32581 + Interview Questions in Mathematics Page 259 InterviewSolution

12901.

Find the mean, mode and median of the following data: [CBSE 2008] Class 0−20 20−40 40−60 60−80 80−100 100−120 120−140 Frequency 6 8 10 12 6 5 3

Answer»

Find the mean, mode and median of the following data: [CBSE 2008]

Class	0−20	20−40	40−60	60−80	80−100	100−120	120−140
Frequency	6	8	10	12	6	5	3

Discussion

12902.	Prove that equal chords subtend equal angles at the centre of the circle.
Answer» Prove that equal chords subtend equal angles at the centre of the circle.

Discussion

12903.	Prove that tan2 A sec2B - sec2 A tan2 B = tan2 A - tan2 B
Answer» Prove that tan² A sec²B - sec² A tan² B = tan² A - tan² B

12903.

Prove that tan2 A sec2B - sec2 A tan2 B = tan2 A - tan2 B

Answer»

Prove that

tan² A sec²B - sec² A tan² B = tan² A - tan² B

Discussion

12904.	A copper wire of diameter 6 mm is evenly wrapped on a cylinder oflength 18 cm and diameter 49 cm to cover its whole surface. Find thelength and the volume of the wire. If the density of copper be 8.8 g percu-cm, find the weight of the wire.\lbrack HOTS\rbrack
Answer» A copper wire of diameter 6 mm is evenly wrapped on a cylinder oflength 18 cm and diameter 49 cm to cover its whole surface. Find thelength and the volume of the wire. If the density of copper be 8.8 g percu-cm, find the weight of the wire.\lbrack HOTS\rbrack

Discussion

12905.	if height of a cone is 10 cm. the cone is divided into two parts using a plane parallel to the base
Answer» if height of a cone is 10 cm. the cone is divided into two parts using a plane parallel to the base

Discussion

12906.	In the given figure, PT is a tangent of a circle, with centre O, at point R. If diameter SQ is produced, it meets with PT at point P with ∠SPR=x and ∠QSR=y,then find the value of x+2y (in degrees).
Answer» $In the given figure, PT is a tangent of a circle, with centre O, at point R. If diameter SQ is produced, it meets with PT at point P with ∠ S P R = x and ∠ Q S R = y, then find the value of x + 2 y (in degrees) .$

Discussion

12907.	A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60∘ and the angle of depression of the base of hill as 30∘. Find the distance of the hill from the ship and the height of the hill
Answer» A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as $60^{\circ}$ and the angle of depression of the base of hill as $30^{\circ}$ . Find the distance of the hill from the ship and the height of the hill

Discussion

12908.	In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.
Answer» In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

12908.

In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

Answer»

In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

Discussion

12909.	Find ‘x’ in the Pythagorean triplet – {24, 25, x}. ‘x’ is a natural number. Ans.___
Answer» Find ‘x’ in the Pythagorean triplet – {24, 25, x}. ‘x’ is a natural number. Ans.___

Discussion

12910.	A, B and C shared profits and losses in the ratio of 3 : 2 : 1 respectively. With effect from 1st April, 2019, they agreed to share profits equally. The goodwill of the firm was valued at ₹ 18,000. Pass necessary Journal entries when: (a) Goodwill is adjusted through Partners' Capital Accounts; and (b) Goodwill is raised and written off.
Answer» A, B and C shared profits and losses in the ratio of 3 : 2 : 1 respectively. With effect from 1st April, 2019, they agreed to share profits equally. The goodwill of the firm was valued at ₹ 18,000. Pass necessary Journal entries when: (a) Goodwill is adjusted through Partners' Capital Accounts; and (b) Goodwill is raised and written off.

Discussion

12911.	Prove the following trigonometric identities.sin2 A cot2 A + cos2 A tan2 A = 1
Answer» Prove the following trigonometric identities. sin² A cot² A + cos² A tan² A = 1

Discussion

12912.	Write the family of quadratic polynomials having -14 and 1 as its zeros.
Answer» Write the family of quadratic polynomials having $- \frac{1}{4}$ and 1 as its zeros.

