32581 + Interview Questions in Mathematics Page 172 InterviewSolution

8551.	In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm2. [CBSE 2015]
Answer» In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm². [CBSE 2015]

Discussion

8552.	Given A=[31−21] and B=[4−32−1] Find sum of all elements in the matrix A+B-2l.1
Answer» Given $A = [\begin{matrix} 3 & 1 - 2 & 1 \end{matrix}] and B = [\begin{matrix} 4 & - 3 2 & - 1 \end{matrix}]$ Find sum of all elements in the matrix A+B-2l. 1

8552.

Given A=[31−21] and B=[4−32−1] Find sum of all elements in the matrix A+B-2l.1

Answer»

Given $A = [\begin{matrix} 3 & 1 - 2 & 1 \end{matrix}] and B = [\begin{matrix} 4 & - 3 2 & - 1 \end{matrix}]$

Find sum of all elements in the matrix A+B-2l.

1

Discussion

8553.	The express sin A in terms of cot A is:
Answer» The express sin A in terms of cot A is:

Discussion

8554.	If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.
Answer» If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.

Discussion

8555.	Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x4 + 9x3 + 6x2 – 11x – 6, g(x) = x – 1
Answer» Using factor theorem, show that g(x) is a factor of p(x), when p(x) = 2x⁴ + 9x³ + 6x² – 11x – 6, g(x) = x – 1

Discussion

8556.	Prove the following trigonometric identities.1sec A+tan A-1cos A=1cos A-1sec A-tan A
Answer» Prove the following trigonometric identities. $\frac{1}{\sec A + \tan A} - \frac{1}{\cos A} = \frac{1}{\cos A} - \frac{1}{\sec A - \tan A}$

Discussion

8557.	An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?
Answer» An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

Discussion

8558.	In triangles BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If ΔBMP∼ΔCNR then find the perimeter of ΔCNR.
Answer» In triangles BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If $Δ B M P \sim Δ C N R$ then find the perimeter of $Δ C N R$ .

Discussion

8559.	The region bounded by a chord and an arc is called a ___
Answer» The region bounded by a chord and an arc is called a ___

Discussion

8560.	Product of two numbers is 27.HCF of that numbers is 3 what is LCM
Answer» Product of two numbers is 27.HCF of that numbers is 3 what is LCM

Discussion

8561.	Let f(x) be a non-constant, thrice differentiable function defined on R such that f(x)=f(6−x) and f′(0)=0=f′(2)=f′(5). If n is the minimum number of roots of (f′(x))2+f′(x)⋅f′′′(x)=0 in the interval [0,6], then the value of n2 is
Answer» Let $f (x)$ be a non-constant, thrice differentiable function defined on $R$ such that $f (x) = f (6 - x)$ and $f^{'} (0) = 0 = f^{'} (2) = f^{'} (5) .$ If $n$ is the minimum number of roots of ${(f^{'} (x))}^{2} + f^{'} (x) \cdot f^{'''} (x) = 0$ in the interval $[0, 6]$ , then the value of $\frac{n}{2}$ is

Discussion

8562.	Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.
Answer» Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

Discussion

8563.	Two circles of radii 4 cm and 2.5 cm have their centres 5.5 cm apart. Draw direct common tangents to the circles.
Answer» Two circles of radii 4 cm and 2.5 cm have their centres 5.5 cm apart. Draw direct common tangents to the circles.

Discussion

8564.	Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
Answer» Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.

Discussion

8565.	Question 11 (i)State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1.
Answer» Question 11 (i) State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1.

Discussion

8566.	If sinA=817, find the value of secA cosA + cosecA cosA.
Answer» If $s i n A = \frac{8}{17}$ , find the value of secA cosA + cosecA cosA.

Discussion

8567.	Question 7 (i) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs. 400.
Answer» Question 7 (i) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs. 400.

Discussion

8568.	Question 4Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).
Answer» Question 4 Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

Discussion

8569.	In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF [CBSE 2013]
Answer» In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF [CBSE 2013]

Discussion

8570.	What is the arithmetic mean of the numbers a and b?
Answer» What is the arithmetic mean of the numbers $a$ and $b$ ?

