3694 + Interview Questions in Maths in Class 10 Page 35 InterviewSolution

1701.	Two buses start from opposite points on a man road, 120 km apart. The first bus X runs for 25 kms and takes a right turn and runs for another 15 kms. It then turns left and runs for another 25 kms and takes the direction back to reach the main road. In the mean time, due to minor breakdown, the other bus Y has run only 35 kms along the main road. What would be the distance between the two buses at his point ?
Answer» <P>35 kms 45 kms 50 kms 55 kms Solution :The rotate Bus X is `P rarr A rarr L rarrM rarr B` Clearly PB = 50 kms Bus Y TRAVELS along the route `Q rarr C`. The distance between the two bushes X and Y is BC = 120 - (50 + 35) = 35kms

Discussion

1702.	A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?
Answer» Answer :Isosceles trapeziumA' = (-1,-1) , B' = (-5,-1), C' = (-4,-2) and D' = (-2,-2) , Yes D, AA' and D' are collinear

Discussion

1703.	If A=[{:(,3,a),(,-4,8):}], B=[{:(,c,4),(,-3,0):}] , C=[{:(,-1,4),(,3,b):}] and 3A-2C=6B. Find the values of a,b and c.
Answer» ANSWER :`a=10 2/3, b=12 and c=1 5/6`

Discussion

1704.	A conical tent is to accomodate 11 persons. Each person must have 4 sq. m of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.
Answer» ANSWER :` 15 m `

Discussion

1705.	A boy is designing a diamond shaped kite , as shown in the figure where AE = 16 cm , EC = 81 cm .He wants to use a straight cross bar BD. How long should it be ?
Answer» ANSWER :72CM

Discussion

1706.	100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows Determine the median number of letters in the surnames . Find the mean number of letters in the surnames ? Also, find the modal size of the surnames.
Answer» ANSWER :MEDIAN = 8.05, MEAN = 8.32, MODAL SIZE = 7.88

Discussion

1707.	Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Answer» ANSWER :15 HOURS, 25 hours

Discussion

1708.	A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30^(@) to 60^(@) as he walks towards the building. Find the distance he walked towards the building.
Answer» ANSWER :`32.87m`

Discussion

1709.	PQ is a chord of the circle with centre at C and of radius 4 cm.The tangents drawn at P and Q to the circle intersects at R at a distance of 2sqrt7 from the centr of the circle. Then the length of the chord PQ is
Answer» 3 CM 4 cm 5 cm 6 cm ANSWER :D

Discussion

1710.	Statements: 1. No gentleman is poor. 2. All gentlemen are rich. Conclusions: 1. No poor man is rich. 2. No rich man is poor.
Answer» Solution :STATEMENTS 1 and 2 GIVE the Venn-diagram. Clearly neither the conclusion 1 nor 2 FOLLOW.

Discussion

1711.	List the teeth under each of the following type Incisors
Answer» ANSWER :8

Discussion

1712.	Show thattan ^(2) theta +tan ^(4) theta =sec ^(4) theta -sec ^(2) theta
Answer» ANSWER :`=SEC ^(4) THETA -sec^(2) theta =`R.H.S

Discussion

1713.	Which one of the following four loogical diagrams represents correclty the relationship between:Musicians,Instrumentalist,Violinists?
Answer» SOLUTION :All VIOLINISTS are INSTRUMENTALISTS.All instrumentalists are MUSICIANS.

Discussion

1714.	Count the number of triangles in the following figure
Answer» 27 25 23 21 Answer :A

Discussion

1715.	How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm , each bullet being 4cm in diameter. OR A circus tent is cylindericalupto a height of 3m and conical above it. The diameter of the base is 105m and the slant height of th conial part is 53m, find the total canvas used in making the tent.
Answer» ANSWER :2541

Discussion

1716.	Which of the following forms an AP? If they form an AP, then write the next two items? (i) 4,10,16,22,….. , (ii) 1,-1,-3,-5,……, (iii) -2,2,-2,2,-2,……… (iv) 1,1,1,2,2,2,3,3,3,……, (v) x,2x,3x,4x,…………
Answer» Answer :(i) forms an AP next forms are 22+6 = 28 and 28 + 6 = 34 (ii) is AP. next TWO terms are: `-7` and `-9` (iii) not an AP (iv) not an ap (v) is an AP two terms are `4X +x=5x` and `5x+x=6x`