Discussion

12913.	6. P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.
Answer» 6. P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.

Discussion

12914.	The are small metal pieces each 1 cm long. ‘L’ number of metal pieces are put together to form a long thin rod. What is the length of the rod in cm?
Answer» The are small metal pieces each 1 cm long. ‘L’ number of metal pieces are put together to form a long thin rod. What is the length of the rod in cm?

Discussion

12915.	12 Derive the formula of arithmetic progression.
Answer» 12 Derive the formula of arithmetic progression.

Discussion

12916.	A number is selected at random from the numbers from 1 to 30. Find the probability that the selected number is either even or odd.
Answer» A number is selected at random from the numbers from 1 to 30. Find the probability that the selected number is either even or odd.

Discussion

12917.	Water is falling in a cylidrical tank from an inlet pipe at the rate of 10 litres/minute. if the diameter aand height of the tank are 1m and 7m respectively.find the time required to fill the tank .
Answer» Water is falling in a cylidrical tank from an inlet pipe at the rate of 10 litres/minute. if the diameter aand height of the tank are 1m and 7m respectively.find the time required to fill the tank .

Discussion

12918.	What is a harmonic progression and how is it helpful?
Answer» What is a harmonic progression and how is it helpful?

Discussion

12919.	In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system.[Assume π=227]
Answer» In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system. $[A s s u m e π = \frac{22}{7}]$

Discussion

12920.	In ΔABC, D is the midpoint of BC and ED is the bisector of ∠ADB. If EF \|\| BC meeting AC at F. The measure of ∠EDF is:
Answer» In $Δ A B C$ , D is the midpoint of BC and ED is the bisector of $∠ A D B$ . If EF \|\| BC meeting AC at F. The measure of $∠ E D F$ is:

Discussion

12921.	Mark the correct alternative in the following question:lf 2a = 3b = 4c, then a : b : c =(a) 2 : 3 : 4 (b) 3 : 4 : 6 (c) 4 : 3 : 2 (d) 6 : 4 : 3
Answer» Mark the correct alternative in the following question: lf 2a = 3b = 4c, then a : b : c = (a) 2 : 3 : 4 (b) 3 : 4 : 6 (c) 4 : 3 : 2 (d) 6 : 4 : 3

Discussion

12922.	Two circles of radii 13 cm and 5 cm touch each other internally. Find the distance between their centers.
Answer» Two circles of radii $13 c m$ and $5 c m$ touch each other internally. Find the distance between their centers.

Discussion

12923.	x^2-3a/2x-a^2 =0 solve by factorization method
Answer» x^2-3a/2x-a^2 =0 solve by factorization method

Discussion

12924.	In an equilateral ΔABC,E is any point on BC such that BE=14BC. Prove that 16AE2=13AB2.
Answer» In an equilateral $Δ A B C, E$ is any point on BC such that $B E = \frac{1}{4} B C .$ Prove that $16 A E^{2} = 13 A B^{2} .$

Discussion

12925.	A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .
Answer» A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .

Discussion

12926.	A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Answer» A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Discussion

12927.	why h20 has 8 netrons??
Answer» why h20 has 8 netrons??

Discussion

12928.	If fz=7-z1-z2, where z=1+2i, then fz is(a) z2(b) z(c) 2z(d) none of these
Answer» If $f (z) = \frac{7 - z}{1 - z^{2}}$ , where $z = 1 + 2 i$ , then $\|f (z)\|$ is (a) $\frac{\|z\|}{2}$ (b) $\|z\|$ (c) $2 \|z\|$ (d) none of these

Discussion

12929.	Question 111 (ii)What will happen to the volume of the cube, if its edge is reduced to one-fourth?
Answer» Question 111 (ii) What will happen to the volume of the cube, if its edge is reduced to one-fourth?

12929.

Question 111 (ii)What will happen to the volume of the cube, if its edge is reduced to one-fourth?

Answer»

Question 111 (ii)

What will happen to the volume of the cube, if its edge is reduced to one-fourth?

