3694 + Interview Questions in Maths in Class 10 Page 34 InterviewSolution

1651.	A solid is in the form of a right circular cone mounted on a hemisphere. The diameter of the base of the cone, which exactly coincides with hemisphere, is 7 cm and its height is 8 cm. The solid is placed in a cylindrical vessel of internal radius 7 cm and height 10 cm. How much water, in cm^(3), will be required to fill the vessel completely ?
Answer» ANSWER :`1,347 CM ^(3)`

Discussion

1652.	Find the volume and the total surface area of a hemisphere of radius 3.5 cm . (pi= (22)/(7))
Answer» ANSWER :`115.5 cm^2`

Discussion

1653.	A person 1.65m tall casts 1.8m shadow.At the same instance, a lamp post casts a shadow of 5.4 m.Find the height of the lamppost.
Answer» ANSWER :4.95 m

Discussion

1654.	A survey reagarding the heights ( in cm) of 50 girls of class X of a school was conducted and the following data was obtained. Findthe mean, median and mode of the above data.
Answer» Solution : (i) Mean : Mean =(Sigmaf_(i)x_(i))/(Sigmaf_(i)) =7490/50 =149.80` (ii) Median : Here, `N/2=50/2 =25` `:.` Median class is 150 -160 `:.` Median `=l_(1)+((N/2-C))/FXXI` `=150+(25-22)/20xx10` `=150+1.5=151.5` (iii) Mode : CLEARLY the modal class is 150-160 as it has the maximum frequency Mode =`l+((f_(1)-f_(0))/(2f_(1)-f_(0)-f_(2)))xxh` `=150+((20-12)/(40-12-8)) xx10` `=150+8/20xx10` =150+4=154 Hence, the mean height of the girls =149.80 cm the median height =151.5 cm and the modal height =154 cm

Discussion

1655.	How many terms of the G.P. (2)/(9),-(1)/(3),(1)/(2), . . . . . . . . . . . must be added to get the sum equal to (55)/(72) ?
Answer» ANSWER :5

Discussion

1656.	All squares are ……………… . (congruent, similar)
Answer» ANSWER :SIMILAR

Discussion

1657.	Evaluate the following (sec^(2) 60^(@) -tan ^(2) 60^(@) )/( sin ^(2) 30^(@) +cos ^(2) 30^(@) )
Answer» ANSWER :` 1`

Discussion

1658.	If the radius of a circle is doubled, what about its area ?
Answer» ANSWER :4

Discussion

1659.	State whether the following statements are true of false. If false, give a reason. If A and B are two matrices of orders 3 xx 2 and 2 xx 3 respectively, then their sum A+B is possible.
Answer» ANSWER :FALSE

Discussion

1660.	For all y ne 5, (y^(3)-6y^(2)+3y+10)/(y^(2)-10y+25)=
Answer» `(y^(2)-y+2)/(y+5)` `(y^(2)-y-2)/(y-5)` `(y^(2)+y-2)/(y+5)` `(y^(2)+y-2)/(y-5)` Solution :Since the DENOMINATOR has a lower POWER, factor that expression first. `y^(2)-10 y + 25 = (y-5)(y-5)` Cheq each numerator in the answer options to determine which polynomial gives a PRODUCT of `y^(3)-6y^(2)+3y+10` when multiplied by `(y-5). Y^(3)-6y^(2)+3y+10 = (y-5)(y^(2)-y-2)`. Then `(y^(3)-6y^(2)+3y+10)/(y^(2)-10y+25)=((y-5)(y^(2)-y-2))/((y-5)(y-5))` `= (y^(2)-y-2)/(y-5)`.

