3694 + Interview Questions in Maths in Class 10 Page 16 InterviewSolution

751.	Describe the locus of points at distances greater than or equal to 35 mm from a given point.
Answer» ANSWER :35 MM

Discussion

752.	Hema’s age is 4 times the age of Mary. Write a linear equation in two variables to represent this information.
Answer» ANSWER :(i) 6x - 5y - 10 = 0 (ii) 4X + 6Y - 10 = 0 (iii) 6x +9Y - 24 = 0

Discussion

753.	A(1,7), B(2,4) and C(k,5) are the vertices of a right triangle . Find k (1) if angle A = 90^(@) (2) if angle B = 90^(@)and (3) if angle C = 90^(@)
Answer» ANSWER :(1) k = - 5 (2) k = 5 (3) k = 0 or k = 3

Discussion

754.	A cylindrical pencil is sharpened to produce a perfect cone at one end with no over all its length. The diameter of the pencil is 1 cm and the length of the conical portion is 2 cm. Calculate the volume of the peels. Give your answer correct to two places if it is in decimal [use pi=(355)/(113)]
Answer» ANSWER :`1.05 cm^3`

Discussion

755.	A person, walking 20 mts from a point towards a flagpost along a horizontal passing through its base, observes that its angle of elevation changes from 30^(@) to 45^(@) . Find the height of the flag-post.
Answer» ANSWER :`10(sqrt(3)+1)`MTS

Discussion

756.	On a particular day, the number of vehicles passing a crossing is given below: {:("Vehicle","Frequency"),("Two wheeler",52),("Three wheeler",51),("Four wheeler",77):} What is the probability of a two wheeler passing the crossing on that day?
Answer» 0.26 0.71 0.385 0.615 Answer :A

Discussion

757.	Find the roots of the equation x-(1)/(3x)=(1)/(6)(x ne 0)
Answer» ANSWER :`(2)/(3) and -(1)/(2)`

Discussion

758.	Use the properties of proportionality to solve : (sqrt(12x+1)+sqrt(2x-3))/(sqrt(12x+1)-sqrt(2x-3))=3/2
Answer» ANSWER :2

Discussion

759.	Determine k such that (3k - 2), (4k - 6) and (k + 2) are three consecutive terms of AP.
Answer» ANSWER :`RARR k = (12)/(4) = 3`.

Discussion

760.	Determine whether the following points are collinear A(-1, -1), B(0, 1), C(1, 3)
Answer» ANSWER :A, B, C are COLLINEAR

Discussion

761.	Which is the minimum number of straight lines that is needed to construct the following figure
Answer» 12 13 15 18 Answer :B

Discussion

762.	If 50 shares of FV 10 were purchased for MV of 25. Company declared 30% dividend on the shares then find i. Sum investment ii. Dividend received iii. Rate of return.
Answer» Answer :(i) 1250 (II) 150 (III) 12%

Discussion

763.	The volume of a sphere is 38808 cm^(3), find its diameter and the surface area.
Answer» ANSWER :`42 CM; 5544 cm ^(2)`

Discussion

764.	Find the sum of the AP 3, 9/2 , 6,15/2 ...... to 25 terms.
Answer» ANSWER :525

Discussion

765.	If the height of the cylindrical part of a hemisphere is equal to the radius of the semi-circle of it, then the total volume of the hemisphere is equal to ________ cubic-units.
Answer» ANSWER :`3/2 PI R^(3)`

Discussion

766.	Solve : sqrt((x)/(1-x))+sqrt((1-x)/(x))=2(1)/(6), x ne 0 "and" x ne 1.
Answer» ANSWER :`X=(9)/(13)`, or `(4)/(13)`

Discussion

767.	Sides AB and BC and median AD of a DeltaABC are respectively proportional to sides PQ and QR and median PM of DeltaPQR (see the given figure). Show that DeltaABC ~ DeltaPQR.
Answer» ANSWER :SAS CRITERION, `DELTAABC ~ DELTAPQR`

Discussion

768.	If two tangents from point P to a circle are inclinedto each other at a angle of 14 0^(@), at what angle will the radii from the points of contact of those tangents be inclined ?
Answer» ANSWER :`40^(@)`