Discussion

1717.	If the vertices of triangle PQR are P-= (1, -9), Q -= (2, 5) and R -= (6, 7), then find the co-ordinate of point G which divides the median PT in the ratio 2 : 1
Answer» ANSWER :(3, 1)

Discussion

1718.	A company wants to manufacture 1000 hemispherical basins from a steel sheet . If the radius of each basin is 21 cm, find the area of steel required to manufacture the above hemispherical basins ?
Answer» ANSWER :`277.2 m^2`

Discussion

1719.	If in a DeltaPQR,XY\|\|QR,PX=22x,XQ=3x,PY=x, and YR = 9x, find the value of x.
Answer» ANSWER :10 m

Discussion

1720.	O is any point on the line segment AB. Draw a perpendicular PQ at O on AB. Draw two cirles with centres at A and B and radius equal to AO and BO. Also write what PQ is called with respect to these circles.
Answer» SOLUTION : Here PQ is said to be a direct common TANGENT with RESPECT to the circles with CENTRES at A and B .

Discussion

1721.	Using ruler and compasses only, construct a triangle ABC in which angle ABC = 45°, AB = 8.6 cm and BC = 9.8 cm
Answer» ANSWER :43 MARKS

Discussion

1722.	Find the number of rectangles contained in the figure given below :
Answer» Solution :RECTANGLES from small to big are FEJH, HJKA , FEKA, EDCJ, JCBK , FDCH, HCBA, EDBK AND FDBA=9

Discussion

1723.	If A sec 4A = "cosec"(A - 20^@) , where 4A is an acute angle, then find the value of A.
Answer» ANSWER :`(3sqrt(2) - SQRT(6))/8`

Discussion

1724.	Draw A DeltaABC in which BC=6 cm, CA=5 cm and AB=4 cm. Construct a triangle similar to it and of scale factor (5)/(3)
Answer» Solution :Steps of construction 1. Draw a line segment BC=6 cm. 2. Taking B and C as centres, draw TWO arcs of radii 4 cm and 5 cm intersecting each other at A. 3. Join BA and CA. `DeltaABC` is the required triangle. 4. From B, draw any ray BX downwards making at acute angle. 5. Mark five points `B_(1),B_(2),B_(3),B_(4) " and " B_(5)` on BX, such that `BB_(1)=B_(1)B_(2)=B_(2)B_(3)=B_(3)B_(4)=B_(4)B_(5)` 6. Join `B_(3)C` and from `B_(5)` draw `B_(5)M\|\|B_(3)C` intersecting the extended line segment BC at M. 7. From point M draw MN\|\|CA intersecting the extended line segment BA at N. Then, `DeltaNBM` is the required triangle whose side is equal to `(5)/(3)` of the CORRESPONDING sides of the `DeltaABC`. HENCE, `DeltaNBM` is the required triangle.

Discussion

1725.	Oceans seas, and bays represent about 96.5% of Earth's including the water found in our atmost phere. If the volume of the water contained in oceans, seas, and bays is about 3221, 000, 000 cubic miles, which of the following best represents the approximate volume, in cubic miles, of all the world's water?
Answer» `308,160,000` `309,765,000` `332,642,000` `334,375,000 Answer :C

Discussion

1726.	Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550. How many packets of bread are supplied in the school?
Answer» 63 PACKETS 86 packets 65 packets 84 packets Solution :For equal distribution of bread among each student, we need 504 PIECES of bread. HENCE, we need (504/8=63) i.e. 63 packets of bread. Thus (a) is CORRECT OPTION.

Discussion

1727.	Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550. How many students are there in school?
Answer» 508 504 512 548 Solution :FIRSTLY we will find LCM (8, 6) =24. Now we will find a multiple of 24 in between 500 and 550 i.e., 504 or 528. THUS there 504 students in school. Thus (b) is correct option.

Discussion

1728.	Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550. How many packets of jams are supplied in the hospital?
Answer» 248 packets 252 packets 165 packets 288 packets Solution :Since, number of BREAD pieces are `189 xx 8 = 1512` , so we need same number of jam pieces. Hence `(1512)/(6)=252`packets of jam are distributed in the hospital. THUS (b) is correct option.

