32581 + Interview Questions in Mathematics

1.	The value of k for which the quadratic equation x2+4kx+4=0 has equal roots is/are ____.
Answer» The value of k for which the quadratic equation $x^{2} + 4 k x + 4 = 0$ has equal roots is/are ____.

Discussion

2.	Given A = x:11x−5>7x+3,xϵR and B=x:18x−9≥15+12x,xϵR. Find the range of set A∩B and represent it on a number line. [3 MARKS]
Answer» Given A = $x : 11 x - 5 > 7 x + 3, x ϵ R$ and $B = x : 18 x - 9 \geq 15 + 12 x, x ϵ R .$ Find the range of set $A \cap B$ and represent it on a number line. [3 MARKS]

Discussion

3.	A coin was tossed 10 times, out of which 7 times, heads turned up. Based on the given data, what is the probability of getting heads in the next toss?
Answer» A coin was tossed 10 times, out of which 7 times, heads turned up. Based on the given data, what is the probability of getting heads in the next toss?

Discussion

4.	Question 2 (iii) E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF \|\| QR. (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm
Answer» Question 2 (iii) E and F are points on the sides PQ and PR respectively of a $Δ P Q R$ . For the following case, state whether EF \|\| QR. (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

Discussion

5.	From the above triangles, which of the following is true?
Answer» From the above triangles, which of the following is true?

5.

From the above triangles, which of the following is true?

Answer»

From the above triangles, which of the following is true?

Discussion

6.	tan (90o−θ) = _______.
Answer» $t a n (90^{o} - θ)$ = _______.

Discussion

7.	Which of the following is a unit vector
Answer» Which of the following is a unit vector

Discussion

8.	Nature of roots of x−2x−1=x+42x+2 is
Answer» Nature of roots of $\frac{x - 2}{x - 1}$ = $\frac{x + 4}{2 x + 2}$ is

Discussion

9.	Construct a triangle ABC with AB is equal to 6cm ,BC iapz equal to 7cm and an angle Bis equal to 60.Then construct a similar triangle whose sides are3/5 of triangle ABC
Answer» Construct a triangle ABC with AB is equal to 6cm ,BC iapz equal to 7cm and an angle Bis equal to 60.Then construct a similar triangle whose sides are3/5 of triangle ABC

Discussion

10.	In Fig. 7.178, ΔACB∼ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ).
Answer» In Fig. 7.178, $Δ A C B \sim Δ A P Q$ . If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area $(Δ A C B)$ : area $(Δ A P Q)$ .

10.

In Fig. 7.178, ΔACB∼ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ).

Answer»

In Fig. 7.178, $Δ A C B \sim Δ A P Q$ . If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area $(Δ A C B)$ : area $(Δ A P Q)$ .

Discussion

11.	Match the following type of matrices to their general order.
Answer» Match the following type of matrices to their general order.

Discussion

12.	If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is
Answer» If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is

Discussion

13.	A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household: FAMILY SIZE1−33−55−77−99−1NUMBER78212OF FAMILIES Find the mode of the data.
Answer» A survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household: $\begin{matrix} FAMILY SIZE & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 9 & 9 - 1 NUMBER & 7 & 8 & 2 & 1 & 2 OF FAMILIES \end{matrix}$ Find the mode of the data.

13.

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household: FAMILY SIZE1−33−55−77−99−1NUMBER78212OF FAMILIES Find the mode of the data.

Answer»

A survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

$\begin{matrix} FAMILY SIZE & 1 - 3 & 3 - 5 & 5 - 7 & 7 - 9 & 9 - 1 NUMBER & 7 & 8 & 2 & 1 & 2 OF FAMILIES \end{matrix}$

Find the mode of the data.

Discussion

14.	If the rational number ab has a terminating decimal expansion, what is the condition to be satisfied by b?
Answer» If the rational number $\frac{a}{b}$ has a terminating decimal expansion, what is the condition to be satisfied by $b$ ?

Discussion

15.	One side of a rectangle is 12 cm long and its diagonal measures 37 cm.Find the other side and the area of the rectangle.
Answer» One side of a rectangle is 12 cm long and its diagonal measures 37 cm.Find the other side and the area of the rectangle.

Discussion

16.	Show graphically that each of the following given systems of equations is inconsistent,i.e.,has no solution: 2x+y=6,6x+3y=20.
Answer» Show graphically that each of the following given systems of equations is inconsistent,i.e.,has no solution: $2 x + y = 6, 6 x + 3 y = 20.$

16.