Discussion

12930.	Determine, if 3 is a root of the equation given below: √x2−4x+3+√x2−9=√4x2−14x+16
Answer» Determine, if 3 is a root of the equation given below: $\sqrt{x^{2} - 4 x + 3} + \sqrt{x^{2} - 9} = \sqrt{4 x^{2} - 14 x + 16}$

Discussion

12931.	If α+β=24 and α−β=8. Find the polynomial having alpha and beta as its zeroes. Also verify the relationship between the zeroes and the coefficients of the polynomial
Answer» If $α + β = 24$ and $α - β = 8$ . Find the polynomial having alpha and beta as its zeroes. Also verify the relationship between the zeroes and the coefficients of the polynomial

Discussion

12932.	By increasing the speed of a car by 10km/hr , the time of journey for a distance of 72km is reduced by 36 minutes . Find the original speed of car .
Answer» By increasing the speed of a car by 10km/hr , the time of journey for a distance of 72km is reduced by 36 minutes . Find the original speed of car .

Discussion

12933.	If ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQRrespectively. The ratio of areas of ΔABC and ΔPQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___
Answer» If $Δ A B C$ and $Δ P Q R$ are two similar triangles shown in the figure. AM and PN are the medians on $Δ A B C$ and $Δ P Q R$ respectively. The ratio of areas of $Δ A B C$ and $Δ P Q R$ is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

Discussion

12934.	In ∆ABC, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.
Answer» In ∆ABC, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Discussion

12935.

Calculate missing frequency, if mean of the distribution is 28. C.I 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 12 ? 27 20 17 6

Answer» Calculate missing frequency, if mean of the distribution is 28.

C.I	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	12	?	27	20	17	6

Discussion

12936.	Question 19In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD+∠BED.
Answer» Question 19 In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of $∠ A C D + ∠ B E D$ .

Discussion

12937.	Solve for x : 2x+1+32(x−2)=235x
Answer» Solve for x : $\frac{2}{x + 1} + \frac{3}{2 (x - 2)} = \frac{23}{5 x}$

Discussion

12938.	If the angle of elevation of a cloud from a point 100 metres above a lake is 30o and the angle of depression of its reflection in the lake is 60o, then the height of the cloud above the lake is
Answer» If the angle of elevation of a cloud from a point 100 metres above a lake is 30^o and the angle of depression of its reflection in the lake is 60^o, then the height of the cloud above the lake is

Discussion

12939.	Mr Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20%. Calculate : (i) the number of shares bought by Mr Tiwari (ii) Mr Tiwari's income from the investment (iii) the percentage return on his investment [3 MARKS]
Answer» Mr Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20%. Calculate : (i) the number of shares bought by Mr Tiwari (ii) Mr Tiwari's income from the investment (iii) the percentage return on his investment [3 MARKS]

Discussion

12940.	A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years on simple interest. What is the rate of interest on the sum?
Answer» A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years on simple interest. What is the rate of interest on the sum?

Discussion

12941.	What is the probability of getting a black ace or a red jack when drawing a card from a deck of 52?
Answer» What is the probability of getting a black ace or a red jack when drawing a card from a deck of 52?

Discussion

12942.	Why 100 has only one significant figure while 20 have infinite number of significant figure ?
Answer» Why 100 has only one significant figure while 20 have infinite number of significant figure ?

Discussion

12943.	If cos3θ=√32; 0<θ<200, then value of θ is:
Answer» If $cos 3 θ = \frac{\sqrt{3}}{2}$ ; $0 < θ < 200$ , then value of $θ$ is:

Discussion

12944.	A rectangular sheet of size 22 cm × 10 cm is folded along its length to form a cylinder. Find the volume of the cylinder formed in cm3.
Answer» A rectangular sheet of size 22 cm × 10 cm is folded along its length to form a cylinder. Find the volume of the cylinder formed in ${c m}^{3}$ .

Discussion

12945.	The area of a rectangular plot is 528m. The length of the plot is 1m more than twice its breadth. Find length and breadth.
Answer» The area of a rectangular plot is 528m. The length of the plot is 1m more than twice its breadth. Find length and breadth.