Discussion

1729.	Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550. How many packets of bread are supplied in the hospital?
Answer» 189 packets 252 packets 165 packets 288 packets Solution :For hospital, we NEED 3x packets of BREAD i.e. `3 xx 63 = 189` packets of bread. THUS (a) is correct option.

Discussion

1730.	Ashish supplies bread and jams to a hospital and a school. Bread and jam are supplied in equal number of pieces. Bread comes in a bunch of 8 pieces and Jam comes in a pack of 6 pieces. On a particular day, Ashish has supplied x packets of bread and y packets of jam to the school. On the same day, Ashish has supplied 3x packets of bread along with sufficient packets of jam to hospital. It is known that the number of students in the school are between 500 and 550. How many packets of jams are supplied in the school?
Answer» 63 packets 86 packets 65 packets 84 packets Solution :For EQUAL distribution of jam pieces among each student, we NEED 504 pieces of jam. Hence, we need (504/6=84) i.e. 84 packets of jam. Thus (d) is correct option.

Discussion

1731.	Find the ratio in which point P (k,7) divides the segment joining A (8,9) and B (1,2) . Also find find k.
Answer» <P> ANSWER :`therefore` POINT P DIVIDES seg AB in the ratio2:5 , and the value of k is 6.

Discussion

1732.	Anjali in an electrician and she has to repair an electric fault on a pole of height 5 m. She needs to reach to a point on the pole of 1.3 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at angle of 60° from the horizontal, would enable her to reach the required position? Further, how far from the foot of the pole should she place the foot of the ladder? What value is indicated from the question?
Answer» ANSWER :length of ladder =7.4 `sqrT(3)/(3)`m FOOT of ladder must be placed 3.7 `sqrt(3)/(3)` m away from the foot of the pole Value: “Dignity of LABOUR”. WOMEN can do any work for their livelihood.

Discussion

1733.	Two dice are thrown simultaneously. Find the probability that : the product of the numbers on the dice is 8.
Answer» ANSWER :`1/18`

Discussion

1734.	Evaluate the cot^(2) 30^(@) - 2 cos^(2) 60^(@) - (3)/(4) sec^(2) 45^(@) - 4 sec^(2) 30^(@)
Answer» ANSWER :`(-13)/(3)`

Discussion

1735.	1077 boxes of oranges were loaded in three trucks. While unloading them 7, 12 and 8 boxes were found rotten in the trucks respectively. If the number of remaining boxes in the three trucks are in the ratio 4:6: 5, find the number of boxes loaded originally in each truck
Answer» ANSWER :287, 432 and 358

Discussion

1736.	If acos^(3)theta+3acosthetasin^(2)theta=mandasin^(3)theta+3acos^(2)theta=n,then show that (m+n)^(2//3)
Answer»

Discussion

1737.	The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their : surface areas.
Answer» ANSWER :`9:1`

Discussion

1738.	A die is thrown once. The probabilty of getting a number 3 or 4 is:
Answer» `1/3` `2/3` 0 1 Answer :A

Discussion

1739.	If sinx+sin^2 x=1, then which one of the following is true
Answer» `COSX +cos^2 x=1` `cosx-cos^2x=1` `cos^2x+cos^4x=1` `cos^4x+cos^3x=1` ANSWER :C

Discussion

1740.	If x+y+z=0, then what is the value of (1)/( x^(2) + y^(2) -z^(2) )+ (1)/( y^(2) +z^(2) -x^(2) )+ (1)/( z^(2) + x^(2) - y^(2) )?
Answer» ANSWER :`0`

Discussion

1741.	Find the coordinates of the points which divides the line segment joining A(-2, 2) and B(2, 8) into four equal parts.
Answer» Answer :`(1,(13)/(2)), (-1, (7)/(2)), (0,5)9. ( (5a-b)/(5),(5a+b)/(5))`

Discussion

1742.	(i) There is a group of five persons-A, B, C, D and E.(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate. (iii) Three of them-A, C and advocate prefer tea to coffee and two of them--B and the journalist prefer coffee to tea. (iv) The industrialist and D and A are friends to one another but two of these prefer coffee to tea.(v) The horticulturist is C's brother. Which of the above statements is superfluous?
Answer» (iii) (iv) (ii) None Solution :A prefers tea, so from (iv), the industrialist and D prefers COFFEE. But from (iii), B and the journalist prefer coffee. So, B is the industrialist and D is the journalist. Now A, C and advocate REMAIN, clearly, E is the advocate. All statements are required so none of them is superfluous.

