32581 + Interview Questions in Mathematics

1.	Match the correct expression for volume of the following 3D - shapes.
Answer» Match the correct expression for volume of the following 3D - shapes.

Discussion

2.	Question 19 There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B but, if 20 students are sent from B to A, the number of students in A becomes double the number of students in B, then find the number of students in the both halls.
Answer» Question 19 There are some students in the two examination halls A and B. To make the number of students equal in each hall, 10 students are sent from A to B but, if 20 students are sent from B to A, the number of students in A becomes double the number of students in B, then find the number of students in the both halls.

Discussion

3.	A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.
Answer» A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

Discussion

4.	For a pair of linear equationsa1x+b1+c1=0 and a2x+b2+c2=0a1=12, b1=2, c1=6 and a2=24, b2=4, c2=7.Find the number of solutions the pair of equations will have.
Answer» For a pair of linear equations $a_{1} x + b_{1} + c_{1} = 0$ and $a_{2} x + b_{2} + c_{2} = 0$ $a_{1} = 12, b_{1} = 2, c_{1} = 6$ and $a_{2} = 24, b_{2} = 4, c_{2} = 7$ . Find the number of solutions the pair of equations will have.

Discussion

5.	The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cubic units and the total surface area is 312 square units. The length of the longest edge is
Answer» The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cubic units and the total surface area is 312 square units. The length of the longest edge is

Discussion

6.	Calculate mode of the following data: 20,60,70,70,60,70,60,10,70,80
Answer» Calculate mode of the following data: 20,60,70,70,60,70,60,10,70,80

Discussion

7.	Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then the distance between the lines is
Answer» Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25 $π$ ${c m}^{2}$ , then the distance between the lines is

Discussion

8.	A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Answer» A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

Discussion

9.	If matrix A=⎡⎢⎣abcbcacab⎤⎥⎦ where a, b, c are real positive numbers, abc = 1 and ATA=I, then the value of a3+b3+c3 is ___
Answer» If matrix $A = ⎡ ⎢ ⎣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ⎤ ⎥ ⎦$ where a, b, c are real positive numbers, abc = 1 and $A^{T} A = I,$ then the value of $a^{3} + b^{3} + c^{3}$ is ___

Discussion

10.	Find Domain of ((x+8)^1/2 - (x+2))^1/2
Answer» Find Domain of ((x+8)^1/2 - (x+2))^1/2

Discussion

11.	Obtain all zeros of the polynomial f(x) = 2x4 + x3 − 14x2 − 19x − 6, if two of its zeros are −2 and −1.
Answer» Obtain all zeros of the polynomial f(x) = 2x⁴ + x³ − 14x² − 19x − 6, if two of its zeros are −2 and −1.

Discussion

12.

What is the cumulative frequency of the modal class of the following distribution? Class 3−6 6−9 9−12 12−15 15−18 18−21 21−24 Frequency 7 13 10 23 4 21 16

Answer» What is the cumulative frequency of the modal class of the following distribution?

Class	3−6	6−9	9−12	12−15	15−18	18−21	21−24
Frequency	7	13	10	23	4	21	16

Discussion

13.	All three circles are tangents to the same line and also to each other. Circles C2 and C3 have equal radii. Find the radius of C2, if the radius of C1 is equal to 10 cm.
Answer» All three circles are tangents to the same line and also to each other. Circles C2 and C3 have equal radii. Find the radius of C2, if the radius of C1 is equal to 10 cm.

Discussion

14.	The product of two successive integral multiples of 5 is 300. Determine the multiples.
Answer» The product of two successive integral multiples of 5 is 300. Determine the multiples.

Discussion

15.	If (2m+5),4,3m are in AP,then, find the value of m. 0.6
Answer» $If (2 m + 5), 4, 3 m are in AP,$ $then, find the value of m .$ 0.6

Discussion

16.	The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?
Answer» The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

Discussion

17.	The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.Salary(in thousands)No. of people5−10710−151215−201520−25825−301130−351835−4010
Answer» The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given. $\begin{matrix} Salary(in thousands) & No. of people 5 - 10 & 7 10 - 15 & 12 15 - 20 & 15 20 - 25 & 8 25 - 30 & 11 30 - 35 & 18 35 - 40 & 10 \end{matrix}$

17.

The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.Salary(in thousands)No. of people5−10710−151215−201520−25825−301130−351835−4010

Answer»

The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.

