3694 + Interview Questions in Maths in Class 10 Page 59 InterviewSolution

2901.	Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image : A" of A under reflection in the y-axis.
Answer» ANSWER :(-3,4)

Discussion

2902.	Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image : A' of A under reflection in the x-axis.
Answer» ANSWER :(8,-5)

Discussion

2903.	Find 6 rational number between5 and 6 .
Answer»

Discussion

2904.	A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire is 14mm and the diameter of the capsule is 5mm. Find its surface area.
Answer» ANSWER :220 `m m^(2)`

Discussion

2905.	Solve for x, 0^@le x le 90^@ 2 sin^2x-sinx=0
Answer» ANSWER :`0^@` or `30^@`

Discussion

2906.	Find the mean from the following table using short cut method :
Answer» ANSWER :`29.3`

Discussion

2907.	Find the mean from the following table using short cut method :
Answer» ANSWER :351

Discussion

2908.	Find roots of the equation by quadratic formula : x^(2)+x-(a+2)(a+1)=0
Answer» Solution :The given equation is `x^(2)+x-(a+2)(a+1)=0` Comparing it with `AX^(2)+Bx+C=0`, we get `A=1,B=1andC=-(a+2)(a+1)` `:.x-B+-sqrt(B^(2)-4AC)/(2A)` `x=(-1+-sqrt(1^(2)-4xx1xx[-(a+2)(a+1)]))/(2XX1)` `impliesx=(-1+-sqrt(1+4(a^(2)+33a+2)))/(2)` `impliesx=(-1+-sqrt(1+4a^(2)+12a+8))/(2)` `impliesx=(-1+-sqrt(4a^(2)+12a+9))/(2)` `impliesx=(-1+-sqrt((2a+3)^(2)))/(2)` `impliesx=(-1+-(2a+3)^(2))/(2)` `impliesx=(-1+2a+3^(2))/(2)and (-1-2a-3)/(2)` `impliesx=(2a+2)/(2)and (-2a-4)/(2)` `impliesx=(a+1)and-(a+2)` are ROOTS of the equation.

Discussion

2909.	Find the probability to getting a head when a coin is tossed once.
Answer» ANSWER :`(1)/(2)`

Discussion

2910.	A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be 1.4 m. and its length be 8 m. Find the cost of painting it on the outside at rate of Rs. 20 per m^(2).
Answer» ANSWER :RS. 827.20

Discussion

2911.	If tan theta = (1)/(3) , find other five trigonometric ratios.
Answer» Answer :sin `THETA = (1)/(sqrt(10)) , cos theta = "" (3)/(sqrt(10)) , "COSEC" theta = sqrt(10) , SEC theta = (sqrt(10))/(3), COT theta = 3 `

Discussion

2912.	A golf ball has diameter equal to 4.1 cm. Its surface has 150 dimples each of radius 2mm. Calculate total surface which is exposed to the surroundings. (Assume that the dimples are all hemispherical) ""[pi=22//7]
Answer» ANSWER :`15.12 CM^(2)`

Discussion

2913.	A sum of Rs. 700 to be used to give seven cash prizes to students of a school for thir overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.
Answer» ANSWER :160,140,120,100,80,60,40

Discussion

2914.	-a
Answer» 2A `-a^2` `3b-a` `3A` ANSWER :A

Discussion

2915.	In the following figure, AC \|\| BD and CE \|\| DF. If OA = 13 cm, AB = 9 cm, OC = 8 cm and EF = 4.5 cm, find OE.
Answer» ANSWER :6 CM

Discussion

2916.	barPA and barPB are the tangents to a circle,with centre O as shown in figure.IF angleAOB=140^(@),then the measure of angleAPB is:
Answer» `40^(@) CM` `20^(@) cm` `90^(@) cm` `140^(@) cm` Answer :A

Discussion

2917.	Solve for x, 0^@le x le 90^@ 4 cos^(2)2x-3=0
Answer» ANSWER :`15^@`

Discussion

2918.	Find the distance between the pair of points (-5, 7) and (-1, 3)
Answer» ANSWER :`4sqrt(2)`

Discussion

2919.	Let A(4,2) ,B (6,5) andC(1,4) be the vertices of DeltaABC . (i) The medium fromA meetsBC at D . Find the coordinates of the point D. (ii) Find the coordinatesof the point P on AD such that AP:PD = 2:1 (iii) Find the coordinates of points Q and R onmedians BE and CF respectively such that BQ:QE = 2:1 and CR:RF = 2:1 . (iv) What do you observe? [ Note : The point which is commonto all the three medians is called the centroidand this pointdivides each medianin the ratio 2:1] (v) If A(x_(1),y_(1)),B(x_(2),y_(2))and C(x_(3),y_(3))are the vertices of triangleABC , find the coordinates of the centroid of the triangle .
Answer» ANSWER :`=((x_(1)+x_(2)+x_(3))/3,(y_(1)+y_(2)+y_(1))/3)`