Discussion

1661.	Mention the two roots of quadratic equation ax^(2)+bx+C=0?
Answer» ANSWER :`X=(-b+sqrt(b^(2)-4AC))/(2a)` and `x=(-b-sqrt(b^(2)-4ac))/(2a)`

Discussion

1662.	Inand segBDbotside ACand AD=DC then ……..
Answer» ` BD^(2) = DCxxAC` `BD^(2) = ADxxAC` `BD^(2) = DCxx AC ` NONE of these ANSWER :A

Discussion

1663.	The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its volume .
Answer» ANSWER :`33.1%`

Discussion

1664.	The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: radius
Answer» ANSWER :`10%`

Discussion

1665.	Which term of the AP, 8, 14, 20, 26......will be 72 more than its 41st term?
Answer» ANSWER :`53^(RD)` TERM

Discussion

1666.	triangle ABC~triangle LBN. In triangleABC, AB=5.1 cm, /_B=40^(@), BC=4.8 cm, (AC)/(LN)=(4)/(7). Construct triangle ABC " and"triangle LBN.
Answer» Answer :If seg BC is DIVIDED into 4 EQUAL parts, then seg BN will be 7 times each part of seg BC. So, if we construct `triangle ABC`, point N will be on side BC, at a distance equal to 7 parts from B. Now, point L is the point of INTERSECTION of ray BA and a line through N, PARALLEL to AC. `triangle LBN` is the required triangle similar to `triangle ABC`.

Discussion

1667.	If x-2 is a factor of x^(2)-7x+2a, find the value of a.
Answer» ANSWER :a=5

Discussion

1668.	( 2tan 30 ^(@) )/( 1+tan ^(2) 45^(@) ) =(a) sin60(b) cos60(c)tan30(d)sin30
Answer» `sin 60^(@) ` ` COS 60 ^(@) ` ` tan 30^(@) ` ` sin 30 ^(@) ` ANSWER :C

Discussion

1669.	Solve the equation 3x2 - X - 7 = 0 and give your answer correct to two decimal places.
Answer» ANSWER :`1. 70 and -1.37 `

Discussion

1670.	The model of a building is constructed with the scale factor 1 : 30.If the actual volume of a tank at the top of the building is 27m^(3), find thevolume of the tank on the top of the model.
Answer» ANSWER :`1000 CM^(3)`

Discussion

1671.	A is a dealer in Meerut (UP). He supplies goods/services, worth Rs. 15,000 to a dealer B in Ratlam (M.P.). Dealer B, in turn, supplies the same goods/servies to dealer C in Jabalpur (MP) at a profit of Rs. 3,000. If rate of tax (under GST system) is 18% find : net tax payable by dealer B.
Answer» ANSWER :RS. 540

Discussion

1672.	A is a dealer in Meerut (UP). He supplies goods/services, worth Rs. 15,000 to a dealer B in Ratlam (M.P.). Dealer B, in turn, supplies the same goods/servies to dealer C in Jabalpur (MP) at a profit of Rs. 3,000. If rate of tax (under GST system) is 18% find : the cost of goods/services to the dealer C in Jabalpur (assuming that the dealer C does not sell the goods/services further).
Answer» ANSWER :RS. 21,240

Discussion

1673.	From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm. The radius of the circle is 13 cm. The radius of the circle is :
Answer» 12 cm 13 cm 5 cm None of these Answer :B

Discussion

1674.	A heap of rice is in the form of a cone of diameter 12 cm and height8 cm . Find its volume ? How much canvas cloth is required to cover the heap ? (Use pi=3.14)
Answer» ANSWER :`188.57 m^2`

Discussion

1675.	As observed from the top of a75 m high lighthouse from the sea-level, the angles of depression of two ships are 30^(@) and 45^(@). If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.
Answer» ANSWER :`75(sqrt3-1)`

Discussion

1676.	Find the ratio in which the line x + 3y -14 = 0 divides the line segment joining the points A (-2, 4) and B(3. 7).
Answer» ANSWER :k=7

Discussion

1677.	Vivek invests 4500rs in 8% 10rs shares at 15rs. He sells the shares when the price rises to 30rs, and invests the proceeds in 12% 100rs shares at 125rs. Calculate (i) the sale proceeds (ii) the number of 125rs shares he buys (iii) the change in his annual income from dividend.
Answer» ANSWER :`(i)9000RS` `(II) 72` `(III) 624rs`