$\begin{matrix} Salary(in thousands) & No. of people 5 - 10 & 7 10 - 15 & 12 15 - 20 & 15 20 - 25 & 8 25 - 30 & 11 30 - 35 & 18 35 - 40 & 10 \end{matrix}$

Discussion

18.	Solve the equation y=x2−2x−3.
Answer» Solve the equation $y = x^{2} - 2 x - 3$ .

Discussion

19.	Question 54 The reciprocal of 47is47.
Answer» Question 54 The reciprocal of $\frac{4}{7} i s \frac{4}{7}$ .

19.

Question 54 The reciprocal of 47is47.

Answer»

Question 54

The reciprocal of $\frac{4}{7} i s \frac{4}{7}$ .

Discussion

20.	Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Answer» Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

20.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Answer»

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Discussion

21.	Prove that for any prime positive integer p , √p is an irrational number.
Answer» Prove that for any prime positive integer p , √p is an irrational number.

Discussion

22.	2x+3x=31 17x-11x=8Substitute the values
Answer» 2x+3x=31 17x-11x=8Substitute the values

22.

2x+3x=31 17x-11x=8Substitute the values

Answer»

2x+3x=31

17x-11x=8Substitute the values

Discussion

23.	Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.
Answer» Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.

Discussion

24.	The ratio of BCCC′ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lieon the same ray BY.
Answer» The ratio of $\frac{B C}{C C^{'}}$ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lie on the same ray BY.

Discussion

25.	The sum of two numbers is 135 and their H.C.F. is 27. If their L.C.M. is 162, the numbers are:
Answer» The sum of two numbers is 135 and their H.C.F. is 27. If their L.C.M. is 162, the numbers are:

Discussion

26.	If the mean of the following frequency distibution is 24, find the value of p. Class0−1010−2020−3030−4040−50Frequency34p32
Answer» If the mean of the following frequency distibution is 24, find the value of p. $\begin{matrix} Class & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequency & 3 & 4 & p & 3 & 2 \end{matrix}$

Discussion

27.	sin4θ can be written as______, if θ lies in first quadrant
Answer» $s i n 4 θ$ can be written as______, if $θ$ lies in first quadrant

Discussion

28.	A motor boat has a speed of 18 kmhr in still water. It takes 2 hours and 45 minutes more to go 66 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.
Answer» A motor boat has a speed of 18 $\frac{k m}{h r}$ in still water. It takes 2 hours and 45 minutes more to go 66 km upstream than to return downstream to the same spot. Find the speed of the stream in $k m / h r .$

Discussion

29.	Question 1 (ii)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(ii) 2x2+x−4=0
Answer» Question 1 (ii) Find the roots of the following quadratic equations, if they exist, by the method of completing the square: (ii) $2 x^{2} + x - 4 = 0$

Discussion

30.	Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Answer» Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Discussion

31.	For what value of `m` is one zero of the polynomial (m^2+9)x^2+13x+6m, the reciprocal of each other?
Answer» For what value of `m` is one zero of the polynomial (m^2+9)x^2+13x+6m, the reciprocal of each other?

Discussion

32.	A bucket made up oa a meta sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used is Rs.20 per 100 cm2. (Use π = 3.14)
Answer» A bucket made up oa a meta sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used is Rs.20 per 100 $c m^{2}$ . (Use $π$ = 3.14)

Discussion

33.	A mechanic sold a scooter for ₹9900 at the loss of 10% in order to gain 5% at what price should he sell it
Answer» A mechanic sold a scooter for ₹9900 at the loss of 10% in order to gain 5% at what price should he sell it

Discussion

34.	The tangent makes a _____ angle with the radius at the point of contact.
Answer» The tangent makes a _____ angle with the radius at the point of contact.

Discussion

35.	In the given figure, a transversal is intersecting two parallel lines at distinct points. Find the value of x.
Answer» In the given figure, a transversal is intersecting two parallel lines at distinct points. Find the value of x.

Discussion

36.	Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which 25 of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?
Answer» Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which $\frac{2}{5}$ of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant?

Discussion

37.	Prove the following trigonometric identities: (i) √1+sin A1−sin A=sec A+tan A (ii) √1−cos A1+cos A+√1+cos A1−cos A=2 cosec A
Answer» Prove the following trigonometric identities: (i) $\sqrt{\frac{1 + s i n A}{1 - s i n A}} = s e c A + t a n A$ (ii) $\sqrt{\frac{1 - c o s A}{1 + c o s A}} + \sqrt{\frac{1 + c o s A}{1 - c o s A}} = 2 c o s e c A$

37.