Discussion

2920.	A sphere, a cylinder and a cone have the same radius and same heightthen the ratio of their curved surface areas is ……….
Answer» ANSWER :`4:4:SQRT5`

Discussion

2921.	Fill in the blank using the correct word given in bracket. All ...............triangles are similar. (Isosceles/Equilateral)
Answer» ANSWER :EQUILATERAL

Discussion

2922.	A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside If the height of the cone is 24 cm the total height of the toy is 60 cm and the radius of the base of the cone= twice the radius of the base of the cylinder = 10 cm .Find the total surface area of the you.
Answer» ANSWER :2260.8 `CM^(2)`

Discussion

2923.	The marks distribution of 30 students in a mathematics examination are given in the adjacent table. Find the mode of this data. Also compare and interpret the mode and the mean .
Answer» ANSWER :52

Discussion

2924.	Prove that, sqrt((1+sin theta)/(1-sin theta))=sec theta + tan theta
Answer» ANSWER :L.H.S = R.H.S

Discussion

2925.	From a point on a groud the angle of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45^@ and 60^@ respectively . Find the height of the tower.
Answer» ANSWER :30 m

Discussion

2926.	A die is numbered in such a way that its faces show the number 1,2,2,3,3,6 . It is thrown two times and the total score in two throws is noted. Complete the following table which given a few values of the total score on the two throws: What is the probability that the total score is (i) even ? (ii) 6 ? (iii) at least 6 ?
Answer» ANSWER :(i) `1/2` (II) `1/9` (III) `5/12`

Discussion

2927.	Three hundred sixty bricks are stacked in the following manner: 30 bricks in the bottom row, 29 in the next row, 28 in the row next to it and so on. In how many rows are the 360 bricks placed and how many bricks are there in the top row?
Answer» ANSWER :16 ROWS 15

Discussion

2928.	Santosh wants to invest a maximum of Rs. 150,000 in saving certificates and national saving bonds. Which are in denominations of Rs. 4000 and Rs. 5000. respectively . The rate of interest on saving certificate is 10% per annum, and the rate of interest on national saving bond is 12% per annums. Forulate the above formation as a linear programmingproblem.
Answer» ANSWER : `4X +5y LE 150 and x gt 0, y ge 0`

Discussion

2929.	The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3 If each of them manages to save Rs.200 per month, find their monthly income.
Answer» ANSWER :INCOME of `1^st` PERSON = Rs.18000; Income of `2^nd Person = Rs.14000

Discussion

2930.	23, 13, 34, 25, 56, 51
Answer» 23 13 34 51 Solution :The number in the ALTERNATE places is the SUM of the square of the integer on the other e.g. `13=2^(2)+3^(2),25=3^(2)+4^(2)`. Now `56+5^(2)+6^(2)=61`.

Discussion

2931.	Find the sum of the A.P. : 14, 21, 28………….. 168.
Answer» ANSWER :n=23 and SUM =2093

Discussion

2932.	If M and M_(g)represents the mean of the rawand grouped data, respectively then
Answer» `M GT M_g` `M GE M_g` `M_g ge M` `M = M_g` ANSWER :D

Discussion

2933.	Two A.Ps have the samecommon difference . The differencebetween their100^(th) term is 100 what is the differencebetween their 1000^(th) term ?
Answer» ANSWER :100

Discussion

2934.	A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of115^(@) . Find the total area cleaned at the sweep of the blades .(use pi=(22)/(7))
Answer» ANSWER :`1254.96cm^(2)`

Discussion

2935.	Write a pair of linear equations which has the unique solution x = -1 and y = 3. How many such pairs can you write ?
Answer» Solution :Condition for the pair of SYSTEM to have unique solution `(a_(1))/(a_(2))!=(b_(1))/(b_(2))` Let the equations are, `a_(1)x+b_(1)y+c_(1)=0` and `" " a_(2)x+b_(2)y+c_(2)=0` Since, x=-1 and y=3 is the unique solution of these two equations, then `a_(1)(-1)+b_(1)(3)+c_(1)=0` `rArr " " -a_(1)+3b_(1)+c_(1)=0 " " ...(i)` and `" " a_(2)(-1)+b_(2)(3)+c_(2)=0 ` `rArr " " -a_(2)+3b_(2)+c_(2)=0 " " ...(ii)` So, the different VALUES of `a_(1), a_(2), b_(1), b_(2), c_(1)` and `c_(2)` SATISFY the Eqs. (i) and (ii). Hence, infinitely many pairs of linear equations are possible.