Discussion

12946.	Solve the following quadratic equations by factorization:48x2 − 13x − 1 = 0
Answer» Solve the following quadratic equations by factorization: 48x² − 13x − 1 = 0

Discussion

12947.	The age wise participation of students in the Annual Function of a school is shown in the following distribution.Age (in years)5−77−99−1111−1313−1515−1717−19Number ofstudentsx1518305048xFind the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.
Answer» The age wise participation of students in the Annual Function of a school is shown in the following distribution. $\begin{matrix} Age (in years) & 5 - 7 & 7 - 9 & 9 - 11 & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 Number of students & x & 15 & 18 & 30 & 50 & 48 & x \end{matrix}$ Find the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.

12947.

The age wise participation of students in the Annual Function of a school is shown in the following distribution.Age (in years)5−77−99−1111−1313−1515−1717−19Number ofstudentsx1518305048xFind the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.

Answer»

The age wise participation of students in the Annual Function of a school is shown in the following distribution.
$\begin{matrix} Age (in years) & 5 - 7 & 7 - 9 & 9 - 11 & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 Number of students & x & 15 & 18 & 30 & 50 & 48 & x \end{matrix}$

Find the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.

Discussion

12948.	In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:(i) the height of the tunnel(ii) the perimeter of the cross-section(iii) the area of the cross-section.figure
Answer» In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate: (i) the height of the tunnel (ii) the perimeter of the cross-section (iii) the area of the cross-section. figure

Discussion

12949.	ntFind out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee.n nta. 0.78% b. 12.5% c. 25% d.50%n
Answer» ntFind out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee.n nta. 0.78% b. 12.5% c. 25% d.50%n

Discussion

12950.

A man can swim at a speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. He keeps himself always at an angle of 120^° with the river flow while swimming. (a) Find the time he takes to cross the river. (b) At what point on the opposite bank will he arrive?

Answer»

A man can swim at a speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. He keeps himself always at an angle of 120^° with the river flow while swimming.

(a) Find the time he takes to cross the river.

(b) At what point on the opposite bank will he arrive?

Discussion

Explore topic-wise InterviewSolutions in .

Find the mean, mode and median of the following data: [CBSE 2008] Class 0−20 20−40 40−60 60−80 80−100 100−120 120−140 Frequency 6 8 10 12 6 5 3

Prove that equal chords subtend equal angles at the centre of the circle.

Prove that tan2 A sec2B - sec2 A tan2 B = tan2 A - tan2 B

A copper wire of diameter 6 mm is evenly wrapped on a cylinder oflength 18 cm and diameter 49 cm to cover its whole surface. Find thelength and the volume of the wire. If the density of copper be 8.8 g percu-cm, find the weight of the wire.\lbrack HOTS\rbrack

if height of a cone is 10 cm. the cone is divided into two parts using a plane parallel to the base

In the given figure, PT is a tangent of a circle, with centre O, at point R. If diameter SQ is produced, it meets with PT at point P with ∠SPR=x and ∠QSR=y,then find the value of x+2y (in degrees).

A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60∘ and the angle of depression of the base of hill as 30∘. Find the distance of the hill from the ship and the height of the hill

In the figure PQ and PR are tangents to the circle with centre ‘O’. If , shown that PQOR is a square.

Find ‘x’ in the Pythagorean triplet – {24, 25, x}. ‘x’ is a natural number. Ans.___

Prove the following trigonometric identities.sin2 A cot2 A + cos2 A tan2 A = 1

Write the family of quadratic polynomials having -14 and 1 as its zeros.

6. P is a point inside an equilateral triangle ABC of side 2014 units.Then find the sum of lengths of the perpendicular drawn from P to the sides.

The are small metal pieces each 1 cm long. ‘L’ number of metal pieces are put together to form a long thin rod. What is the length of the rod in cm?

12 Derive the formula of arithmetic progression.

A number is selected at random from the numbers from 1 to 30. Find the probability that the selected number is either even or odd.