Discussion

8571.	If ∆ABC and ∆DEF are similar such that 2AB = DE and BC = 8 cm, then EF =(a) 16 cm(b) 12 cm(c) 8 cm(d) 4 cm
Answer» If ∆ABC and ∆DEF are similar such that 2AB = DE and BC = 8 cm, then EF = (a) 16 cm (b) 12 cm (c) 8 cm (d) 4 cm

Discussion

8572.	The table below contains different sports and the number of people who like it. If a person likes football, he makes an entry in the table as football and so on. SportsNumber of EntriesFootball10Badminton11Volley Ball15Cricket25Basket Ball20 What is the frequency of the sport volleyball in the table?
Answer» The table below contains different sports and the number of people who like it. If a person likes football, he makes an entry in the table as football and so on. $\begin{matrix} Sports & Number of Entries Football & 10 Badminton & 11 Volley Ball & 15 Cricket & 25 Basket Ball & 20 \end{matrix}$ What is the frequency of the sport volleyball in the table?

Discussion

8573.	Question 5ABC is an isosceles triangle with AC = BC. If AB2=2AC2, prove that ABC is a right triangle.
Answer» Question 5 ABC is an isosceles triangle with AC = BC. If $A B^{2} = 2 A C^{2}$ , prove that ABC is a right triangle.

Discussion

8574.	The distributions X and Y with total number of observations 36 and 64,and mean 4 and 3 respectively are combined.What is the mean of the resulting distribution X+Y?
Answer» The distributions X and Y with total number of observations 36 and 64,and mean 4 and 3 respectively are combined.What is the mean of the resulting distribution X+Y?

Discussion

8575.	triangle ABC, if D is a point on AC such that AB=AD and AC>AB. Prove that BC>CD
Answer» triangle ABC, if D is a point on AC such that AB=AD and AC>AB. Prove that BC>CD

Discussion

8576.

Find the mean of the following frequency distribution using step-deviation method: Class 84−90 90−96 96−102 102−108 108−114 114−120 Frequency 15 22 20 18 20 25

Answer»

Find the mean of the following frequency distribution using step-deviation method:

Class	84−90	90−96	96−102	102−108	108−114	114−120
Frequency	15	22	20	18	20	25

Discussion

8577.	A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is__.
Answer» A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is__.

Discussion

8578.	A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. OR A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/ hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed ?
Answer» A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. OR A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/ hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed ?

Discussion

8579.	The sum of the first n terms of an A.P. is 3n2−4n. Find the nth term of this A.P.
Answer» The sum of the first n terms of an A.P. is $3 n^{2} - 4 n$ . Find the nth term of this A.P.

Discussion

8580.

From the following Trial Balance of M/s Arjun and Sons as on 31st March, 2018, prepare Trading and Profit and Loss Account and Balance Sheet: Heads of Accounts Debit Balances (₹) Credit Balances (₹) Drawings ................................................................................ 1,80,000 … Capital ................................................................................ … 8,00,000 Purchases ................................................................................ 8,26,000 ... Sales ................................................................................ … 15,50,000 Opening Stock ................................................................................ 4,20,000 … Returns Outward ................................................................................ … 16,000 Carriage Inwards ................................................................................ 12,000 … Wages ................................................................................ 40,000 … Power ................................................................................ 60,000 … Machinery ................................................................................ 5,00,000 … Furniture ................................................................................ 1,40,000 … Rent ................................................................................ 2,20,000 … Salary ................................................................................ 1,50,000 … Insurance ................................................................................ 36,000 … 8% Bank Loan ................................................................................ … 2,50,000 Debtors ................................................................................ 2,06,000 … Creditors ................................................................................ … 1,89,000 Cash in Hand ................................................................................ 15,000 … Total 28,05,000 28,05,000 Adjustments:(i) Closing Stock ₹ 6,40,000.(ii) Wages Outstanding ₹ 24,000.(iii) Bad Debts ₹ 6,000 and Provision for Bad and Doubtful Debts to 5% on Debtors.(iv) Rent is paid for 11 months.(v) Loan from bank was taken on 1st October, 2017.(vi) Provide Depreciation on Machinery 10% p.a.(vii) Provide Manager’s Commission at 10% on net profit after charging such commission.