Discussion

2936.	A triangle ABC is drawn to circumscribe a circle of radius 3cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 9cm. And 3cm. Respectively ( See adjacent figure ). Find the sides AB and AC.
Answer» ANSWER :`AB=15cm,AC=9cm`

Discussion

2937.	A cistern, internally measuring 150 cm xx120 cm xx110 cm has 129600 cm^(3) of water in it. Porous brickes are placed in the water until the cistern is full to the brim. Each brick absorbs one-seveneenth of its own volumeof water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm xx7.5 cm xx 6.5 cm ?
Answer» ANSWER :1792

Discussion

2938.	Determine the value of the following. log_(81)3
Answer» ANSWER :`1/4`

Discussion

2939.	A solid toy is in the form of a right circular cylinder with hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the height of the cylindrical and conical portions are 12 cm and 7 cm respectively. Find the volume of the solid toy. (Use pi= (22)/(7))
Answer» ANSWER :`218.064 cm^3`

Discussion

2940.	A dealer in a city buys some worth Rs. 6,000 from the same city. If the rate of GST is 18%, find how much will the dealer pay for the goods bought.
Answer» ANSWER :7080

Discussion

2941.	The triangle A(1,2),B(4,4) and C(3,7) is first reflected in the line y = 0 onto triangle A'B'C' and then triangle A'B'C' is reflected in the origin onto triangle A''B''C'' . Write down the co-ordinates of : A'' , B'' and C''
Answer» ANSWER :A''(-1,2) B'' = (-4,4) and C'' = (-3,7)

Discussion

2942.	The triangle A(1,2),B(4,4) and C(3,7) is first reflected in the line y = 0 onto triangle A'B'C' and then triangle A'B'C' is reflected in the origin onto triangle A''B''C'' . Write down the co-ordinates of : A', B' and C'
Answer» Answer :A' (1,-2) B' = (4,-4) and C' = (3,-7)

Discussion

2943.	For drawing the graph of3x + 7y = 27, if y = 3what is the value of x ?
Answer» 2 `20/3` 9 `13/3` ANSWER :A

Discussion

2944.	{:(A , B , C , D , E , F , G, H , I , J , K , L , M , N , O , P , Q , R ,S , T ,U , V , W ,X , Y , Z), (1 ,2 , 3 , 4 ,5, 6 , 7,8,9,10 , 11 , 12, 13, 14, 15 , 16 , 17 , 18 , 19, 20 , 21 ,22 , 23 , 24 , 25 , 26):} EJOT : VOLG:: BGLQ: ?
Answer» AEIM AFKP YTOJ ZUPK SOLUTION :Each LETTER of the first group occupies the same POSITION from the end of the alphabet to FORM the CODE.

Discussion

2945.	A ladder25m long reaches a window of building 20m above the ground.Determine the distance from the foot of the ladder to the building.
Answer» Answer :Hence, the FOOT of the LADDER is at a distance of 15m from the BUILDING.

Discussion

2946.	Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines 45^(@)
Answer» 1 2 `(1)/(2)` `(1)/(SQRT2)` ANSWER :A

Discussion

2947.	Which point on x-axis is equidistant from (7, 6) and (-3, 4) ?
Answer» `(2,0)` `(3,0)` `(-5,0)` `(1,0)` ANSWER :B

Discussion

2948.	Fill in the blank : A tangent to a circle intersects it is .........Point(s).
Answer» ANSWER :ONE POINT.

Discussion

2949.	For what value of n , are the nth terms of two Aps 63 , 65 , 67 , ........and 3,10,17 , .....equal ?
Answer» ANSWER :13

Discussion

2950.	Show that a_(1), a_(2),……, a_(n)…. Form an AP where a_(n) is defined as below: (i) a_(n) = 3 + 4n, (ii) a_(n) = 9-5n Also find the sum of the first 15 terms in each case.
Answer» ANSWER :(i) 525, (II) `- 465`

Discussion

Explore topic-wise InterviewSolutions in .

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image : A" of A under reflection in the y-axis.

Points A and B have co-ordinates (3, 4) and (0, 2) respectively. Find the image : A' of A under reflection in the x-axis.

Find 6 rational number between5 and 6 .

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire is 14mm and the diameter of the capsule is 5mm. Find its surface area.

Solve for x, 0^@le x le 90^@ 2 sin^2x-sinx=0

Find the mean from the following table using short cut method :

Find the mean from the following table using short cut method :

Find roots of the equation by quadratic formula : x^(2)+x-(a+2)(a+1)=0

Find the probability to getting a head when a coin is tossed once.

A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be 1.4 m. and its length be 8 m. Find the cost of painting it on the outside at rate of Rs. 20 per m^(2).

If tan theta = (1)/(3) , find other five trigonometric ratios.