Discussion

1678.	If n^(th)term of an A.P. is (2n - 1), find its 7^(th) term.
Answer» ANSWER :13

Discussion

1679.	A gardener wanted to reward a boy for his good deeds by giving some mangoes. He gave the boy two choices. He could either have 1000 mangoes at once or he could get 1 mango on the first day, 2 on the second day, 4 on the third day, 8 mangoes on the fourth day and so on for ten days. Which option should the boy choose to get the maximum number of mangoes?
Answer» ANSWER :1023

Discussion

1680.	A sphere , a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. [Hint : Diameter of the sphere is equal to the heights of the cylinder and the cone]
Answer» ANSWER :`2:3:1`

Discussion

1681.	A right circular cylinder has base radius 14 cm and height 21 cm. Find its volume.
Answer» ANSWER :`12936 cm^3`

Discussion

1682.	A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response. What is the probability of favourite colour being blue or green ?
Answer» <P>0.1 0.2 0.3 0.4 Solution :P(BLUE of green) `=(72^(@)+36^(@))/(360^(@))=(108^(@))/(360^(@))=(3)/(10)=0.3` Thus ( c ) is CORRECT option.

Discussion

1683.	A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response. What is the probability of favourite colour being red ?
Answer» <P>0.1 0.2 0.3 0.4 Solution :PROBABILITY `=("Area of region")/("Area of circle")` `=("Total ANGLE in region")/(360^(@))` P(RED) `=(36^(@))/(360^(@))=(1)/(10)=0.1` Thus (a) is correct OPTION.

Discussion

1684.	A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response. What is the probability of favourite colour being red or blue?
Answer» 0.2 0.3 0.1 0.4 Solution :P(RED or blue) = 1 - P(not red or blue) `=1-0.7=0.3` Thus (B) is CORRECT OPTION.

Discussion

1685.	A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response. What is the probability of favourite colour not being orange or green ?
Answer» 0.65 0.75 0.25 `0.50` SOLUTION :P(not orange or green) = 1 - P(orange or green) `=1-(144^(@)+36^(@))/(360^(@))=1-(180^(@))/(360^(@))=1-(1)/(2)=0.5` THUS (d) is correct OPTION.

Discussion

1686.	A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favourite colours. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response. What is the probability of favourite colour not being red or blue?
Answer» <P>0.35 0.7 0.15 `0.50` Solution :P(not red or BLUE) `=1-(36^(@)+72^(@))/(360^(@))=1-(108^(@))/(360^(@))` `=1-(3)/(10)=1-0.3=0.7` Thus (B) is correct option.

Discussion

1687.	DeltaABC~DeltaPQR. Then complete the following (AB)/(PQ)=(BC)/(square)=(square)/(PR)
Answer» ANSWER :QR,AC

Discussion

1688.	Simplify (1-cos theta ) (1+cos theta ) (1+ cot ^(2) theta) .
Answer» ANSWER :`1`

Discussion

1689.	State the co-ordinates of the following points under reflection in the line y = 0, (i) (-3, 0) (ii)(8, -5) (iii)(-1, -3)
Answer» ANSWER :(i) (-3, 0) (ii)(8, 5) (III)(-1, 3)

Discussion

1690.	Step 1 : Take a chart and cut it like a triangle as shown in Fig. (a). Step 2 : Then fold it along the symmetric line AD. Then C and B will be one upon the other. Step 3 : Similarly fold it along CE, then B and A will be one upon the other. Step 4 : Similarly fold it along BF, then A and C will be one upon the other.Find AB, AC, BD, DC using a scale. Find (AB)/(AC), (BD)/(DC) check if they are equal ? In the three cases, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle. What do you conclude from this activity ?
Answer» ANSWER :`(AB)/(AC)=(BD)/(DC)`

