32581 + Interview Questions in Mathematics Page 180 InterviewSolution

8951.	The standard deviation of first 10 natural numbers is(a) 5.5 (b) 3.87 (c) 2.97 (d) 2.87
Answer» The standard deviation of first 10 natural numbers is (a) 5.5 (b) 3.87 (c) 2.97 (d) 2.87

Discussion

8952.	23 spoons and 17 forks together cost ₹1,770, while 17 spoons and 23 forks togethercost ₹1,830. Find the cost of a spoon and that of a fork.
Answer» 23 spoons and 17 forks together cost ₹1,770, while 17 spoons and 23 forks together cost ₹1,830. Find the cost of a spoon and that of a fork.

Discussion

8953.	A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2 . (Note that the base of the tent will not be covered with canvas).
Answer» A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per $m^{2}$ . (Note that the base of the tent will not be covered with canvas).

Discussion

8954.	Question 4 (xiv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiv) 12,32,52,72……
Answer» Question 4 (xiv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiv) $1^{2}, 3^{2}, 5^{2}, 7^{2} \dots \dots$

Discussion

8955.	The pair of equations given by: y = 0 and y = -7, have ________.
Answer» The pair of equations given by: y = 0 and y = -7, have ________.

Discussion

8956.	Assertion (A) in the given figure, O is the centre of the circle with D, E and F as mid-points of AB, BO and OA respectively. If ∠DEF is 30∘, then ∠ACB is 60∘Reason (R) Angle subtended by an arc at the centre is twice the angle subtended by it on the remaining part of the circle.which of the following is true?
Answer» Assertion (A) in the given figure, O is the centre of the circle with D, E and F as mid-points of AB, BO and OA respectively. If $∠ D E F$ is $30^{\circ}$ , then $∠ A C B$ is $60^{\circ}$ Reason (R) Angle subtended by an arc at the centre is twice the angle subtended by it on the remaining part of the circle. which of the following is true?

Discussion

8957.	A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.
Answer» A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Discussion

8958.	The length of subnormal of the curve y=x^3+x^2+x+1 at (1,4)
Answer» The length of subnormal of the curve y=x^3+x^2+x+1 at (1,4)

Discussion

8959.	In △ABC, sides opposite to angles A,B,C are denoted by a,b,c respectively. If ∠A=60∘,a=5,b=2√3, then ∠B=
Answer» In $△ A B C,$ sides opposite to angles $A, B, C$ are denoted by $a, b, c$ respectively. If $∠ A = 60^{\circ}, a = 5, b = 2 \sqrt{3},$ then $∠ B =$

Discussion

8960.	A motor boat whose speed is 20 km/h is still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the steam. OR Find the roots of the equation 1x+4−1x−7=1130,x≠−4,7
Answer» A motor boat whose speed is 20 km/h is still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the steam. OR Find the roots of the equation $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

8960.

A motor boat whose speed is 20 km/h is still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the steam. OR Find the roots of the equation 1x+4−1x−7=1130,x≠−4,7

Answer»

A motor boat whose speed is 20 km/h is still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the steam.

OR

Find the roots of the equation $\frac{1}{x + 4} - \frac{1}{x - 7} = \frac{11}{30}, x \neq - 4, 7$

Discussion

8961.	Match the following commodities with their standard GST% as per the indian GST tax rates.
Answer» Match the following commodities with their standard GST% as per the indian GST tax rates.

Discussion

8962.	Q26. Some toffees were bought at 6 toffees for Rs. 5 and sold at 5 toffees for Rs. 6. Gain percent is: 5 रू. की 6 टॉफी की दर से कुछ टॉफियाँ खरीदी गई और 6 रू. की 5 टॉफी की दर से बेची गई। लाभ % होगा?
Answer» Q26. Some toffees were bought at 6 toffees for Rs. 5 and sold at 5 toffees for Rs. 6. Gain percent is: 5 रू. की 6 टॉफी की दर से कुछ टॉफियाँ खरीदी गई और 6 रू. की 5 टॉफी की दर से बेची गई। लाभ % होगा?

8962.

Q26. Some toffees were bought at 6 toffees for Rs. 5 and sold at 5 toffees for Rs. 6. Gain percent is: 5 रू. की 6 टॉफी की दर से कुछ टॉफियाँ खरीदी गई और 6 रू. की 5 टॉफी की दर से बेची गई। लाभ % होगा?

Answer»

Q26. Some toffees were bought at 6 toffees for Rs. 5 and sold at 5 toffees for Rs. 6. Gain percent is:

5 रू. की 6 टॉफी की दर से कुछ टॉफियाँ खरीदी गई और 6 रू. की 5 टॉफी की दर से बेची गई। लाभ % होगा?