Answer» From the following Trial Balance of M/s Arjun and Sons as on 31st March, 2018, prepare Trading and Profit and Loss Account and Balance Sheet:

Heads of Accounts		Debit Balances (₹)	Credit Balances (₹)
Drawings	................................................................................	1,80,000	…
Capital	................................................................................	…	8,00,000
Purchases	................................................................................	8,26,000	...
Sales	................................................................................	…	15,50,000
Opening Stock	................................................................................	4,20,000	…
Returns Outward	................................................................................	…	16,000
Carriage Inwards	................................................................................	12,000	…
Wages	................................................................................	40,000	…
Power	................................................................................	60,000	…
Machinery	................................................................................	5,00,000	…
Furniture	................................................................................	1,40,000	…
Rent	................................................................................	2,20,000	…
Salary	................................................................................	1,50,000	…
Insurance	................................................................................	36,000	…
8% Bank Loan	................................................................................	…	2,50,000
Debtors	................................................................................	2,06,000	…
Creditors	................................................................................	…	1,89,000
Cash in Hand	................................................................................	15,000	…
Total		28,05,000	28,05,000

Adjustments:

(i) Closing Stock ₹ 6,40,000.

(ii) Wages Outstanding ₹ 24,000.

(iii) Bad Debts ₹ 6,000 and Provision for Bad and Doubtful Debts to 5% on Debtors.

(iv) Rent is paid for 11 months.

(v) Loan from bank was taken on 1^st October, 2017.

(vi) Provide Depreciation on Machinery 10% p.a.

(vii) Provide Manager’s Commission at 10% on net profit after charging such commission.

Discussion

8581.	A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.
Answer» A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.

Discussion

8582.	A and B are square matrices of the same order 3, such that AB = 2I and \|A\| = 2, write the value of \|B\|.
Answer» A and B are square matrices of the same order 3, such that AB = 2I and \|A\| = 2, write the value of \|B\|.

Discussion

8583.	Find the largest number which divides 615 and 963 leaving remainder 6 in each case.
Answer» Find the largest number which divides 615 and 963 leaving remainder 6 in each case.

Discussion

8584.	Question 2 (iii) Verify that each of the following is an AP and then write its next three terms. √3, 2√3, 3√3,⋯
Answer» Question 2 (iii) Verify that each of the following is an AP and then write its next three terms. $\sqrt{3}, 2 \sqrt{3}, 3 \sqrt{3}, \dots$

Discussion

8585.	How to take out median?
Answer» How to take out median?

Discussion

8586.	x−12x+1+2x+1x−1=2 find x
Answer» $\frac{x - 1}{2 x + 1} + \frac{2 x + 1}{x - 1} = 2$ find x

Discussion

8587.	What is the sum of 3 digit numbers divisible by 3 and 7?
Answer» What is the sum of 3 digit numbers divisible by 3 and 7?

Discussion

8588.	The angle of elevation of a jet fighter from a point A on the ground is 60∘. After a flight of 15 seconds, the angle of elevation changes to 30∘. If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use √3=1.732] [4 MARKS]
Answer» The angle of elevation of a jet fighter from a point A on the ground is $60^{\circ}$ . After a flight of 15 seconds, the angle of elevation changes to $30^{\circ}$ . If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use $\sqrt{3} = 1.732$ ] [4 MARKS]

Discussion

8589.	Secant intersects the circle at ___ distinct points.
Answer» Secant intersects the circle at ___ distinct points.

Discussion

8590.	15. If mean and variance of a binomial distribution are 4 and 2 then P(Ix-4I
Answer» 15. If mean and variance of a binomial distribution are 4 and 2 then P(Ix-4I<2) where x is binomial variate is given by

Discussion

8591.	Find the next number in the following sequence: 4.00, 2.00, 1.00, 0.50...
Answer» Find the next number in the following sequence: 4.00, 2.00, 1.00, 0.50...