Show graphically that each of the following given systems of equations is inconsistent,i.e.,has no solution: 2x+y=6,6x+3y=20.

Answer»

Show graphically that each of the following given systems of equations is inconsistent,i.e.,has no solution:

$2 x + y = 6, 6 x + 3 y = 20.$

Discussion

17.	What do you mean by Euclid’s division lemma ?
Answer» What do you mean by Euclid’s division lemma ?

Discussion

18.	Prove the following trigonometric identities: 1−sin θ1+sin θ=(sec θ−tan θ)2
Answer» Prove the following trigonometric identities: $\frac{1 - s i n θ}{1 + s i n θ} = (s e c θ - t a n θ)^{2}$

18.

Prove the following trigonometric identities: 1−sin θ1+sin θ=(sec θ−tan θ)2

Answer»

Prove the following trigonometric identities:

$\frac{1 - s i n θ}{1 + s i n θ} = (s e c θ - t a n θ)^{2}$

Discussion

19.	Prove the following trigonometric identities: cos A1−tan A+sin A1−cot A=sin A+cos A
Answer» Prove the following trigonometric identities: $\frac{c o s A}{1 - t a n A} + \frac{s i n A}{1 - c o t A} = s i n A + c o s A$

19.

Prove the following trigonometric identities: cos A1−tan A+sin A1−cot A=sin A+cos A

Answer»

Prove the following trigonometric identities:

$\frac{c o s A}{1 - t a n A} + \frac{s i n A}{1 - c o t A} = s i n A + c o s A$

Discussion

20.	The cost of 11 pencils and 3 eraser is Rs 50 and cost of 8 pencils and 3 eraser is Rs 38 Find the cost of each pencil and each eraser
Answer» The cost of 11 pencils and 3 eraser is Rs 50 and cost of 8 pencils and 3 eraser is Rs 38 Find the cost of each pencil and each eraser

Discussion

21.	If a,b,c,d∈R+ and a+b+c+d=2,then the maximum value of∣∣∣∣∣a−c2aba2−ac2−c1+c1+b1+a+acb+bcb2−dab+b+abc∣∣∣∣∣ is
Answer» $If a, b, c, d \in R^{+} and a + b + c + d = 2, then the maximum value of ∣ ∣∣∣ ∣ \begin{matrix} a - c^{2} & a b & a^{2} - a c^{2} - c 1 + c & 1 + b & 1 + a + a c b + b c & b^{2} - d & a b + b + a b c \end{matrix} ∣ ∣∣∣ ∣ is$

Discussion

22.	If (ma+nb):b::(mc+nd):d, prove that a,b,c,d are are in proportion.
Answer» If (ma+nb):b::(mc+nd):d, prove that a,b,c,d are are in proportion.

Discussion

23.	If tan 2A = cot (A+6) , then value of A is
Answer» If tan 2A = cot (A+6) , then value of A is

Discussion

24.	If (x-2) and (x-1) two of the factors of a cubic polynomial whose product of roots is zero, then sum of roots of given cubic polynomial is:
Answer» If (x-2) and (x-1) two of the factors of a cubic polynomial whose product of roots is zero, then sum of roots of given cubic polynomial is:

Discussion

25.	Four years ago Rahim,s age was three time family,s age after two years of would just be double. What is their age. Answer with all steps.
Answer» Four years ago Rahim,s age was three time family,s age after two years of would just be double. What is their age. Answer with all steps.

Discussion

26.	Find the greatest number of 4 digits which is exactly divisible by 15 24 and 36.
Answer» Find the greatest number of 4 digits which is exactly divisible by 15 24 and 36.

Discussion

27.	If sin =x,sec=y find tan
Answer» If sin =x,sec=y find tan

Discussion

28.	Use Euclid's algorithm to find HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.
Answer» Use Euclid's algorithm to find HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.

Discussion

29.	Respected Sir, Please help me in solving my below mentioned doubt: If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e, then 1. a+c+e=b+d 2.a+b+e=c+d 3. a+b+c=d+e 4. b+c+d=a+e
Answer» Respected Sir, Please help me in solving my below mentioned doubt: If x² - 1 is a factor of ax⁴+ bx³+ cx²+ dx + e, then 1. a+c+e=b+d 2.a+b+e=c+d 3. a+b+c=d+e 4. b+c+d=a+e

29.