Discussion

1743.	(i) There is a group of five persons-A, B, C, D and E.(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate. (iii) Three of them-A, C and advocate prefer tea to coffee and two of them--B and the journalist prefer coffee to tea. (iv) The industrialist and D and A are friends to one another but two of these prefer coffee to tea.(v) The horticulturist is C's brother. Who is an industrialist?
Answer» E C B D Solution :A prefers tea, so from (IV), the industrialist and D prefers COFFEE. But from (iii), B and the journalist prefer coffee. So, B is the industrialist and D is the journalist. Now A, C and ADVOCATE REMAIN, clearly, E is the advocate. B is an industrialist

Discussion

1744.	(i) There is a group of five persons-A, B, C, D and E.(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate. (iii) Three of them-A, C and advocate prefer tea to coffee and two of them--B and the journalist prefer coffee to tea. (iv) The industrialist and D and A are friends to one another but two of these prefer coffee to tea.(v) The horticulturist is C's brother. Who is a horticulturist?
Answer» A B C D Solution :A prefers tea, so from (iv), the INDUSTRIALIST and D prefers coffee. But from (iii), B and the JOURNALIST prefer coffee. So, B is the industrialist and D is the journalist. Now A, C and ADVOCATE remain, clearly, E is the advocate. A is a HORTICULTURIST.

Discussion

1745.	Point P (a, b) is reflected in the x-axis to P' (5,-2). Write down the values of a and b.
Answer» ANSWER :a = 5 , B = 2

Discussion

1746.	(i) There is a group of five persons-A, B, C, D and E.(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate. (iii) Three of them-A, C and advocate prefer tea to coffee and two of them--B and the journalist prefer coffee to tea. (iv) The industrialist and D and A are friends to one another but two of these prefer coffee to tea.(v) The horticulturist is C's brother. Who is a physicist?
Answer» A E D C Solution :A prefers tea, so from (IV), the INDUSTRIALIST and D prefers coffee. But from (III), B and the journalist prefer coffee. So, B is the industrialist and D is the journalist. Now A, C and advocate remain, clearly, E is the advocate. C is the physicist.

Discussion

1747.	(i) There is a group of five persons-A, B, C, D and E.(ii) One of them is a horticulturist, one is a physicist, one is a journalist, one is an industrialist and one is an advocate. (iii) Three of them-A, C and advocate prefer tea to coffee and two of them--B and the journalist prefer coffee to tea. (iv) The industrialist and D and A are friends to one another but two of these prefer coffee to tea.(v) The horticulturist is C's brother. Which of the following groups includes a per son who likes tea but is not an advocate?
Answer» ACE DE BCE None of these SOLUTION :A prefers tea, so from (iv), the industrialist and D prefers coffee. But from (iii), B and the JOURNALIST prefer coffee. So, B is the industrialist and D is the journalist. Now A, C and advocate remain, clearly, E is the advocate. A and C are the persons who LIKE tea but are not advocates.

Discussion

1748.	To find out the concentration of SO_(2) in the air (in parts per million, i.e, ppm), the data was collected for 30 localities in a certain city and is presented below : Find the mean concentration of SO_(2) in the air.
Answer» ANSWER :0.099 PPM

Discussion

1749.	The point P(a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P'has co-ordinates (4, 6), evaluate a and b.
Answer» ANSWER :a = 4 and B = 6

Discussion

1750.	Solve each the following pairs of equations by reducing them to a pair of linear equations. (vii) 10/x+y+ 2/x-y = 4 15/x+y - 5/x-y = -2
Answer» ANSWER :(3,2)

Discussion

Explore topic-wise InterviewSolutions in .

A (1, 1), B (5, 1), C (4, 2) and D (2, 2) are vertices of a quadrilateral. Name the quadrilateral ABCD. A, B, C, and D are reflected in the origin on to A', B', C' and D' respectively. Locate A', B', C' and D' on the graph sheet and write their co-ordinates. Are D, A, A' and D' collinear ?

If A=[{:(,3,a),(,-4,8):}], B=[{:(,c,4),(,-3,0):}] , C=[{:(,-1,4),(,3,b):}] and 3A-2C=6B. Find the values of a,b and c.