Discussion

8963.	Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the following ratios.(1) Ratio of Shubham’s age today to his mother’s age today.(2) Ratio of Shubham’s mother’s age today to his father’s age today(3) The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.
Answer» Shubham’s age today is 12 years and his father’s is 42 years. Shubham’s mother is younger than his father by 6 years. Find the following ratios. (1) Ratio of Shubham’s age today to his mother’s age today. (2) Ratio of Shubham’s mother’s age today to his father’s age today (3) The ratio of Shubham’s age to his mother’s age when Shubham was 10 years old.

Discussion

8964.	Question 8In figure, if PA and PB are tangents to the circle with centre O such that ∠APB=50∘, then ∠ OAB is equal to(A) 25°(B) 30°(C) 40°(D) 50°
Answer» Question 8 In figure, if PA and PB are tangents to the circle with centre O such that $∠ A P B = 50^{\circ}$ , then $∠$ OAB is equal to (A) 25° (B) 30° (C) 40° (D) 50°

Discussion

8965.	The volume of the sphere is 90517 cm3. find its radius.
Answer» The volume of the sphere is $905 \frac{1}{7} c m^{3}$ . find its radius.

Discussion

8966.	Renu sold an article at a loss of 8%. Had she bought it at 10% less and sold for ₹36 more; she would have gained 20%. Find the cost price of the article.
Answer» Renu sold an article at a loss of 8%. Had she bought it at 10% less and sold for ₹36 more; she would have gained 20%. Find the cost price of the article.

Discussion

8967.	In the given figure, O is the centre of a circle and PQ is a diameter. If ∠ROS = 40°, find ∠RTS.
Answer» In the given figure, O is the centre of a circle and PQ is a diameter. If ∠ROS = 40°, find ∠RTS.

Discussion

8968.	The circumcentre of the triangle having vertices as A(0,0), B(0,3) and C(4,0) is
Answer» The circumcentre of the triangle having vertices as A(0,0), B(0,3) and C(4,0) is

Discussion

8969.	The angle of elevation of the top of a tower 60∘. If the height of the tower is 60m then find the distance between the person and tower.
Answer» The angle of elevation of the top of a tower 60 $^{\circ}$ . If the height of the tower is 60m then find the distance between the person and tower.

Discussion

8970.

Find the mean of each of the following frequency distributions : Classes: 25−29 30−34 35−39 40−44 45−49 50−54 55−59 Frequency: 14 22 16 6 5 3 4

Answer» Find the mean of each of the following frequency distributions :

Classes:	25−29	30−34	35−39	40−44	45−49	50−54	55−59
Frequency:	14	22	16	6	5	3	4

Discussion

8971.	Name the different flavours of ice cream the Ice-cream Man has in his cart.
Answer» Name the different flavours of ice cream the Ice-cream Man has in his cart.

Discussion

8972.	The value of θ in √3 tan 2θ – 3 = 0 is
Answer» The value of θ in √3 tan 2θ – 3 = 0 is

Discussion

8973.	Question 6Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.
Answer» Question 6 Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Discussion

8974.	Draw the figure below according to the given specifications:
Answer» Draw the figure below according to the given specifications:

8974.

Draw the figure below according to the given specifications:

Answer»

Draw the figure below according to the given specifications:

Discussion

8975.	If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?
Answer» If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?

Discussion

8976.	The area of an equilateral ΔABC is 17320.5 cm2. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in cm2) . (π = 3.14 , √3 =1.73205) ___
Answer» The area of an equilateral $Δ$ ABC is 17320.5 $c m^{2}$ . A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in $c m^{2}$ ) . ( $π$ = 3.14 , $\sqrt{3}$ =1.73205) ___

8976.

The area of an equilateral ΔABC is 17320.5 cm2. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in cm2) . (π = 3.14 , √3 =1.73205) ___

Answer»

The area of an equilateral $Δ$ ABC is 17320.5 $c m^{2}$ . A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in $c m^{2}$ ) . ( $π$ = 3.14 , $\sqrt{3}$ =1.73205)

___

Discussion

8977.	Find the HCF of 180,252 and 324by Euclid's division algorithm.
Answer» Find the HCF of 180,252 and 324by Euclid's division algorithm.

Discussion

8978.	Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.
Answer» Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.

8978.

Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.

Answer»

Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.

Discussion

8979.	The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.
Answer» The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

Discussion

8980.	What is the factorization of x2−16x15−1?
Answer» What is the factorization of $x^{2} - \frac{16 x}{15} - 1$ ?

Discussion

8981.	The equation, x3−8x2+37x−50=0 is factored and it has (3+4i) as one of tis roots. What is the real root of this equation?
Answer» The equation, $x^{3} - 8 x^{2} + 37 x - 50 = 0$ is factored and it has ( $3 + 4 i)$ as one of tis roots. What is the real root of this equation?