Water is falling in a cylidrical tank from an inlet pipe at the rate of 10 litres/minute. if the diameter aand height of the tank are 1m and 7m respectively.find the time required to fill the tank .

What is a harmonic progression and how is it helpful?

In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface of the system.[Assume π=227]

In ΔABC, D is the midpoint of BC and ED is the bisector of ∠ADB. If EF || BC meeting AC at F. The measure of ∠EDF is:

Mark the correct alternative in the following question:lf 2a = 3b = 4c, then a : b : c =(a) 2 : 3 : 4 (b) 3 : 4 : 6 (c) 4 : 3 : 2 (d) 6 : 4 : 3

Two circles of radii 13 cm and 5 cm touch each other internally. Find the distance between their centers.

x^2-3a/2x-a^2 =0 solve by factorization method

In an equilateral ΔABC,E is any point on BC such that BE=14BC. Prove that 16AE2=13AB2.

A cylinder has a radius of 7 cm and height of 25 mm. If ten such cylinders are stacked up, then the total volume will be .

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

why h20 has 8 netrons??

If fz=7-z1-z2, where z=1+2i, then fz is(a) z2(b) z(c) 2z(d) none of these

Question 111 (ii)What will happen to the volume of the cube, if its edge is reduced to one-fourth?

Determine, if 3 is a root of the equation given below: √x2−4x+3+√x2−9=√4x2−14x+16

If α+β=24 and α−β=8. Find the polynomial having alpha and beta as its zeroes. Also verify the relationship between the zeroes and the coefficients of the polynomial

By increasing the speed of a car by 10km/hr , the time of journey for a distance of 72km is reduced by 36 minutes . Find the original speed of car .

If ΔABC and ΔPQR are two similar triangles shown in the figure. AM and PN are the medians on ΔABC and ΔPQRrespectively. The ratio of areas of ΔABC and ΔPQR is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

In ∆ABC, the bisector of ∠A intersects BC in D. If AB = 18 cm, AC = 15 cm and BC = 22 cm, find BD.

Calculate missing frequency, if mean of the distribution is 28. C.I 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 12 ? 27 20 17 6

Question 19In the figure, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD+∠BED.

Solve for x : 2x+1+32(x−2)=235x

If the angle of elevation of a cloud from a point 100 metres above a lake is 30o and the angle of depression of its reflection in the lake is 60o, then the height of the cloud above the lake is

Mr Tiwari invested Rs 29,040 in 15% Rs 100 shares quoted at a premium of 20%. Calculate : (i) the number of shares bought by Mr Tiwari (ii) Mr Tiwari's income from the investment (iii) the percentage return on his investment [3 MARKS]

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years on simple interest. What is the rate of interest on the sum?

What is the probability of getting a black ace or a red jack when drawing a card from a deck of 52?

Why 100 has only one significant figure while 20 have infinite number of significant figure ?

If cos3θ=√32; 0&lt;θ&lt;200, then value of θ is:

A rectangular sheet of size 22 cm × 10 cm is folded along its length to form a cylinder. Find the volume of the cylinder formed in cm3.

The area of a rectangular plot is 528m. The length of the plot is 1m more than twice its breadth. Find length and breadth.

Solve the following quadratic equations by factorization:48x2 − 13x − 1 = 0

The age wise participation of students in the Annual Function of a school is shown in the following distribution.Age (in years)5−77−99−1111−1313−1515−1717−19Number ofstudentsx1518305048xFind the missing frequencies when the sum of frequencies is 181. Also, find the mode of the data.

In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:(i) the height of the tunnel(ii) the perimeter of the cross-section(iii) the area of the cross-section.figure

ntFind out the frequency of AabbCcDdee if parents are AabbCCddEe and AabbccDdee.n nta. 0.78% b. 12.5% c. 25% d.50%n

A man can swim at a speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. He keeps himself always at an angle of 120^° with the river flow while swimming. (a) Find the time he takes to cross the river. (b) At what point on the opposite bank will he arrive?

If cos3θ=√32; 0<θ<200, then value of θ is: