Solve 2x + 3y = 11 and 2x − 4y = − 24 and hence find the value of ‘m’ for which y = mx + 3.

Discussion

3187.	PAQ is a tangent to the circle with center O at a point A as shown in figure. If ∠OBA=35∘, find the value of ∠BAQ and ∠ACB. [4 MARKS]
Answer» PAQ is a tangent to the circle with center O at a point A as shown in figure. If $∠ O B A = 35^{\circ}$ , find the value of $∠ B A Q$ and $∠ A C B$ . [4 MARKS]

3187.

PAQ is a tangent to the circle with center O at a point A as shown in figure. If ∠OBA=35∘, find the value of ∠BAQ and ∠ACB. [4 MARKS]

Answer»

PAQ is a tangent to the circle with center O at a point A as shown in figure. If $∠ O B A = 35^{\circ}$ , find the value of $∠ B A Q$ and $∠ A C B$ . [4 MARKS]

Discussion

3188.	The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 metets more than the shorter side, find the side of the field.
Answer» The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 metets more than the shorter side, find the side of the field.

Discussion

3189.	If a/x+y=b/y+z=c/z-x,then which of the following equation is true-(1)a=b+c(2)c=a+b(3)b=a*c(4)b=a+c
Answer» If a/x+y=b/y+z=c/z-x,then which of the following equation is true- (1)a=b+c (2)c=a+b (3)b=a*c (4)b=a+c

Discussion

3190.	If A+ B+ C =0 then AxB is(1) CxB(2) BxC(3) АxC4) Zero
Answer» If A+ B+ C =0 then AxB is(1) CxB(2) BxC(3) АxC4) Zero

Discussion

3191.	How can we solve questions of Continuity Differentiability involving cubic equations?
Answer» How can we solve questions of Continuity Differentiability involving cubic equations?

Discussion

3192.	if alpha beta and gamma are the roots of the equation of the equation x^3+4x+1=0 then find the value of (alpha + beta)^-1 + (alpha + gamma)^-1 + (beta + gamma)^-1
Answer» if alpha beta and gamma are the roots of the equation of the equation x^3+4x+1=0 then find the value of (alpha + beta)^-1 + (alpha + gamma)^-1 + (beta + gamma)^-1

Discussion

3193.	Find the number of non-negative terms of the following sequence: 987, 932, 877,…
Answer» Find the number of non-negative terms of the following sequence: 987, 932, 877,…

Discussion

3194.	In the given figure, a square OACE is inscribed in a quadrant OBCD. If OA=8√2 cm, then the radius of the circle is
Answer» In the given figure, a square $O A C E$ is inscribed in a quadrant $O B C D$ . If $O A = 8 \sqrt{2} cm$ , then the radius of the circle is

Discussion

3195.	In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?
Answer» In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?

Discussion

3196.	A child has a die whose 6 faces show the letters given below: The die is thrown once. What is the probability of (i) getting A, (ii) getting D
Answer» A child has a die whose 6 faces show the letters given below: The die is thrown once. What is the probability of (i) getting A, (ii) getting D

3196.

A child has a die whose 6 faces show the letters given below: The die is thrown once. What is the probability of (i) getting A, (ii) getting D

Answer»

A child has a die whose 6 faces show the letters given below:

The die is thrown once. What is the probability of

(i) getting A, (ii) getting D

Discussion

3197.	Prove the following trigonometric identities.sec4 A(1 − sin4 A) − 2 tan2 A = 1
Answer» Prove the following trigonometric identities. sec⁴ A(1 − sin⁴ A) − 2 tan² A = 1

Discussion

3198.	What is the quotient when x3+2x2–3 is divided by x – 2?
Answer» What is the quotient when $x^{3} + 2 x^{2} - 3$ is divided by x – 2?

Discussion

3199.	Jamila sold a table and a chair for ₹ 1050 , thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065. Find the cost price of each .
Answer» Jamila sold a table and a chair for ₹ 1050 , thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065. Find the cost price of each .

Discussion

3200.	combination of errors(1) errors in differences
Answer» combination of errors (1) errors in differences

Discussion

Explore topic-wise InterviewSolutions in .

Decide whether 52.123456789 is a rational number or not. If rational (in the form pq), what can you say about the prime factors of q?

The same value of x satisfies the equations 4x + 5 = 0 and 4x2+ (5 + 3p)x + 3p2=0, then p is

14. If M and N are the mid points of the diagonals AC and BD respectively of a quadrilateral ABCD, then the value of ABvector + ADvector + CBvector + CDvector equals (1) 2MNvector) (2) 2NMvector (3) 4NMvector (4) 4MNvector

Question 08.When we toss a coin, there are two possible outcomes - head or tail. Therefore, the probability of each outcome is 12. Justify your answer.