Discussion

769.	In the given Fig. 12.30, find the area of the shaded region.
Answer» ANSWER :`30.50cm^2`

Discussion

770.	Write the next three terms of the given arithmetic progression: i] 3, -2, -7, ….. ii] 0, 5, 10,….. iii] 119, 136, 157, ….
Answer» Answer :i] NEXT terms: `-7-5=-12` `-12 - 7 = -19` `-19 -7 = -26` ii] Next terms: `10+5 = 15 ` `15+ 5 = 20` `20 + 5 = 25` iii] Next terms: `153+17 = 170` `170 + 17 = 187` `187 + 17 = 204`

Discussion

771.	Using prime factorisation, find the HCF and LCM of : , (i) 36, 84(ii) 23,31 (iii) 96,404(iv) 144,198(v) 396, 1080(vi) 1152, 1664In each case, verify that :HCFxxLCM = product of given number .
Answer» Answer :(i) HCF= 12, LCM= 252,(ii) HCF= 1, LCM= 713 (iii) HCF = 4, LCM= 9696, (IV) HCF = 18, LCM= 1548 (v) HCF= 36, LCM= 11880,(iv) HCF = 18, LCM= 14976

Discussion

772.	One fourth of a group of people claim theyare creative, twice the squareroot of the group claim tobe caringand the remaining15 claim they are optimistic . Find the total number of people in the group.(a)Howmany personsin the group are creative ?(b)According to you which one of the above three values is more importantfor developmentof a society ?
Answer» Answer :36 (a)9 persons (B)HENCE, any value with JUSTIFICATION is CORRECT.

Discussion

773.	A point P is reflected in the origin. Co-ordinates of its image are (-2, 7). Find the co-ordinates of the image of P under reflection in the x-axis.
Answer» ANSWER :(2,7)

Discussion

774.	From a circular cylinder of diameter 10 cm and height 12 cma conical cavity of the same base radius and of the same height in hollowed out. Find the volume and the whole surfce of the remianing solid .Leave the answer in pi.
Answer» Answer :200 `pi CM^(3)` and 210 `pi cm^(2)`

Discussion

775.	The product of 3^(rd) and 8^(th) terms of a G.P. is 243. If its 4^(th) term is 3, find its 7^(th) term.
Answer» ANSWER :81

Discussion

776.	The total surface area of a hemi-sphere is how much times the square of its radius.
Answer» `PI` `4pi` `3pi` `2pi` ANSWER :C

Discussion

777.	Find the angle in radians between the hands of a clock at 7: 20 PM
Answer» ANSWER :`(5PI)/(9)`

Discussion

778.	P^^Q means (P+Q)/(Q-P)andPvvQ means (Q-P)/(Q+P) Answer the following questions: 5^^6+5vv6
Answer» `100/11` `108/11` `113/11` `115/11` ANSWER :A

Discussion

779.	A. circle is circumscribed an equilateral triangle ABC whereAB=6cm the area of the circumcircle is find the value of k cm^2.
Answer» ANSWER :YES

Discussion

780.	A man invests 3072rs in a company paying 5% per annum, when its 10rs share can be bought for 16rs 16 each. Find. (i) his annual income (ii) his percentage income on his investment
Answer» ANSWER :`(i)96RS` `(ii) 3.125%=3.(1)/(8)%`

Discussion

781.	Pointing towards a person, a man said to a woman "His mother is the only daughter of your father”. How is the woman related to that person?
Answer» Daughter Sister MOTHER Wife Solution :The only daughter of WOMAN.s father is she herself. So, the PERSON is woman.s SON i.e. The woman is the person.s mother.