A conical tent is to accomodate 11 persons. Each person must have 4 sq. m of the space on the ground and 20 cubic metre of air to breath. Find the height of the cone.

A boy is designing a diamond shaped kite , as shown in the figure where AE = 16 cm , EC = 81 cm .He wants to use a straight cross bar BD. How long should it be ?

Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30^(@) to 60^(@) as he walks towards the building. Find the distance he walked towards the building.

PQ is a chord of the circle with centre at C and of radius 4 cm.The tangents drawn at P and Q to the circle intersects at R at a distance of 2sqrt7 from the centr of the circle. Then the length of the chord PQ is

Statements: 1. No gentleman is poor. 2. All gentlemen are rich. Conclusions: 1. No poor man is rich. 2. No rich man is poor.

List the teeth under each of the following type Incisors

Show thattan ^(2) theta +tan ^(4) theta =sec ^(4) theta -sec ^(2) theta

Which one of the following four loogical diagrams represents correclty the relationship between:Musicians,Instrumentalist,Violinists?

Count the number of triangles in the following figure

Which of the following forms an AP? If they form an AP, then write the next two items? (i) 4,10,16,22,….. , (ii) 1,-1,-3,-5,……, (iii) -2,2,-2,2,-2,……… (iv) 1,1,1,2,2,2,3,3,3,……, (v) x,2x,3x,4x,…………

If the vertices of triangle PQR are P-= (1, -9), Q -= (2, 5) and R -= (6, 7), then find the co-ordinate of point G which divides the median PT in the ratio 2 : 1

A company wants to manufacture 1000 hemispherical basins from a steel sheet . If the radius of each basin is 21 cm, find the area of steel required to manufacture the above hemispherical basins ?

If in a DeltaPQR,XY||QR,PX=22x,XQ=3x,PY=x, and YR = 9x, find the value of x.

O is any point on the line segment AB. Draw a perpendicular PQ at O on AB. Draw two cirles with centres at A and B and radius equal to AO and BO. Also write what PQ is called with respect to these circles.

Using ruler and compasses only, construct a triangle ABC in which angle ABC = 45°, AB = 8.6 cm and BC = 9.8 cm

Find the number of rectangles contained in the figure given below :

If A sec 4A = "cosec"(A - 20^@) , where 4A is an acute angle, then find the value of A.

Draw A DeltaABC in which BC=6 cm, CA=5 cm and AB=4 cm. Construct a triangle similar to it and of scale factor (5)/(3)

Find the ratio in which point P (k,7) divides the segment joining A (8,9) and B (1,2) . Also find find k.

Two dice are thrown simultaneously. Find the probability that : the product of the numbers on the dice is 8.

Evaluate the cot^(2) 30^(@) - 2 cos^(2) 60^(@) - (3)/(4) sec^(2) 45^(@) - 4 sec^(2) 30^(@)

1077 boxes of oranges were loaded in three trucks. While unloading them 7, 12 and 8 boxes were found rotten in the trucks respectively. If the number of remaining boxes in the three trucks are in the ratio 4:6: 5, find the number of boxes loaded originally in each truck

If acos^(3)theta+3acosthetasin^(2)theta=mandasin^(3)theta+3acos^(2)theta=n,then show that (m+n)^(2//3)

The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their : surface areas.

A die is thrown once. The probabilty of getting a number 3 or 4 is:

If sinx+sin^2 x=1, then which one of the following is true

If x+y+z=0, then what is the value of (1)/( x^(2) + y^(2) -z^(2) )+ (1)/( y^(2) +z^(2) -x^(2) )+ (1)/( z^(2) + x^(2) - y^(2) )?

Find the coordinates of the points which divides the line segment joining A(-2, 2) and B(2, 8) into four equal parts.

Point P (a, b) is reflected in the x-axis to P' (5,-2). Write down the values of a and b.

To find out the concentration of SO_(2) in the air (in parts per million, i.e, ppm), the data was collected for 30 localities in a certain city and is presented below : Find the mean concentration of SO_(2) in the air.

The point P(a, b) is first reflected in the origin and then reflected in the y-axis to P'. If P'has co-ordinates (4, 6), evaluate a and b.

Solve each the following pairs of equations by reducing them to a pair of linear equations. (vii) 10/x+y+ 2/x-y = 4 15/x+y - 5/x-y = -2