If Sr denotes the sum of the first r terms of an A.P. Then , S3n: (S2n − Sn) is(a) n(b) 3n(c) 3(d) none of these

The shortest side of a right-angled triangle is 6cm shorter than its hypotenuse. The difference in the length of the other two sides is 3cm. If the shortest side is (n-3), show that 2n2=12n. Hence find n.

11. If A(9,-9), (1,-3) are the vertices of a right angled isosceles triangle, then find the third vertex.

Simplify 6x2+13x−59x2+3x−2×3x2−10x−816x2−1.

Draw a circle of radius 4 cm. Construct the two tangents to the circle from a P which is at the distance of 7 cm from centre. Measure the length of the tangents

Divya recorded the shoe sizes of girls in her class : Calculate the Median shoe size from the given data?

Draw an angle ABC=75o.Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.

Question 1The circumference of the base of the cylindrical vessel is 132 cm and its height is 25 cm.How many litres of water can it hold? (1000cm3=1l)[Assume π=227]

Write the value of a30 − a10 for the A.P. 4, 9, 14, 19, ....

During a 360∘ rotation of a regular triangle, the figure identical to the original figure is at and 240∘ angles of rotation.

In the 'less than ' type of ogive the cumulative frequency is plotted against (a) the lower limit of the concerned class interval (b) the upper limit of the concerned class interval (c) the mid-value of the concerned class interval (d) any value of the concernd class interval

The HCF to two numbers is 16 and their product is 3072. Find their LCM.

In ∆ ABC, right angled at B, if tan A = 1/√3 then the value of sin A + cos A is

find the value of k for which the quadratic polynomial kx^2+x+k has equal zeros as 1/2.

What is the total number of factors of a prime number?

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS] ​

If x, 2x + 2, 3x + 3, are in G.P., then the fourth term is _____.

Which of the following is equal to cotθ?

Simplify x+4x+3+x−1x+2.

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. If ∠AOB = ∠AOC, then prove that AB = AC and ∠OAB = ∠OAC.

In the following fig α is

At what point do the lines of equations 3x + 2y + 5 = 0 and 2x − 3y − 1 = 0 intersects each other? Find one more point on each of these lines. Prove that these lines are perpendicular.

The line segment joining points (−3, −4), and (1, −2) is divided by y-axis in the ratio(a) 1 : 3(b) 2 : 3(c) 3 : 1(d) 2 : 3

The probability of getting 2 heads, when two coins are tossed, is (a) 1 (b) 34 (c) 12 (d) 14

If sin x= cos 11x then the value of tan9x+cot 9x is equal to

If A=diag [3 5] and B=diag[2 −3], find A + 2B :

The mean of the following distribution is ____.xi10131619fi2576

Solve 2x + 3y = 11 and 2x − 4y = − 24 and hence find the value of ‘m’ for which y = mx + 3.

PAQ is a tangent to the circle with center O at a point A as shown in figure. If ∠OBA=35∘, find the value of ∠BAQ and ∠ACB. [4 MARKS]

The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 metets more than the shorter side, find the side of the field.

If a/x+y=b/y+z=c/z-x,then which of the following equation is true-(1)a=b+c(2)c=a+b(3)b=a*c(4)b=a+c

If A+ B+ C =0 then AxB is(1) CxB(2) BxC(3) АxC4) Zero

How can we solve questions of Continuity Differentiability involving cubic equations?

if alpha beta and gamma are the roots of the equation of the equation x^3+4x+1=0 then find the value of (alpha + beta)^-1 + (alpha + gamma)^-1 + (beta + gamma)^-1

Find the number of non-negative terms of the following sequence: 987, 932, 877,…

In the given figure, a square OACE is inscribed in a quadrant OBCD. If OA=8√2 cm, then the radius of the circle is

In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?

A child has a die whose 6 faces show the letters given below: The die is thrown once. What is the probability of (i) getting A, (ii) getting D

Prove the following trigonometric identities.sec4 A(1 − sin4 A) − 2 tan2 A = 1

What is the quotient when x3+2x2–3 is divided by x – 2?

Jamila sold a table and a chair for ₹ 1050 , thereby making a profit of 10% on the table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065. Find the cost price of each .

combination of errors(1) errors in differences

In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC+∠BOD=2∠AEC. [4 MARKS]