Prove the following trigonometric identities: (i) √1+sin A1−sin A=sec A+tan A (ii) √1−cos A1+cos A+√1+cos A1−cos A=2 cosec A

Answer»

Prove the following trigonometric identities:

(i) $\sqrt{\frac{1 + s i n A}{1 - s i n A}} = s e c A + t a n A$

(ii) $\sqrt{\frac{1 - c o s A}{1 + c o s A}} + \sqrt{\frac{1 + c o s A}{1 - c o s A}} = 2 c o s e c A$

Discussion

38.	Question 4The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).
Answer» Question 4 The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

38.

Question 4The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

Answer»

Question 4

The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

Discussion

39.	Question 32 In the following question, out of the four options, only one is correct. Write the correct answer. Cube of −12 is (a) 18 (b) 116 (c) −18 (d) −116
Answer» Question 32 In the following question, out of the four options, only one is correct. Write the correct answer. Cube of $- \frac{1}{2}$ is (a) $\frac{1}{8}$ (b) $\frac{1}{16}$ (c) $- \frac{1}{8}$ (d) $- \frac{1}{16}$

39.

Question 32 In the following question, out of the four options, only one is correct. Write the correct answer. Cube of −12 is (a) 18 (b) 116 (c) −18 (d) −116

Answer»

Question 32

In the following question, out of the four options, only one is correct. Write the correct answer.

Cube of $- \frac{1}{2}$ is

(a) $\frac{1}{8}$

(b) $\frac{1}{16}$

(c) $- \frac{1}{8}$

(d) $- \frac{1}{16}$

Discussion

40.	42 The equation of a circle passing through the point ( 1,1), (2,-1) and (3,2) is
Answer» 42 The equation of a circle passing through the point ( 1,1), (2,-1) and (3,2) is

Discussion

41.	A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.
Answer» A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.

Discussion

42.	The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
Answer» The difference of squares of two number is $88.$ If the larger number is $5$ less than twice the smaller number, then find the two numbers.

Discussion

43.	A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Find the height of the tower.
Answer» A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are $α$ and $β$ respectively. Find the height of the tower.

Discussion

44.	If 3rd term of a G.P is 36 and 5th term is 324, find its Common Ratio (r > 0)
Answer» If $3^{r d}$ term of a G.P is 36 and $5^{t h}$ term is 324, find its Common Ratio (r > 0)

Discussion

45.	Which of the following is not a quadratic equation? (i) (√2x+√3)2=3x2−5x (ii) 2x−x2=x2+5 (iii) (x2+2x)2=x4+3+4x2
Answer» Which of the following is not a quadratic equation? (i) $(\sqrt{2} x + \sqrt{3})^{2} = 3 x^{2} - 5 x$ (ii) $2 x - x^{2} = x^{2} + 5$ (iii) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{2}$

Discussion

46.	3. How many times the graph of the polynomial f(x)=x^3+1 will intersect the x -axis?
Answer» 3. How many times the graph of the polynomial f(x)=x^3+1 will intersect the x -axis?

Discussion

47.	If two positive integers m and n are expressible in the form m = a2 b3 and n = a3b2, where a, b are prime numbers, then HCF (m, n) = _______ and LCM (a, b) = _______.
Answer» If two positive integers m and n are expressible in the form m = a² b³ and n = a³b², where a, b are prime numbers, then HCF (m, n) = _______ and LCM (a, b) = _______.

Discussion

48.	Sum of three terms of an arithmetic progression is 13 and their product is 1560 the least of them is
Answer» Sum of three terms of an arithmetic progression is 13 and their product is 1560 the least of them is

Discussion

49.	In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?
Answer» In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

49.

In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

Answer»

In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

Discussion

50.	With vertices a b and c of a triangle abc as centres arcs are drawn with 5cm each .if ab =14 bc = 48. And ca = 50.then find the area of the shaded region
Answer» With vertices a b and c of a triangle abc as centres arcs are drawn with 5cm each .if ab =14 bc = 48. And ca = 50.then find the area of the shaded region

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Match the correct expression for volume of the following 3D - shapes.

A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.

For a pair of linear equationsa1x+b1+c1=0 and a2x+b2+c2=0a1=12, b1=2, c1=6 and a2=24, b2=4, c2=7.Find the number of solutions the pair of equations will have.

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is 216 cubic units and the total surface area is 312 square units. The length of the longest edge is

Calculate mode of the following data: 20,60,70,70,60,70,60,10,70,80

Two parallel lines touch a circle at points A and B respectively. The area of the circle is 25π cm2, then the distance between the lines is

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

If matrix A=⎡⎢⎣abcbcacab⎤⎥⎦ where a, b, c are real positive numbers, abc = 1 and ATA=I, then the value of a3+b3+c3 is ___

Find Domain of ((x+8)^1/2 - (x+2))^1/2

Obtain all zeros of the polynomial f(x) = 2x4 + x3 − 14x2 − 19x − 6, if two of its zeros are −2 and −1.

