3694 + Interview Questions in Maths in Class 10 Page 5 InterviewSolution

201.	Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
Answer» SOLUTION :For CORRECT given, to prove, CONST. and FIGURE For correct proof

Discussion

202.	From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (i) a black card
Answer» ANSWER :`10/23`

Discussion

203.	From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (ii) a king
Answer» ANSWER :`1/23`

Discussion

204.	From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (iii) an ace
Answer» ANSWER :`2/23`

Discussion

205.	From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (iv) a spade card
Answer» ANSWER :`5/23`

Discussion

206.	State whether the following statements are true or false. Justify your answer (i) 5 cancel(in) set of prime numbers (ii) S={5,6,7} implies 8 in S. (iii) -5 cancel(in)W where 'W' is the set of whole numbers (iv) 8/(11) in Z where's 'Z' is the set of integers.
Answer» ANSWER :(i) FALSE (II) False (III) TRUE

Discussion

207.	A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
Answer» ANSWER :`21 CM`

Discussion

208.	A bag contains 3 red and 7 back. A ball is taken out of the bag aty random. Find the probability of getting a black ball.
Answer» ANSWER :`7/10`

Discussion

209.	The radiiof the bases of two right circular solid cones of same height are r_1and r_2respectively.The cones are melted and recast into a solid sphere of radius R. Show thatthe height of each cone is given by h=(4R^3)/(r1 2+r2 2)
Answer» ANSWER :`(4 R ^(3))/(r _(1) ^(2) + r _(2) ^(2)) `14

Discussion

210.	Which term of the sequence 3, 8, 13, is 78?
Answer» ANSWER :16TH TERM

Discussion

211.	If (a−8)/3=(a−3)/2, then a = ?
Answer» ANSWER :a=-7

Discussion

212.	Solve for x by fractorisation sqrt3 x ^(2) + 10x + 7 sqrt3 =0
Answer»

Discussion

213.	Draw a circle of radius 4 cm. From the point 7 cm away from its centre, construct the pair of tangents to the circle.
Answer» ANSWER :5.7 CM

Discussion

214.	Derive the formula for the volume of the frustum of a cone, using the symbols explain.
Answer» ANSWER :`=(h)/(3)(A_(1)+A_(2)+SQRT(A_(1).A_(2)))`

Discussion

215.	Construct a DeltaABC in which AB=6cm, /_A=30^(@) and /_B=60^(@). Construct another DeltaAB'C' similar to DeltaABC with base AB'=8cm.
Answer» Solution :CONSTRUCT `DELTAABC`. Produce `AB` to `B'` such that `AB'=8cm`. Draw `B'C'\|\|BC` such that `B'C'` MEETS `AC` PRODUCED at `C'`.

Discussion

216.	A kite is flying at a height of 60 m above the ground. The string attached to kite is temporarily tied to a point on the ground. The inclination on the string with the ground is 60^(@). Find the length of the string assuming that there is no slack in the string.
Answer» ANSWER :`40 SQRT(3)m`

Discussion

217.	Find the solution of sqrt(x-2)+sqrt(4-x)=sqrt(6-x).
Answer» ANSWER :`:.X=3` or `x= -5`

Discussion

218.	Number of roots in a quadratic equation is
Answer» 1 2 3 4

Discussion

219.	Solve the following equations : 1.5x-(5)/(3)y+2=0 (1)/(3)x+0.5y-(13)/(6)=0
Answer» ANSWER :`x=2,y=3`

Discussion

220.	Draw the two tangents from a point which is 10 cm away from the centre of a circle of raiud 5 cm. Also, measure the lengths of the tangents.
Answer» ANSWER :`=8.7 CM`

Discussion

221.	A man buys 24 shares at Rs. 150 per share having the par value of Rs. 100. If the dividend is 7.5% per annum, then the ratio of total annual income to his total inverstent is _______.
Answer» `1 : 10` `10 : 1` `1 : 20` `20 : 1` Solution :(i) Require rates = ANNUAL income `=MV` of 1 share. (ii) Incomefrom 1 share `=((FVxx"Rate of dividend"))/100` (III) Then find the total income from 24 shares. (iv) `MV=(150+100)` Total INVESTMENT `=MVxx24`.