Discussion

782.	Centre of a circle Q is on the Y-axis. The circle passes through the points (0, 7) and (0, -1). If it intersects the positive X-axis at (P, 0), what is the value of ‘P’?
Answer» <P> ANSWER :`:. p PM SQRT(7)`

Discussion

783.	The owner of a taxi company decides to run all the taxis on CNG fuel instead of petrol/diesel. Taxi charges in city comprise of fixed charges together with the charge for the distance covered. For a journey of 13 km, the charge is Rs. 129 and for a journey of 22 km, the charge is Rs. 210. [i]What will a person have to pay for traveling a distance of 32 km? (ii) Why did he decided to use CNG for his taxi as fuel
Answer» Answer :(i) For traveling 32 km, a PERSON pays = Rs. 300 (II) CNG is pollution free. It is good for the ENVIRONMENT and cheaper than PETROL and diesel.

Discussion

784.	A vertical pole of length 6 m casts a shadow 4 m long on the ground and the same time a tower casts a shadow 28 m long. Find the height of the tower.
Answer» ANSWER :42 m

Discussion

785.	What is Nitin's rank from the top in a class of forty students? I. There are ten students between Nitin and Deepak. II. Deepak is twentieth from the top.
Answer» if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question, if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question, if the data either in statement I alone or in statement II alone are sufficient to answer the question, if the data given in both STATEMENTS I and II together are not sufficient to answer the question, Solution :Since there are ten students between NITIN and Deepak, so Nitin may be ELEVEN ranks above or below Deepak. THUS, Nitin may be `9^(th)or31^(st)` from the top.

Discussion

786.	Fill up blanks in each of the following:(a) The negation of the statement "Zero is a positive number" is_____.(b) The negation of the statement "For every real number x, either x > 1 or x < 1." is_____.(c) The Converse of the statement "If a number x is even, then x^(2) is also even" is_____.(d) The Converse of the statement "If n is a prime number, then n is odd." is____.(e) The quantifier used in the statement "There exists a number which is equal to its square" is_____.(f) The Contra positive of the statement "If a triangle is equilateral, it is isosceles" is_____.
Answer» Answer :(a) Zero is not a POSITIVE number. (b) There exists a real number X such that `x <=1` and `x>=1`. (c) If `x^(2)` is even, then x is also even. (d) If n is odd then n is PRIME number. (e) There Exists. (f) If triangle is not ISOSCELES then it is not equilateral.

Discussion

787.	Statements: 1. All roads are poles. 2. No pole is a house. Conclusions: 1. Some roads are houses. 2. Some houses are poles.
Answer» If only CONCLUSION I FOLLOWS, If only conclusion 2 follows, If either conclusion 1 or 2 follows, If NEITHER conclusion 1 nor 2 follows, Solution :Clearly from the two STATEMENTS neither 1 nor 2 follow.

Discussion

788.	A mansion has 12 right cylindrical pillars each having radius 50cm and height 3.5m. Find the cost to paint the lateral surface of the pillars at Rs.20 per square metre.
Answer»

Discussion

789.	Is -156 a term of the AP 17, 14, 11, 8 .......... ?
Answer» ANSWER :no

Discussion

790.	Angle C of a DeltaACB is right angle in which AB=29 units, BC = 21 units and angle ABC=theta the value of tan theta is :
Answer» `(21)/(29)` `(20)/(29)` `(20)/(21)` `(29)/(20)`. ANSWER :C

Discussion

791.	write the set Qof rational numbers in the rule method.
Answer» <P> SOLUTION :`{(p)/(Q)\|p,q in I q != 0`

Discussion

792.	Choose the correct answer and give justification for each. In the figure XY and X^(1)Y^(1) are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X^(1)Y^(1) at B then /_AOB=
Answer» `80^(@)` `100^(@)` `90^(@)` `60^(@)` Answer :C

Discussion

793.	A metallic cylinder has radius 3 cm and height 5 cm. To reduce it weight ,a conical hole is drilled in the cylinder .The conical hole has a of metal left in depth 8//9cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out inconical shape.
Answer» ANSWER :`502.04 CM^(2)`