Discussion

8592.	Question 1 (iii)Which of the following form an AP? Justify your answer.1, 1, 2, 2, 3, 3, ….
Answer» Question 1 (iii) Which of the following form an AP? Justify your answer. 1, 1, 2, 2, 3, 3, ….

Discussion

8593.	In ∆ PQR PQ> PR and PS is angle bisector of angle P then:(1) PS=PR(2) PSPS(4) PQ
Answer» In ∆ PQR PQ> PR and PS is angle bisector of angle P then: (1) PS=PR (2) PSPS (4) PQ

Discussion

8594.	Zero of the polynomial p(x)=ax+d is __________ .
Answer» Zero of the polynomial $p (x) = a x + d$ is __________ .

Discussion

8595.	If alpha and beta are the zeroes of the quadratic polynomial f(x)=2x2-5x+7 , find a polynomial whose zeroes are 2 alpha +3 beta and 3 alpha+2 beta.
Answer» If alpha and beta are the zeroes of the quadratic polynomial f(x)=2x²-5x+7 , find a polynomial whose zeroes are 2 alpha +3 beta and 3 alpha+2 beta.

Discussion

8596.	If the angle of elevation of a tower from a distance of 100 metres from its foot is 60°, then the height of the tower is(a) 1003 m(b) 1003 m(c) 50 3(d) 2003 m
Answer» If the angle of elevation of a tower from a distance of 100 metres from its foot is 60°, then the height of the tower is (a) 100 $\sqrt{3}$ m (b) $\frac{100}{\sqrt{3}} m$ (c) $50 \sqrt{3}$ (d) $\frac{200}{\sqrt{3}} m$

Discussion

8597.	A square is inscribed in another square such that each vertex of inscribed square divides a side of the outside square into intervals of length x and y where x > y. If the area of the inscribed square is 4/5 th of the area of the outside square, find the ratio x/y.
Answer» A square is inscribed in another square such that each vertex of inscribed square divides a side of the outside square into intervals of length x and y where x > y. If the area of the inscribed square is 4/5 th of the area of the outside square, find the ratio x/y.

Discussion

8598.	The circumference of a circle is 8 cm. Find the approximate area of the sector whose central angle is 72∘.
Answer» The circumference of a circle is $8 cm$ . Find the approximate area of the sector whose central angle is $72^{\circ}$ .

Discussion

8599.	From a solid right circular cylinder of height h and base radius r, a conical cavity of the same height and base is scooped out. Then the ratio of the volume of the cone and the remaining solid is __________.
Answer» From a solid right circular cylinder of height h and base radius r, a conical cavity of the same height and base is scooped out. Then the ratio of the volume of the cone and the remaining solid is __________.

Discussion

8600.	A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is(a) 12π cm3(b) 15π cm3(c) 16π cm3(d) 20π cm3
Answer» A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is (a) 12π cm³ (b) 15π cm³ (c) 16π cm³ (d) 20π cm³

Discussion

Explore topic-wise InterviewSolutions in .

In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm2. [CBSE 2015]

Given A=[31−21] and B=[4−32−1] Find sum of all elements in the matrix A+B-2l.1

The express sin A in terms of cot A is:

If in a rectangle, the length is increased and breadth reduced each by 2 units, the area is reduced by 28 square units. If, however the length is reduced by 1 unit and the breadth increased by 2 units, the area increases by 33 square units. Find the area of the rectangle.

Using factor theorem, show that g(x) is a factor of p(x), whenp(x) = 2x4 + 9x3 + 6x2 – 11x – 6, g(x) = x – 1

Prove the following trigonometric identities.1sec A+tan A-1cos A=1cos A-1sec A-tan A

An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

In triangles BMP and CNR it is given that PB = 5 cm, MP = 6 cm, BM = 9 cm and NR = 9 cm. If ΔBMP∼ΔCNR then find the perimeter of ΔCNR.