Discussion

222.	(x + 1/x)^(2) - (y + 1/y)^(2) - (xy - 1/(xy)), (x/y - y/x)=
Answer» 0 1 XY `1/(xy)` ANSWER :A

Discussion

223.	Which is a better investment : 12%, 100rs shares at 120 or 8% 100rs shares at 90 ?
Answer» ANSWER :The FIRST INVESTMENT is BETTER

Discussion

224.	Find the radius of the circle passing through the vertices of a right angled traingle the lengths of whose perpendicular sides are 8 and 15.
Answer» ANSWER :8.5cm

Discussion

225.	Which of the following is rational?
Answer» `SQRT(3)` `PI` `4/0` `0/4` ANSWER :D

Discussion

226.	Two circles intersect each other. Then the total number of common tangents that can be drawn to them is :
Answer» 0 1 2 3 Answer :C

Discussion

227.	How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
Answer» ANSWER :64

Discussion

228.	The two opposite vertices of a square are (-1,2) and (3, 2). Find the coordinates of the other two vertices.
Answer» ANSWER :So, the REQUIRED VERTICES are (1,0) and D(1,4)

Discussion

229.	Find the area of the shaded region in the adjacent figure, where ABCD is a square of side 10cm and semicircles are drawn with each side of the square as diameter (usepi=3.14)
Answer» ANSWER :`57CM^(2)`

Discussion

230.	A bag contains 50 balls. Some of them are white, some are blue and some are red. The number of white balls is 11 times the number of blue balls. The number of red balls is less than the number of white balls but more than the number of blue balls.If one ball is taken out of random from the bag, what is the probability that it is red?
Answer» Solution :Let the number of BLUE balls be X. DECIDE the number of white balls. The REMAINING are red balls. Form two inequations from the given CONDITION. Find the number of red balls.

Discussion

231.	In the following Distribution Where A is positive integer, has a variance of 160. Determine the value of A.
Answer» ANSWER :A=7

Discussion

232.	If in a certain language A is coded as 1, B is coded as 2, and so on, how is BIDDIC coded in that code?
Answer» 294493 284563 375582 394492 Answer :A

Discussion

233.	If the angle of elevation of an object from a point 100 m above a lake is found to be 30° and the angle of depression of its image in lake is 45°, then the height of the object above the lake is
Answer» `100(2-SQRT(3))m` `100(2+sqrt(3))`m `100(sqrt(3)-1)` METRES `1000(sqrt(3)+1)` m Answer :B

Discussion

234.	M/s. Jay Chemicals purchased a liquid soap having taxable value 10,000. Rate of GST is 18%. Find the CGST and SGST payable by M/s. Jay Chemicals.
Answer» ANSWER :CGST=SGST=180

Discussion

235.	If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, which term of it is zero ?
Answer» ANSWER :5TH TERM

Discussion

236.	Name the type of quadrilateral formed, if any by the following points, and give reasons for your answer : (-1, -2), (1,0), (-1, 2), (-3, 0)
Answer» ANSWER :SQUARE

Discussion

237.	Which of the following arguments are correct and which are incorrect ? Give reason if incorrect. If a dice is thrown , there are two possible outcomes :- an odd numbers or aneven number.Therefore the probability of an odd numbers is (1)/(2).
Answer» ANSWER :CORRECT

Discussion

238.	Calculate the mean deviation about median for the following data:
Answer» ANSWER :11.44

Discussion

239.	Calculate the mean deviation about median for the following data:
Answer» ANSWER :10.1

Discussion

240.	If A=[{:(,-2,3),(,4,1):}] and B=[{:(,1,2),(,3,5):}], find (i) AB (ii) BA (iii) Is AB=BA? (iv) Write the conclusion that you draw from the result obtained above in (iii).
Answer» Answer :(i) `[{:(,7,11),(,7,13):}]` (II) `[{:(,6,15),(,14,14):}]` (iii) No, `AB NE BA`

Discussion

241.	Three identical coins are tossed together. What is the probability of obtaining : exactly one head ?
Answer» ANSWER :`3/8`