Discussion

794.	Which term of the AP: 21,18,15,…….. Is -81?
Answer» ANSWER :n=8

Discussion

795.	Find the slope of the lines passing through the given points E(-4, -2) and F(6, 3)
Answer» ANSWER :`EF = (1)/(2)`

Discussion

796.	A company manufactures two type of novelty souvenirs made of plywood, Souvenirs of type A recquire 8 minutes each for cutting and 10 minuteseach for assembling. Souvenirs of type B require10 minutes each for cutting and 15 minutes each for assembling. There are 4 hours available forfor assembling. THere are 4 hours available for cutting and 5 hours available for assembling. The profit is 60 paise on each itme of type A and 75 paise on eachitem of tyep B.Formulate the above informationas a linearprogramming problem.
Answer» ANSWER :`8x+10y le240` `10x+15y le 300` ` x GE 0, y ge 0`

Discussion

797.	Check whether the following equations are quadratic or not . (i) x^(2) - 6x - 4 = 0 (ii) x^(3) - 6x^(2) + 2 x -1 = 0 (iii)7x = 2x^(2) (iv) x^(2) + (1)/(x^(2)) = 2 (v) (2x + 1 ) (3 x + 1 ) = 6 (x - 1) (x - 2) (vi) 3y^(2) = 192
Answer» ANSWER :(i) Yes , (II) No , (iii) Yes , (iv) No , (V) No , (VI) Yes

Discussion

798.	Divide 2x^2 + 3x + 1 by x + 2.
Answer» ANSWER :`-2 and -5`

Discussion

799.	Ashok and Sandeep invest 18000rs each in buying shares of two different companies. Ashok buys 7.5% 100rs shares at a discount of 20%, whereas Sandeep buys 50rs shares at a premium of 20% . If both receive equaldividend at the end of the year, find the rate of dividend received by Sandeep.
Answer» ANSWER :`11.25%`

Discussion

800.	Describe the locus of point at distances less than or equal to 2.5 cm from a given point.
Answer» ANSWER :2.5 CM

Discussion

Explore topic-wise InterviewSolutions in .

Describe the locus of points at distances greater than or equal to 35 mm from a given point.

Hema’s age is 4 times the age of Mary. Write a linear equation in two variables to represent this information.

A(1,7), B(2,4) and C(k,5) are the vertices of a right triangle . Find k (1) if angle A = 90^(@) (2) if angle B = 90^(@)and (3) if angle C = 90^(@)

A cylindrical pencil is sharpened to produce a perfect cone at one end with no over all its length. The diameter of the pencil is 1 cm and the length of the conical portion is 2 cm. Calculate the volume of the peels. Give your answer correct to two places if it is in decimal [use pi=(355)/(113)]

A person, walking 20 mts from a point towards a flagpost along a horizontal passing through its base, observes that its angle of elevation changes from 30^(@) to 45^(@) . Find the height of the flag-post.

On a particular day, the number of vehicles passing a crossing is given below: {:("Vehicle","Frequency"),("Two wheeler",52),("Three wheeler",51),("Four wheeler",77):} What is the probability of a two wheeler passing the crossing on that day?

Find the roots of the equation x-(1)/(3x)=(1)/(6)(x ne 0)

Use the properties of proportionality to solve : (sqrt(12x+1)+sqrt(2x-3))/(sqrt(12x+1)-sqrt(2x-3))=3/2

Determine k such that (3k - 2), (4k - 6) and (k + 2) are three consecutive terms of AP.

Determine whether the following points are collinear A(-1, -1), B(0, 1), C(1, 3)

Which is the minimum number of straight lines that is needed to construct the following figure

If 50 shares of FV 10 were purchased for MV of 25. Company declared 30% dividend on the shares then find i. Sum investment ii. Dividend received iii. Rate of return.

The volume of a sphere is 38808 cm^(3), find its diameter and the surface area.

Find the sum of the AP 3, 9/2 , 6,15/2 ...... to 25 terms.

If the height of the cylindrical part of a hemisphere is equal to the radius of the semi-circle of it, then the total volume of the hemisphere is equal to ________ cubic-units.

Solve : sqrt((x)/(1-x))+sqrt((1-x)/(x))=2(1)/(6), x ne 0 "and" x ne 1.

Sides AB and BC and median AD of a DeltaABC are respectively proportional to sides PQ and QR and median PM of DeltaPQR (see the given figure). Show that DeltaABC ~ DeltaPQR.