What is the cumulative frequency of the modal class of the following distribution? Class 3−6 6−9 9−12 12−15 15−18 18−21 21−24 Frequency 7 13 10 23 4 21 16

All three circles are tangents to the same line and also to each other. Circles C2 and C3 have equal radii. Find the radius of C2, if the radius of C1 is equal to 10 cm.

The product of two successive integral multiples of 5 is 300. Determine the multiples.

If (2m+5),4,3m are in AP,then, find the value of m. 0.6

The tops of two poles of height 14 m and 20 m are connected by a wire which makes an angle of 30° with the horizontal. What is the length of the wire?

The given table shows the salaries of 81 people in thousands. Calculate the Median from the data given.Salary(in thousands)No. of people5−10710−151215−201520−25825−301130−351835−4010

Solve the equation y=x2−2x−3.

Question 54 The reciprocal of 47is47.

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

Prove that for any prime positive integer p , √p is an irrational number.

2x+3x=31 17x-11x=8Substitute the values

Point P is the centre of the circle and AB is a diameter . Find the coordinates of point B if coordinates of point A and P are (2, –3) and (–2, 0) respectively.

The ratio of BCCC′ is 3:5. What will the ratio of corresponding sides be if triangles ABC and A'BC' are similar? Given that BC and BC' lieon the same ray BY.

The sum of two numbers is 135 and their H.C.F. is 27. If their L.C.M. is 162, the numbers are:

If the mean of the following frequency distibution is 24, find the value of p. Class0−1010−2020−3030−4040−50Frequency34p32

sin4θ can be written as______, if θ lies in first quadrant

A motor boat has a speed of 18 kmhr in still water. It takes 2 hours and 45 minutes more to go 66 km upstream than to return downstream to the same spot. Find the speed of the stream in km/hr.

Question 1 (ii)Find the roots of the following quadratic equations, if they exist, by the method of completing the square:(ii) 2x2+x−4=0

Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

For what value of `m` is one zero of the polynomial (m^2+9)x^2+13x+6m, the reciprocal of each other?

A bucket made up oa a meta sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used is Rs.20 per 100 cm2. (Use π = 3.14)

A mechanic sold a scooter for ₹9900 at the loss of 10% in order to gain 5% at what price should he sell it

The tangent makes a _____ angle with the radius at the point of contact.

In the given figure, a transversal is intersecting two parallel lines at distinct points. Find the value of x.

Prove the following trigonometric identities: (i) √1+sin A1−sin A=sec A+tan A (ii) √1−cos A1+cos A+√1+cos A1−cos A=2 cosec A

Question 4The diameter of a circle is a line, which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure AB is a diameter of the circle; C is its centre). Express the diameter of the circle (d) in terms of its radius (r).

Question 32 In the following question, out of the four options, only one is correct. Write the correct answer. Cube of −12 is (a) 18 (b) 116 (c) −18 (d) −116

42 The equation of a circle passing through the point ( 1,1), (2,-1) and (3,2) is

A solid metal sphere of 6 cm diameter is melted and a circular sheet of thickness 1 cm is prepared. Determine the diameter of the sheet.

The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are α and β respectively. Find the height of the tower.

If 3rd term of a G.P is 36 and 5th term is 324, find its Common Ratio (r &gt; 0)

Which of the following is not a quadratic equation? (i) (√2x+√3)2=3x2−5x (ii) 2x−x2=x2+5 (iii) (x2+2x)2=x4+3+4x2

3. How many times the graph of the polynomial f(x)=x^3+1 will intersect the x -axis?

If two positive integers m and n are expressible in the form m = a2 b3 and n = a3b2, where a, b are prime numbers, then HCF (m, n) = _______ and LCM (a, b) = _______.

Sum of three terms of an arithmetic progression is 13 and their product is 1560 the least of them is

In the given circle, O is the centre of the circle and AD, AE are the two tangents. If BC is also a tangent, then which of the given options is true?

With vertices a b and c of a triangle abc as centres arcs are drawn with 5cm each .if ab =14 bc = 48. And ca = 50.then find the area of the shaded region

If 3rd term of a G.P is 36 and 5th term is 324, find its Common Ratio (r > 0)

If two positive integers m and n are expressible in the form m = a2 b3 and n = a3b2, where a, b are prime numbers, then HCF (m, n) = _ and LCM (a, b) = _.