Respected Sir, Please help me in solving my below mentioned doubt: If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e, then 1. a+c+e=b+d 2.a+b+e=c+d 3. a+b+c=d+e 4. b+c+d=a+e

Answer»

Respected Sir,

Please help me in solving my below mentioned doubt:

If x² - 1 is a factor of ax⁴+ bx³+ cx²+ dx + e, then

1. a+c+e=b+d

2.a+b+e=c+d

3. a+b+c=d+e

4. b+c+d=a+e

Discussion

30.	If x = asec σ + btanσ and y = atanσ + bsecσ, then, x2 - y2 =
Answer» If x = asec σ + btanσ and y = atanσ + bsecσ, then, x² - y² =

Discussion

31.	In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?
Answer» In the figure $△ A B C$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

31.

In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Answer»

In the figure $△ A B C$ is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Discussion

32.	Show that (a, 1), (b, 1) and (c, 1) are collinear points
Answer» Show that (a, 1), (b, 1) and (c, 1) are collinear points

Discussion

33.	x+2 /2 + y-1 /3 =8 and x-3 /2 + y-1 /3 =8 Solve x and y
Answer» x+2 /2 + y-1 /3 =8 and x-3 /2 + y-1 /3 =8 Solve x and y

33.

x+2 /2 + y-1 /3 =8 and x-3 /2 + y-1 /3 =8 Solve x and y

Answer»

x+2 /2 + y-1 /3 =8 and x-3 /2 + y-1 /3 =8

Solve x and y

Discussion

34.	Can (x-7) be the reminder on division of a polynomial P(x)by(7x+2)? Justify your answer
Answer» Can (x-7) be the reminder on division of a polynomial P(x)by(7x+2)? Justify your answer

Discussion

35.	If the roots of the quadratic equation (a-b)x2+(b-c)x+(c-a)=0 are equal prove that 2a=b+c.
Answer» If the roots of the quadratic equation (a-b)x²+(b-c)x+(c-a)=0 are equal prove that 2a=b+c.

Discussion

36.	Reena bought a washing machine for Rs. 9800 including a tax of 10%. Find the price of the washing machine before VAT was added.
Answer» Reena bought a washing machine for Rs. 9800 including a tax of 10%. Find the price of the washing machine before VAT was added.

Discussion

37.	State, true or false : (i) the line x2+y3=0 passes through the point (2, 3). (ii) the line x2+y3=0 passes through the point (4, -6). (iii) the point (8, 7) lies on the line y - 7 = 0 (iv) the point (-3, 0) lies on the line x + 3 = 0 (v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.
Answer» State, true or false : (i) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (2, 3). (ii) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (4, -6). (iii) the point (8, 7) lies on the line y - 7 = 0 (iv) the point (-3, 0) lies on the line x + 3 = 0 (v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

37.

State, true or false : (i) the line x2+y3=0 passes through the point (2, 3). (ii) the line x2+y3=0 passes through the point (4, -6). (iii) the point (8, 7) lies on the line y - 7 = 0 (iv) the point (-3, 0) lies on the line x + 3 = 0 (v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

Answer»

State, true or false :

(i) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (2, 3).

(ii) the line $\frac{x}{2} + \frac{y}{3} = 0$ passes through the point (4, -6).

(iii) the point (8, 7) lies on the line y - 7 = 0

(iv) the point (-3, 0) lies on the line x + 3 = 0

(v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

Discussion

38.	If the points (1,-1), (2,1) and (4,x) lie on a staright line, then x is __
Answer» If the points (1,-1), (2,1) and (4,x) lie on a staright line, then x is __

Discussion

39.	In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?
Answer» In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?

Discussion

40.	A fort had provisions for 150 men for 50 days. After 15 days, 25 men left the fort. How long will food last at the same rate for remaining men?
Answer» A fort had provisions for 150 men for 50 days. After 15 days, 25 men left the fort. How long will food last at the same rate for remaining men?

Discussion

41.	A line that intersects a circle in two distinct points is called a
Answer» A line that intersects a circle in two distinct points is called a

Discussion

42.	A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32cm and 20cm and length 8cm. Find its bearing surface (lateral surface area).
Answer» A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32cm and 20cm and length 8cm. Find its bearing surface (lateral surface area).