Discussion

8982.

The following data is gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes (in hours) 0−20 20−40 40−60 60−80 80−100 100−120 No. of components 10 35 52 61 38 29 Determine the modal lifetimes of the components.

Answer» The following data is gives the information on the observed lifetimes (in hours) of 225 electrical components:

Lifetimes (in hours)	0−20	20−40	40−60	60−80	80−100	100−120
No. of components	10	35	52	61	38	29

Determine the modal lifetimes of the components.

Discussion

8983.	A particle is projected at an angle 30^° withthe horizontal with speed 20 m/s. How high will itstrike a wall 83 m away from point of projection?(g 10 m/s?)(1) 5 m(3) 2.4 m4.8 m(4) 9.6 m
Answer» A particle is projected at an angle 30^° withthe horizontal with speed 20 m/s. How high will itstrike a wall 83 m away from point of projection?(g 10 m/s?)(1) 5 m(3) 2.4 m4.8 m(4) 9.6 m

Discussion

8984.	The data which has maximum probability of being sampled is called
Answer» The data which has maximum probability of being sampled is called

Discussion

8985.	The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,it can go 40 km upstream and 55km downstream.Determine the speed of stream and that of the boat in still water.
Answer» The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,it can go 40 km upstream and 55km downstream.Determine the speed of stream and that of the boat in still water.

Discussion

8986.	ΔABC∼ΔPQR, ∠B = 50° and ∠C = 70° . Then ∠P is equal to:
Answer» $Δ A B C \sim Δ P Q R$ , ∠B = 50° and ∠C = 70° . Then ∠P is equal to:

Discussion

8987.	A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [CBSE 2017]
Answer» A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [CBSE 2017]

Discussion

8988.	If AB and CD are common tangents to two circles of unequal radii, then _________.
Answer» If AB and CD are common tangents to two circles of unequal radii, then _________.

Discussion

8989.	If the end points A and B of the diameter of a circle are such that their abscissas are the roots of the equation x² + 2ax-16=0 and their ordinates are the roots of x2 + 24x-9=0, If a €N and radius 'R' of the circle, with AB as diameter is an integer then, R-a =How to think this
Answer» If the end points A and B of the diameter of a circle are such that their abscissas are the roots of the equation x² + 2ax-16=0 and their ordinates are the roots of x2 + 24x-9=0, If a €N and radius 'R' of the circle, with AB as diameter is an integer then, R-a = How to think this

Discussion

8990.	how to find GCD of polynomials using division algorithm
Answer» how to find GCD of polynomials using division algorithm

Discussion

8991.	The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.
Answer» The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

Discussion

8992.	If 35 is the upper limit of a class interval of class size 10, then the lower limit of the class interval is _____
Answer» If 35 is the upper limit of a class interval of class size 10, then the lower limit of the class interval is _____

Discussion

8993.	A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?
Answer» A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?

Discussion

8994.	The sum of the 3 numbers is 24 and difference between the extremes is 6. Find the numbers {hint= consider number as a-d, a, a+d
Answer» The sum of the 3 numbers is 24 and difference between the extremes is 6. Find the numbers {hint= consider number as a-d, a, a+d

8994.

The sum of the 3 numbers is 24 and difference between the extremes is 6. Find the numbers {hint= consider number as a-d, a, a+d

Answer»

The sum of the 3 numbers is 24 and difference between the extremes is 6. Find the numbers

{hint= consider number as a-d, a, a+d

Discussion

8995.	What is the value of cos2 67° – sin2 23°?
Answer» What is the value of cos² 67° – sin² 23°?

Discussion

8996.	An object is thrown at an angle of A with horizontal , if elevation angle of the object at its highest point as seen from the point of projection is tan inverse of 1/2 (half). So angle A is 1) 30^° 2) 45^° 3) 60^° 4) 37^°
Answer» An object is thrown at an angle of A with horizontal , if elevation angle of the object at its highest point as seen from the point of projection is tan inverse of 1/2 (half). So angle A is 1) 30^° 2) 45^° 3) 60^° 4) 37^°

Discussion

8997.	What ratio does the centroid divide each median into?
Answer» What ratio does the centroid divide each median into?

Discussion

8998.	Find the equation of line joining the points (1,−3) and (4,−2)
Answer» Find the equation of line joining the points $(1, - 3)$ and $(4, - 2)$

Discussion

8999.	2π∫0dx1+tan4x is equal to
Answer» $2 π \int 0 \frac{d x}{1 + {tan}^{4} x}$ is equal to

Discussion

9000.	32. x+1/x=5 then x+1/x =?
Answer» 32. x+1/x=5 then x+1/x =?

Discussion

Explore topic-wise InterviewSolutions in .