If two tangents from point P to a circle are inclinedto each other at a angle of 14 0^(@), at what angle will the radii from the points of contact of those tangents be inclined ?

In the given Fig. 12.30, find the area of the shaded region.

Write the next three terms of the given arithmetic progression: i] 3, -2, -7, ….. ii] 0, 5, 10,….. iii] 119, 136, 157, ….

Using prime factorisation, find the HCF and LCM of : , (i) 36, 84(ii) 23,31 (iii) 96,404(iv) 144,198(v) 396, 1080(vi) 1152, 1664In each case, verify that :HCFxxLCM = product of given number .

A point P is reflected in the origin. Co-ordinates of its image are (-2, 7). Find the co-ordinates of the image of P under reflection in the x-axis.

From a circular cylinder of diameter 10 cm and height 12 cma conical cavity of the same base radius and of the same height in hollowed out. Find the volume and the whole surfce of the remianing solid .Leave the answer in pi.

The product of 3^(rd) and 8^(th) terms of a G.P. is 243. If its 4^(th) term is 3, find its 7^(th) term.

The total surface area of a hemi-sphere is how much times the square of its radius.

Find the angle in radians between the hands of a clock at 7: 20 PM

P^^Q means (P+Q)/(Q-P)andPvvQ means (Q-P)/(Q+P) Answer the following questions: 5^^6+5vv6

A. circle is circumscribed an equilateral triangle ABC whereAB=6cm the area of the circumcircle is find the value of k cm^2.

A man invests 3072rs in a company paying 5% per annum, when its 10rs share can be bought for 16rs 16 each. Find. (i) his annual income (ii) his percentage income on his investment

Pointing towards a person, a man said to a woman "His mother is the only daughter of your father”. How is the woman related to that person?

Centre of a circle Q is on the Y-axis. The circle passes through the points (0, 7) and (0, -1). If it intersects the positive X-axis at (P, 0), what is the value of ‘P’?

A vertical pole of length 6 m casts a shadow 4 m long on the ground and the same time a tower casts a shadow 28 m long. Find the height of the tower.

What is Nitin's rank from the top in a class of forty students? I. There are ten students between Nitin and Deepak. II. Deepak is twentieth from the top.

Statements: 1. All roads are poles. 2. No pole is a house. Conclusions: 1. Some roads are houses. 2. Some houses are poles.

A mansion has 12 right cylindrical pillars each having radius 50cm and height 3.5m. Find the cost to paint the lateral surface of the pillars at Rs.20 per square metre.

Is -156 a term of the AP 17, 14, 11, 8 .......... ?

Angle C of a DeltaACB is right angle in which AB=29 units, BC = 21 units and angle ABC=theta the value of tan theta is :

write the set Qof rational numbers in the rule method.

Choose the correct answer and give justification for each. In the figure XY and X^(1)Y^(1) are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X^(1)Y^(1) at B then /_AOB=

A metallic cylinder has radius 3 cm and height 5 cm. To reduce it weight ,a conical hole is drilled in the cylinder .The conical hole has a of metal left in depth 8//9cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out inconical shape.

Which term of the AP: 21,18,15,…….. Is -81?

Find the slope of the lines passing through the given points E(-4, -2) and F(6, 3)

Check whether the following equations are quadratic or not . (i) x^(2) - 6x - 4 = 0 (ii) x^(3) - 6x^(2) + 2 x -1 = 0 (iii)7x = 2x^(2) (iv) x^(2) + (1)/(x^(2)) = 2 (v) (2x + 1 ) (3 x + 1 ) = 6 (x - 1) (x - 2) (vi) 3y^(2) = 192

Divide 2x^2 + 3x + 1 by x + 2.

Ashok and Sandeep invest 18000rs each in buying shares of two different companies. Ashok buys 7.5% 100rs shares at a discount of 20%, whereas Sandeep buys 50rs shares at a premium of 20% . If both receive equaldividend at the end of the year, find the rate of dividend received by Sandeep.

Describe the locus of point at distances less than or equal to 2.5 cm from a given point.