Discussion

43.	A line through (5, 3) meets the line y = 3x + 8 at right angles at point X. Find the coordinates of X.
Answer» A line through (5, 3) meets the line y = 3x + 8 at right angles at point X. Find the coordinates of X.

Discussion

44.	In the picture, chords AB and CD of the circle are extended to meet at P Then, PA×PB= ___
Answer» In the picture, chords AB and CD of the circle are extended to meet at P Then, $P A \times P B =$ ___

44.

In the picture, chords AB and CD of the circle are extended to meet at P Then, PA×PB= ___

Answer»

In the picture, chords AB and CD of the circle are extended to meet at P

Then, $P A \times P B =$ ___

Discussion

45.	In a right angled triangle PQR, Circumcenter and orthocenter are at a distance of ------ units from each other. (Where R is the circumradius)
Answer» In a right angled triangle PQR, Circumcenter and orthocenter are at a distance of ------ units from each other. (Where R is the circumradius)

Discussion

46.	Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).
Answer» Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).

Discussion

47.	Two circles intersect at A and B. The lines KAL, NBM are parallel. Then ___
Answer» Two circles intersect at A and B. The lines KAL, NBM are parallel. Then ___

47.

Two circles intersect at A and B. The lines KAL, NBM are parallel. Then ___

Answer»

Two circles intersect at A and B. The lines KAL, NBM are parallel. Then ___

Discussion

48.	The ratio of the length of a rod and its shadow is 1:√3. The angle of elevation to the top of the rod from the ground is:
Answer» The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$ . The angle of elevation to the top of the rod from the ground is:

Discussion

49.	Taking O as centre, draw an arc ‘AC’ with radius ‘r’. Cut the arc ‘AC’ at ‘B’, with centre ‘A’ and radius ‘r’. If ‘AB’ is joined in a straight line, what will be the ∠BAO (in degrees)? ___
Answer» Taking O as centre, draw an arc ‘AC’ with radius ‘r’. Cut the arc ‘AC’ at ‘B’, with centre ‘A’ and radius ‘r’. If ‘AB’ is joined in a straight line, what will be the $∠ B A O$ (in degrees)? ___

49.

Taking O as centre, draw an arc ‘AC’ with radius ‘r’. Cut the arc ‘AC’ at ‘B’, with centre ‘A’ and radius ‘r’. If ‘AB’ is joined in a straight line, what will be the ∠BAO (in degrees)? ___

Answer»

Taking O as centre, draw an arc ‘AC’ with radius ‘r’. Cut the arc ‘AC’ at ‘B’, with centre ‘A’ and radius ‘r’. If ‘AB’ is joined in a straight line, what will be the $∠ B A O$ (in degrees)?

___

Discussion

50.	The range of the data 6,8,16,22,8,20,7,25 is _____.
Answer» The range of the data $6, 8, 16, 22, 8, 20, 7, 25$ is $_____$ .

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The value of k for which the quadratic equation x2+4kx+4=0 has equal roots is/are ____.

Given A = x:11x−5&gt;7x+3,xϵR and B=x:18x−9≥15+12x,xϵR. Find the range of set A∩B and represent it on a number line. [3 MARKS]

A coin was tossed 10 times, out of which 7 times, heads turned up. Based on the given data, what is the probability of getting heads in the next toss?

Question 2 (iii) E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

From the above triangles, which of the following is true?

tan (90o−θ) = _______.

Which of the following is a unit vector

Nature of roots of x−2x−1=x+42x+2 is

Construct a triangle ABC with AB is equal to 6cm ,BC iapz equal to 7cm and an angle Bis equal to 60.Then construct a similar triangle whose sides are3/5 of triangle ABC

In Fig. 7.178, ΔACB∼ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ).

Match the following type of matrices to their general order.

If the first, second and last term of an A.P are a, b and 2a respectively, then its sum is

A survey conducted on 20 households in a locality by a group of students resulted in the following frequency table for the number of family members in a household: FAMILY SIZE1−33−55−77−99−1NUMBER78212OF FAMILIES Find the mode of the data.

If the rational number ab has a terminating decimal expansion, what is the condition to be satisfied by b?

One side of a rectangle is 12 cm long and its diagonal measures 37 cm.Find the other side and the area of the rectangle.

Show graphically that each of the following given systems of equations is inconsistent,i.e.,has no solution: 2x+y=6,6x+3y=20.