Discussion

242.	A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides it is just immersed. What fraction of water overflows ?
Answer» ANSWER :`3/8`

Discussion

243.	A TV tower stands vertically on a bank of a canal. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60^(@). From another point 20m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30^(@) (see the given figure). Find the height of the tower and the width of the canal.
Answer» ANSWER :`10 sqrt3m` 10M

Discussion

244.	Given that AB =4 cm , BC = 7 ,CD = 4 cm , angle ABC = 60^(@) , angle BCD= 60^(@). Construct thequardrilateral ABCD. Theconstruct the circumcirleof DeltaABCand alsostate whatothercharacteristics youobserve.
Answer» ANSWER :4CM

Discussion

245.	Solve the pair of linear equations : (3x)/(2)-(5y)/(3)=-2 and (x)/(3)+(y)/(3)=(13)/(6).
Answer» ANSWER :`x=2 and y=3`.

Discussion

246.	Floor of a room is of dimensions5mxx4m and it is covered with circular tiles of diameters 50 cm each as shown infigure . Find area of floor that remains uncovered with tiles. (use pi= 3.14)
Answer» Solution :Given, floor of a ROOM is covered with circular tiles. LENGTH of a floor of a room (l) = 5m and BREADTH of floor of a room (b) = 4m `:.` Area of floor of a room = `lxxb` = ` 5xx4= 20 m^(2)` Diameter of each circular tile = 50 cm `rArr` Redius of each circular tile = `(50)/(2)=25 cm` = `(25)/(100) m =(1)/(4)m` Now, area of a circular tile = `pi ("radius")^(2)` = ` 3.14xx((1)/(4))^(2) = (3.14)/(16)m^(2)` `:.` Area of 80 circular tiles = `80xx(3.14)/(16)= 5xx3.14 = 15.7 m^(2)` [`because` 80 congruent circular tiles covering the floor of a room] So, area of floor that remains uncovered with tiles = Area of floor of a room - Area of 80 circular tiles = `20 - 15.7 = 4.3 m^(2)` Hence, the required area of floor that remains uncovered with tiles is `4.3 m^(2)` .

Discussion

247.	Square : Diamond :: Circle : ?
Answer» Smooth Round Oval Ball Solution :SECOND is the shape OBTAINED by PULLING the OPPOSITE ends of the first.

Discussion

248.	A person bought a certain number of pens for 800. If he had bought 4 pens more for the same money, he would have paid 10 less for each pen. How many pens did he buy?
Answer» ANSWER :16

Discussion

249.	A quadratic equation ax^(2) + bx + c = 0 has two distinct real roots, if….
Answer» `b^(2) - 4ac GT 0` `b^(2) - 4ac lt 0` `b^(2) - 4ac = 0` NONE of the given Answer :A

Discussion

250.	In what ratio is the line joining the points A (4, 4) and B (7, 7) divided by p (-1,-1) ?
Answer» `8:5` `5:8` `5:7` `7:4` ANSWER :B

Discussion

Explore topic-wise InterviewSolutions in .

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.

From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (i) a black card

From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (ii) a king

From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (iii) an ace

From the pack of 52 playing cards, the black face cards are removed. Now the cards are re-shuffled and then a card is drawn from the remaining pack of cards. Find the probability that the card drawn is : (iv) a spade card

State whether the following statements are true or false. Justify your answer (i) 5 cancel(in) set of prime numbers (ii) S={5,6,7} implies 8 in S. (iii) -5 cancel(in)W where 'W' is the set of whole numbers (iv) 8/(11) in Z where's 'Z' is the set of integers.

A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.

A bag contains 3 red and 7 back. A ball is taken out of the bag aty random. Find the probability of getting a black ball.

The radiiof the bases of two right circular solid cones of same height are r_1and r_2respectively.The cones are melted and recast into a solid sphere of radius R. Show thatthe height of each cone is given by h=(4R^3)/(r1 2+r2 2)

Which term of the sequence 3, 8, 13, is 78?

If (a−8)/3=(a−3)/2, then a = ?

Solve for x by fractorisation sqrt3 x ^(2) + 10x + 7 sqrt3 =0

Draw a circle of radius 4 cm. From the point 7 cm away from its centre, construct the pair of tangents to the circle.