The standard deviation of first 10 natural numbers is(a) 5.5 (b) 3.87 (c) 2.97 (d) 2.87

23 spoons and 17 forks together cost ₹1,770, while 17 spoons and 23 forks togethercost ₹1,830. Find the cost of a spoon and that of a fork.

Question 4 (xiv) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiv) 12,32,52,72……

The pair of equations given by: y = 0 and y = -7, have ________.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

The length of subnormal of the curve y=x^3+x^2+x+1 at (1,4)

In △ABC, sides opposite to angles A,B,C are denoted by a,b,c respectively. If ∠A=60∘,a=5,b=2√3, then ∠B=

A motor boat whose speed is 20 km/h is still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the steam. OR Find the roots of the equation 1x+4−1x−7=1130,x≠−4,7

Match the following commodities with their standard GST% as per the indian GST tax rates.

Question 8In figure, if PA and PB are tangents to the circle with centre O such that ∠APB=50∘, then ∠ OAB is equal to(A) 25°(B) 30°(C) 40°(D) 50°

The volume of the sphere is 90517 cm3. find its radius.

Renu sold an article at a loss of 8%. Had she bought it at 10% less and sold for ₹36 more; she would have gained 20%. Find the cost price of the article.

In the given figure, O is the centre of a circle and PQ is a diameter. If ∠ROS = 40°, find ∠RTS.

The circumcentre of the triangle having vertices as A(0,0), B(0,3) and C(4,0) is

The angle of elevation of the top of a tower ​60∘. If the height of the tower is 60m then find the distance between the person and tower.

Find the mean of each of the following frequency distributions : Classes: 25−29 30−34 35−39 40−44 45−49 50−54 55−59 Frequency: 14 22 16 6 5 3 4

Name the different flavours of ice cream the Ice-cream Man has in his cart.

The value of θ in √3 tan 2θ – 3 = 0 is

Question 6Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis.

Draw the figure below according to the given specifications:

If a black bag contains 100 casino chips with values €5, €10, €15, €20, €50. There are ten chips of value €5. You have to withdraw one chip from the box. What is the probability that it has a value more than €5?

The area of an equilateral ΔABC is 17320.5 cm2. A circle is drawn taking the vertex of the triangle as centre. The radius of the circle is half the length of the side of triangle. Find the area of the shaded region (in cm2) . (π = 3.14 , √3 =1.73205) ___

Find the HCF of 180,252 and 324by Euclid's division algorithm.

Find the area of the shaded region in the given figure, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and ∠AOC = 40°.

The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father.

What is the factorization of x2−16x15−1?

The equation, x3−8x2+37x−50=0 is factored and it has (3+4i) as one of tis roots. What is the real root of this equation?

The following data is gives the information on the observed lifetimes (in hours) of 225 electrical components: Lifetimes (in hours) 0−20 20−40 40−60 60−80 80−100 100−120 No. of components 10 35 52 61 38 29 Determine the modal lifetimes of the components.

A particle is projected at an angle 30^° withthe horizontal with speed 20 m/s. How high will itstrike a wall 83 m away from point of projection?(g 10 m/s?)(1) 5 m(3) 2.4 m4.8 m(4) 9.6 m

The data which has maximum probability of being sampled is called

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours,it can go 40 km upstream and 55km downstream.Determine the speed of stream and that of the boat in still water.

ΔABC∼ΔPQR, ∠B = 50° and ∠C = 70° . Then ∠P is equal to:

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy. [CBSE 2017]

If AB and CD are common tangents to two circles of unequal radii, then _________.

If the end points A and B of the diameter of a circle are such that their abscissas are the roots of the equation x² + 2ax-16=0 and their ordinates are the roots of x2 + 24x-9=0, If a €N and radius 'R' of the circle, with AB as diameter is an integer then, R-a =How to think this

how to find GCD of polynomials using division algorithm

The angles of a triangle are in A.P. If the greatest angle is twice the least, find the greatest angle.

If 35 is the upper limit of a class interval of class size 10, then the lower limit of the class interval is _____

A hemisphere and a cone have equal bases. If their heights are also equal, then what is the ratio of their curved surfaces?

The sum of the 3 numbers is 24 and difference between the extremes is 6. Find the numbers {hint= consider number as a-d, a, a+d

What is the value of cos2 67° – sin2 23°?

An object is thrown at an angle of A with horizontal , if elevation angle of the object at its highest point as seen from the point of projection is tan inverse of 1/2 (half). So angle A is 1) 30^° 2) 45^° 3) 60^° 4) 37^°

What ratio does the centroid divide each median into?

Find the equation of line joining the points (1,−3) and (4,−2)

2π∫0dx1+tan4x is equal to

32. x+1/x=5 then x+1/x =?

The angle of elevation of the top of a tower 60∘. If the height of the tower is 60m then find the distance between the person and tower.