What do you mean by Euclid’s division lemma ?

Prove the following trigonometric identities: 1−sin θ1+sin θ=(sec θ−tan θ)2

Prove the following trigonometric identities: cos A1−tan A+sin A1−cot A=sin A+cos A

The cost of 11 pencils and 3 eraser is Rs 50 and cost of 8 pencils and 3 eraser is Rs 38 Find the cost of each pencil and each eraser

If a,b,c,d∈R+ and a+b+c+d=2,then the maximum value of∣∣∣∣∣a−c2aba2−ac2−c1+c1+b1+a+acb+bcb2−dab+b+abc∣∣∣∣∣ is

If (ma+nb):b::(mc+nd):d, prove that a,b,c,d are are in proportion.

If tan 2A = cot (A+6) , then value of A is

If (x-2) and (x-1) two of the factors of a cubic polynomial whose product of roots is zero, then sum of roots of given cubic polynomial is:

Four years ago Rahim,s age was three time family,s age after two years of would just be double. What is their age. Answer with all steps.

Find the greatest number of 4 digits which is exactly divisible by 15 24 and 36.

If sin =x,sec=y find tan

Use Euclid's algorithm to find HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.

Respected Sir, Please help me in solving my below mentioned doubt: If x2 - 1 is a factor of ax4 + bx3 + cx2 + dx + e, then 1. a+c+e=b+d 2.a+b+e=c+d 3. a+b+c=d+e 4. b+c+d=a+e

If x = asec σ + btanσ and y = atanσ + bsecσ, then, x2 - y2 =

In the figure △ABC is a right angled triangle with right angle at B. BD is perpendicular to AC. Then which of the following options will hold true?

Show that (a, 1), (b, 1) and (c, 1) are collinear points

x+2 /2 + y-1 /3 =8 and x-3 /2 + y-1 /3 =8 Solve x and y

Can (x-7) be the reminder on division of a polynomial P(x)by(7x+2)? Justify your answer

If the roots of the quadratic equation (a-b)x​​​​​​2+(b-c)x+(c-a)=0 are equal prove that 2a=b+c.

Reena bought a washing machine for Rs. 9800 including a tax of 10%. Find the price of the washing machine before VAT was added.

State, true or false : (i) the line x2+y3=0 passes through the point (2, 3). (ii) the line x2+y3=0 passes through the point (4, -6). (iii) the point (8, 7) lies on the line y - 7 = 0 (iv) the point (-3, 0) lies on the line x + 3 = 0 (v) if the point (2, a) lies on the line 2x - y = 3, then a = 5.

If the points (1,-1), (2,1) and (4,x) lie on a staright line, then x is __

In a parallelogram ABCD, E is a point on BC such that BE:EC = m:n. If AE and DB intersect at F, then what is the ratio of the area of the triangle FEB to the area of the triangle AFD?

A fort had provisions for 150 men for 50 days. After 15 days, 25 men left the fort. How long will food last at the same rate for remaining men?

A line that intersects a circle in two distinct points is called a

A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32cm and 20cm and length 8cm. Find its bearing surface (lateral surface area).

A line through (5, 3) meets the line y = 3x + 8 at right angles at point X. Find the coordinates of X.

In the picture, chords AB and CD of the circle are extended to meet at P Then, PA×PB= ___

In a right angled triangle PQR, Circumcenter and orthocenter are at a distance of ------ units from each other. (Where R is the circumradius)

Find the coordinates of rectangle whose sides are parallel to the axes and origin 'O' is the mid point. One of the vertices is (4,2).

Two circles intersect at A and B. The lines KAL, NBM are parallel. Then ___

The ratio of the length of a rod and its shadow is 1:√3. The angle of elevation to the top of the rod from the ground is:

Taking O as centre, draw an arc ‘AC’ with radius ‘r’. Cut the arc ‘AC’ at ‘B’, with centre ‘A’ and radius ‘r’. If ‘AB’ is joined in a straight line, what will be the ∠BAO (in degrees)? ___

The range of the data 6,8,16,22,8,20,7,25 is _____.

Given A = x:11x−5>7x+3,xϵR and B=x:18x−9≥15+12x,xϵR. Find the range of set A∩B and represent it on a number line. [3 MARKS]

If the roots of the quadratic equation (a-b)x2+(b-c)x+(c-a)=0 are equal prove that 2a=b+c.