The region bounded by a chord and an arc is called a ___

Product of two numbers is 27.HCF of that numbers is 3 what is LCM

Let f(x) be a non-constant, thrice differentiable function defined on R such that f(x)=f(6−x) and f′(0)=0=f′(2)=f′(5). If n is the minimum number of roots of (f′(x))2+f′(x)⋅f′′′(x)=0 in the interval [0,6], then the value of n2 is

Identify the Theorem:Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

Two circles of radii 4 cm and 2.5 cm have their centres 5.5 cm apart. Draw direct common tangents to the circles.

Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.

Question 11 (i)State whether the following are true or false. Justify your answer.(i) The value of tan A is always less than 1.

If sinA=817, find the value of secA cosA + cosecA cosA.

Question 7 (i) In which of the following situations, do the lists of numbers involved form an AP? Give reasons for your answers. The fee charged from a student every month by a school for the whole session, when the monthly fee is Rs. 400.

Question 4Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at point D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, find the lengths of AD, BE and CF [CBSE 2013]

What is the arithmetic mean of the numbers a and b?

If ∆ABC and ∆DEF are similar such that 2AB = DE and BC = 8 cm, then EF =(a) 16 cm(b) 12 cm(c) 8 cm(d) 4 cm

Question 5ABC is an isosceles triangle with AC = BC. If AB2=2AC2, prove that ABC is a right triangle.

The distributions X and Y with total number of observations 36 and 64,and mean 4 and 3 respectively are combined.What is the mean of the resulting distribution X+Y?

triangle ABC, if D is a point on AC such that AB=AD and AC>AB. Prove that BC>CD

Find the mean of the following frequency distribution using step-deviation method: Class 84−90 90−96 96−102 102−108 108−114 114−120 Frequency 15 22 20 18 20 25

A bag contains three green marbles, four blue marbles and two orange marbles. If a marble is picked at random, then the probability that it is not an orange marble is__.

The sum of the first n terms of an A.P. is 3n2−4n. Find the nth term of this A.P.

A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5 m, its height is 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.

A and B are square matrices of the same order 3, such that AB = 2I and |A| = 2, write the value of |B|.

Find the largest number which divides 615 and 963 leaving remainder 6 in each case.

Question 2 (iii) Verify that each of the following is an AP and then write its next three terms. √3, 2√3, 3√3,⋯

How to take out median?

x−12x+1+2x+1x−1=2 find x

What is the sum of 3 digit numbers divisible by 3 and 7?

The angle of elevation of a jet fighter from a point A on the ground is 60∘. After a flight of 15 seconds, the angle of elevation changes to 30∘. If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying. [Use √3=1.732] [4 MARKS]

Secant intersects the circle at ___ distinct points.

15. If mean and variance of a binomial distribution are 4 and 2 then P(Ix-4I

Find the next number in the following sequence: 4.00, 2.00, 1.00, 0.50...

Question 1 (iii)Which of the following form an AP? Justify your answer.1, 1, 2, 2, 3, 3, ….

In ∆ PQR PQ> PR and PS is angle bisector of angle P then:(1) PS=PR(2) PSPS(4) PQ

Zero of the polynomial p(x)=ax+d is __________ .

If alpha and beta are the zeroes of the quadratic polynomial f(x)=2x2-5x+7 , find a polynomial whose zeroes are 2 alpha +3 beta and 3 alpha+2 beta.

If the angle of elevation of a tower from a distance of 100 metres from its foot is 60°, then the height of the tower is(a) 1003 m(b) 1003 m(c) 50 3(d) 2003 m

A square is inscribed in another square such that each vertex of inscribed square divides a side of the outside square into intervals of length x and y where x > y. If the area of the inscribed square is 4/5 th of the area of the outside square, find the ratio x/y.

The circumference of a circle is 8 cm. Find the approximate area of the sector whose central angle is 72∘.

From a solid right circular cylinder of height h and base radius r, a conical cavity of the same height and base is scooped out. Then the ratio of the volume of the cone and the remaining solid is __________.

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is(a) 12π cm3(b) 15π cm3(c) 16π cm3(d) 20π cm3