A golf ball has diameter equal to 4.1 cm. Its surface has 150 dimples each of radius 2mm. Calculate total surface which is exposed to the surroundings. (Assume that the dimples are all hemispherical) ""[pi=22//7]

A sum of Rs. 700 to be used to give seven cash prizes to students of a school for thir overall academic performance. If each prize is Rs. 20 less than its preceding prize, find the value of each of the prizes.

-a

In the following figure, AC || BD and CE || DF. If OA = 13 cm, AB = 9 cm, OC = 8 cm and EF = 4.5 cm, find OE.

barPA and barPB are the tangents to a circle,with centre O as shown in figure.IF angleAOB=140^(@),then the measure of angleAPB is:

Solve for x, 0^@le x le 90^@ 4 cos^(2)2x-3=0

Find the distance between the pair of points (-5, 7) and (-1, 3)

A sphere, a cylinder and a cone have the same radius and same heightthen the ratio of their curved surface areas is ……….

Fill in the blank using the correct word given in bracket. All ...............triangles are similar. (Isosceles/Equilateral)

A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside If the height of the cone is 24 cm the total height of the toy is 60 cm and the radius of the base of the cone= twice the radius of the base of the cylinder = 10 cm .Find the total surface area of the you.

The marks distribution of 30 students in a mathematics examination are given in the adjacent table. Find the mode of this data. Also compare and interpret the mode and the mean .

Prove that, sqrt((1+sin theta)/(1-sin theta))=sec theta + tan theta

From a point on a groud the angle of elevation of the bottom and top of a transmission tower fixed at the top of a 20 m high building are 45^@ and 60^@ respectively . Find the height of the tower.

Three hundred sixty bricks are stacked in the following manner: 30 bricks in the bottom row, 29 in the next row, 28 in the row next to it and so on. In how many rows are the 360 bricks placed and how many bricks are there in the top row?

The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3 If each of them manages to save Rs.200 per month, find their monthly income.

23, 13, 34, 25, 56, 51

Find the sum of the A.P. : 14, 21, 28………….. 168.

If M and M_(g)represents the mean of the rawand grouped data, respectively then

Two A.Ps have the samecommon difference . The differencebetween their100^(th) term is 100 what is the differencebetween their 1000^(th) term ?

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of115^(@) . Find the total area cleaned at the sweep of the blades .(use pi=(22)/(7))

Write a pair of linear equations which has the unique solution x = -1 and y = 3. How many such pairs can you write ?

A triangle ABC is drawn to circumscribe a circle of radius 3cm such that the segments BD and DC into which BC is divided by the point of contact D are of length 9cm. And 3cm. Respectively ( See adjacent figure ). Find the sides AB and AC.

Determine the value of the following. log_(81)3

A solid toy is in the form of a right circular cylinder with hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the height of the cylindrical and conical portions are 12 cm and 7 cm respectively. Find the volume of the solid toy. (Use pi= (22)/(7))

A dealer in a city buys some worth Rs. 6,000 from the same city. If the rate of GST is 18%, find how much will the dealer pay for the goods bought.

The triangle A(1,2),B(4,4) and C(3,7) is first reflected in the line y = 0 onto triangle A'B'C' and then triangle A'B'C' is reflected in the origin onto triangle A''B''C'' . Write down the co-ordinates of : A'' , B'' and C''

The triangle A(1,2),B(4,4) and C(3,7) is first reflected in the line y = 0 onto triangle A'B'C' and then triangle A'B'C' is reflected in the origin onto triangle A''B''C'' . Write down the co-ordinates of : A', B' and C'

For drawing the graph of3x + 7y = 27, if y = 3what is the value of x ?

{:(A , B , C , D , E , F , G, H , I , J , K , L , M , N , O , P , Q , R ,S , T ,U , V , W ,X , Y , Z), (1 ,2 , 3 , 4 ,5, 6 , 7,8,9,10 , 11 , 12, 13, 14, 15 , 16 , 17 , 18 , 19, 20 , 21 ,22 , 23 , 24 , 25 , 26):} EJOT : VOLG:: BGLQ: ?

A ladder25m long reaches a window of building 20m above the ground.Determine the distance from the foot of the ladder to the building.

Angles made by the line with the positive direction of X-axis are given. Find the slope of these lines 45^(@)

Which point on x-axis is equidistant from (7, 6) and (-3, 4) ?

Fill in the blank : A tangent to a circle intersects it is .........Point(s).

For what value of n , are the nth terms of two Aps 63 , 65 , 67 , ........and 3,10,17 , .....equal ?

Show that a_(1), a_(2),……, a_(n)…. Form an AP where a_(n) is defined as below: (i) a_(n) = 3 + 4n, (ii) a_(n) = 9-5n Also find the sum of the first 15 terms in each case.