Derive the formula for the volume of the frustum of a cone, using the symbols explain.

Construct a DeltaABC in which AB=6cm, /_A=30^(@) and /_B=60^(@). Construct another DeltaAB'C' similar to DeltaABC with base AB'=8cm.

A kite is flying at a height of 60 m above the ground. The string attached to kite is temporarily tied to a point on the ground. The inclination on the string with the ground is 60^(@). Find the length of the string assuming that there is no slack in the string.

Find the solution of sqrt(x-2)+sqrt(4-x)=sqrt(6-x).

Number of roots in a quadratic equation is

Solve the following equations : 1.5x-(5)/(3)y+2=0 (1)/(3)x+0.5y-(13)/(6)=0

Draw the two tangents from a point which is 10 cm away from the centre of a circle of raiud 5 cm. Also, measure the lengths of the tangents.

A man buys 24 shares at Rs. 150 per share having the par value of Rs. 100. If the dividend is 7.5% per annum, then the ratio of total annual income to his total inverstent is _______.

(x + 1/x)^(2) - (y + 1/y)^(2) - (xy - 1/(xy)), (x/y - y/x)=

Which is a better investment : 12%, 100rs shares at 120 or 8% 100rs shares at 90 ?

Find the radius of the circle passing through the vertices of a right angled traingle the lengths of whose perpendicular sides are 8 and 15.

Which of the following is rational?

Two circles intersect each other. Then the total number of common tangents that can be drawn to them is :

How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?

The two opposite vertices of a square are (-1,2) and (3, 2). Find the coordinates of the other two vertices.

Find the area of the shaded region in the adjacent figure, where ABCD is a square of side 10cm and semicircles are drawn with each side of the square as diameter (usepi=3.14)

In the following Distribution Where A is positive integer, has a variance of 160. Determine the value of A.

If in a certain language A is coded as 1, B is coded as 2, and so on, how is BIDDIC coded in that code?

If the angle of elevation of an object from a point 100 m above a lake is found to be 30° and the angle of depression of its image in lake is 45°, then the height of the object above the lake is

M/s. Jay Chemicals purchased a liquid soap having taxable value 10,000. Rate of GST is 18%. Find the CGST and SGST payable by M/s. Jay Chemicals.

If the 3rd and the 9th terms of an arithmetic progression are 4 and -8 respectively, which term of it is zero ?

Name the type of quadrilateral formed, if any by the following points, and give reasons for your answer : (-1, -2), (1,0), (-1, 2), (-3, 0)

Which of the following arguments are correct and which are incorrect ? Give reason if incorrect. If a dice is thrown , there are two possible outcomes :- an odd numbers or aneven number.Therefore the probability of an odd numbers is (1)/(2).

Calculate the mean deviation about median for the following data:

Calculate the mean deviation about median for the following data:

If A=[{:(,-2,3),(,4,1):}] and B=[{:(,1,2),(,3,5):}], find (i) AB (ii) BA (iii) Is AB=BA? (iv) Write the conclusion that you draw from the result obtained above in (iii).

Three identical coins are tossed together. What is the probability of obtaining : exactly one head ?

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides it is just immersed. What fraction of water overflows ?

Given that AB =4 cm , BC = 7 ,CD = 4 cm , angle ABC = 60^(@) , angle BCD= 60^(@). Construct thequardrilateral ABCD. Theconstruct the circumcirleof DeltaABCand alsostate whatothercharacteristics youobserve.

Solve the pair of linear equations : (3x)/(2)-(5y)/(3)=-2 and (x)/(3)+(y)/(3)=(13)/(6).

Floor of a room is of dimensions5mxx4m and it is covered with circular tiles of diameters 50 cm each as shown infigure . Find area of floor that remains uncovered with tiles. (use pi= 3.14)

Square : Diamond :: Circle : ?

A person bought a certain number of pens for 800. If he had bought 4 pens more for the same money, he would have paid 10 less for each pen. How many pens did he buy?

A quadratic equation ax^(2) + bx + c = 0 has two distinct real roots, if….

In what ratio is the line joining the points A (4, 4) and B (7, 7) divided by p (-1,-1) ?