Discussion

1691.	Find the nature of the roots of the following quadratic equations. If real roots exist, find them. (ii) 3x^(2)-4 sqrt(3)+4=0
Answer» Answer :EQUAL roots; `(2)/(sqrt(3)), (2)/(sqrt(3))`

Discussion

1692.	Evaluate tan 26^(@) tan 64^(@)
Answer» ANSWER :`1`

Discussion

1693.	Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. (They have less number of stairs than required forward stairs). Who takes least number of steps to reach near hundred?
Answer» Amar Akbar Anthony All of them take equal NUMBER of STEPS Solution :Amar will take 32 steps, Akbar will take 19 steps and Anthony will take 13 steps to REACH to 96 steps, 95 steps and 91 steps respectively. Thus (c) is correct option.

Discussion

1694.	Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. (They have less number of stairs than required forward stairs). How many times can they meet in between on same step?
Answer» 3 4 5 No, they cannot MEET in between on same step. Solution :LCM (3, 5, 7) =105 step. Since, total steps are 100 steps, they cannot meet in between on same step. Thus (d) is CORRECT option.

Discussion

1695.	Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. (They have less number of stairs than required forward stairs). Who reaches the nearest point?
Answer» Amar Akbar Anthony All TOGETHER reach to the nearest POINT. Solution :Amar will reach up to 93 steps then he will go for 5 steps up and 2 steps down hence covering 96 steps. Since 100 th step is final, so he will not cover more steps. Akbar will reach up to 95 steps, since 100 th step is final, so he will not cover more steps. Anthony will reach up to 91 steps, since 100 th step is final, so she will not cover more steps. THUS akbar REACHES the nearest point. Thus (b) is correct OPTION.

Discussion

1696.	Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. (They have less number of stairs than required forward stairs). What is the second stair where any two out of three will meet together?
Answer» Amar and Akbar will meet after 21 steps. Akbar and ANTHONY will meet after 35 steps. Amar and Anthony will after 21 steps. Amar and Anthony will after 35 steps. Solution :As already calculated , LCM(3, 7) =21 Thus (B) is CORRECT OPTION.

Discussion

1697.	Amar, Akbar and Anthony are playing a game. Amar climbs 5 stairs and gets down 2 stairs in one turn. Akbar goes up by 7 stairs and comes down by 2 stairs every time. Anthony goes 10 stairs up and 3 stairs down each time. Doing this they have to reach to the nearest point of 100th stairs and they will stop once they find it impossible to go forward. (They have less number of stairs than required forward stairs). What is the first stair where any two out of three will meet together?
Answer» AMAR and AKBAR will MEET for the first time after 15 steps. Akbar and Anthony will meet for the first time after 35 steps. Amar and Anthony will meet for the first time after 21 steps. Amar and Akbar will meet for the first time after 21 steps. Solution :Since LCM(3, 5)=15 , LCM(5, 7)=35 , LCM(3, 7)=21. Since, 15 is the smallest so Amar and Akbar will meet for the first time after 15 steps. Thus (a) is correct option.

Discussion

1698.	For what least value of n, (2^(6n) - 6^(2n)) is divisible by ? n being even +ve,
Answer» ANSWER :100

Discussion

1699.	If the first two consecutive terms of a G.P. are 125 and 25, find its 6^(th) term.
Answer» ANSWER :`(1)/(25)`

Discussion

1700.	A dice is thrown once. Find the probability of getting : a number between 2 and 6.
Answer» ANSWER :`1/2`

Discussion

Explore topic-wise InterviewSolutions in .

Find the volume and the total surface area of a hemisphere of radius 3.5 cm . (pi= (22)/(7))

A person 1.65m tall casts 1.8m shadow.At the same instance, a lamp post casts a shadow of 5.4 m.Find the height of the lamppost.

A survey reagarding the heights ( in cm) of 50 girls of class X of a school was conducted and the following data was obtained. Findthe mean, median and mode of the above data.

How many terms of the G.P. (2)/(9),-(1)/(3),(1)/(2), . . . . . . . . . . . must be added to get the sum equal to (55)/(72) ?

All squares are ……………… . (congruent, similar)

Evaluate the following (sec^(2) 60^(@) -tan ^(2) 60^(@) )/( sin ^(2) 30^(@) +cos ^(2) 30^(@) )

If the radius of a circle is doubled, what about its area ?

State whether the following statements are true of false. If false, give a reason. If A and B are two matrices of orders 3 xx 2 and 2 xx 3 respectively, then their sum A+B is possible.

For all y ne 5, (y^(3)-6y^(2)+3y+10)/(y^(2)-10y+25)=

Mention the two roots of quadratic equation ax^(2)+bx+C=0?

Inand segBDbotside ACand AD=DC then ……..

The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its volume .

The surface area of a solid sphere is increased by 21% without changing its shape. Find the percentage increase in its: radius

Which term of the AP, 8, 14, 20, 26......will be 72 more than its 41st term?

triangle ABC~triangle LBN. In triangleABC, AB=5.1 cm, /_B=40^(@), BC=4.8 cm, (AC)/(LN)=(4)/(7). Construct triangle ABC " and"triangle LBN.

If x-2 is a factor of x^(2)-7x+2a, find the value of a.

( 2tan 30 ^(@) )/( 1+tan ^(2) 45^(@) ) =(a) sin60(b) cos60(c)tan30(d)sin30

Solve the equation 3x2 - X - 7 = 0 and give your answer correct to two decimal places.

The model of a building is constructed with the scale factor 1 : 30.If the actual volume of a tank at the top of the building is 27m^(3), find thevolume of the tank on the top of the model.

A is a dealer in Meerut (UP). He supplies goods/services, worth Rs. 15,000 to a dealer B in Ratlam (M.P.). Dealer B, in turn, supplies the same goods/servies to dealer C in Jabalpur (MP) at a profit of Rs. 3,000. If rate of tax (under GST system) is 18% find : net tax payable by dealer B.

From a point Q, the length of the tangent to a circle is 12 cm and the distance of Q from the centre is 13 cm. The radius of the circle is 13 cm. The radius of the circle is :

A heap of rice is in the form of a cone of diameter 12 cm and height8 cm . Find its volume ? How much canvas cloth is required to cover the heap ? (Use pi=3.14)

As observed from the top of a75 m high lighthouse from the sea-level, the angles of depression of two ships are 30^(@) and 45^(@). If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Find the ratio in which the line x + 3y -14 = 0 divides the line segment joining the points A (-2, 4) and B(3. 7).

Vivek invests 4500rs in 8% 10rs shares at 15rs. He sells the shares when the price rises to 30rs, and invests the proceeds in 12% 100rs shares at 125rs. Calculate (i) the sale proceeds (ii) the number of 125rs shares he buys (iii) the change in his annual income from dividend.

If n^(th)term of an A.P. is (2n - 1), find its 7^(th) term.

A sphere , a cylinder and a cone have the same radius and same height. Find the ratio of their volumes. [Hint : Diameter of the sphere is equal to the heights of the cylinder and the cone]

A right circular cylinder has base radius 14 cm and height 21 cm. Find its volume.

DeltaABC~DeltaPQR. Then complete the following (AB)/(PQ)=(BC)/(square)=(square)/(PR)

Simplify (1-cos theta ) (1+cos theta ) (1+ cot ^(2) theta) .

State the co-ordinates of the following points under reflection in the line y = 0, (i) (-3, 0) (ii)(8, -5) (iii)(-1, -3)

Find the nature of the roots of the following quadratic equations. If real roots exist, find them. (ii) 3x^(2)-4 sqrt(3)+4=0

Evaluate tan 26^(@) tan 64^(@)

For what least value of n, (2^(6n) - 6^(2n)) is divisible by ? n being even +ve,

If the first two consecutive terms of a G.P. are 125 and 25, find its 6^(th) term.

A dice is thrown once. Find the probability of getting : a number between 2 and 6.