1847 + Interview Questions in Maths in Class 9 Page 33 InterviewSolution

1601.	Find the total surface area of a hemisphere of radius 10 cm . (use pi =3.14
Answer» ANSWER :` 942( 6)/(7) CM ^(2) `

Discussion

1602.	Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.
Answer» ANSWER :6CM

Discussion

1603.	Axioms are assumed
Answer» definitions theorems universal truth SPECIFIC to geometry universal TRUTHS in all branches of MATHEMATICS SOLUTION :AXIOMS are assumed universal truths in all branches of mathematics

Discussion

1604.	Factorise : x^(3) - 3x^(2) - 9x - 5
Answer» ANSWER :`(x+1)(x+1)(x-5)`

Discussion

1605.	A loan of Rs 18900 is to be paid back in two equal half yearly instalment if the interest is compounded half yearly at 20% per annum then the interest is (in rupees)
Answer» RS 2880 Rs 3000 Rs 3178 Rs 3380 Solution :USE the CONCEPT of compound interest

Discussion

1606.	Find A, if : sin2A=1
Answer» ANSWER :`A=45^(@)`

Discussion

1607.	The marks obtained by 40 students of class IX in an examination are given below: 23,5,12,16,8,6,12,8,18,2,16,10,2,23,7,9,12,20,0,3,5,16,18,3,17,7,23,18,13,10,21,7,1,24,20,15,13,21,13,5. Present the data in the form of a frequency distribution using the same class size, starting with class 0-5 (where 5 is not included.)
Answer» Solution :Minimum observation is 0 and MAXIMUM observation is 24. The classes of EQUAL size covering the GIVEN DATA are: 0-5, 5-10, 10-15, 15-20 and 20-25. Thus, the frequency DISTRIBUTION may be given as under:

Discussion

1608.	A metal pipe is 77 cm .long .The inner diameter of a cross section is 4 cm. the outer diameter being 4.4 cm .Find its (i) inner curved surface area outer curved surface area Total surface area.
Answer» ANSWER :`(i) 968 cm ^(2) ` (II) `10648 cm ^(2) ` (III) ` 2035.44 cm ^(2) `

Discussion

1609.	Find the value of : tan30^(@)tan60^(@)
Answer» ANSWER :1

Discussion

1610.	Without actual calculating the cubes, find the vlaue of each of the following (i) (-10) ^(3) + (7) ^(3) + (3)^(3) (ii) (28) ^(3) + (-15)^(3) + (-13)^(3) (iii)((1)/(2)) ^(3) + ((1)/(3)) ^(3) -((5)/(6)) ^(3) (iv) (0.2)^(3) - (0.3) ^(3) +(0.1)^(3)
Answer» Answer :(i) `-630` (ii) `16380` \|(III) `(-5)/(12) ` (IV) `-0.018`

Discussion

1611.	Construct a Delta ABC in which AB=4.5 cm, BC=6 cm and median AD=4 cm.
Answer» Solution :STEP OF CONSTRUCTION (i) Draw a line segment `AB=4.5` cm. (II) With `A` as CENTRE and radius equal to `4 cm`, draw an arc. (III) With `B` as centre and radius `=1/2 BC=3` cm, draw another arc, CUTTING the previous arc at `D`. (iv) Join `BD` and produce it to `C` such that `BC=6` cm. (v) Join `AC`. Then, `Delta ABC` is the required triangle.

Discussion

1612.	In triangle PQR, ifangle R gt angleQ then
Answer» `PQ GT PR` `QR gt PQ` `PR LT PQ` `PQ gt QR`

Discussion

1613.	ABC is a triangle. Locate a point in the interior of triangle ABC which is equidistant from all the vertices of triangle ABC
Answer» ANSWER :PC

Discussion

1614.	Simplify the following expressions : (sqrt5+sqrt2)^(2)
Answer» ANSWER :`7+2sqrt(10)`

Discussion

1615.	Calculate the amount, if Rs 15,000 is lent at compound interest for 2 years and the rates for the successive years are 8% p.a. and 10% p.a. respectively.
Answer» ANSWER :RS 17,820

Discussion

1616.	Write which of the following statement are true and which are false (i) A simple closed figure made up of three or more line segments is called a polygon (ii) Part of a line with two end points is called a line segment (iii) In geometry we take a point a line and plane as undefined terms (iv) Euclid fourth axiom says that everything equals itself (v) The Euclidean geometry is valid only for figure in the plane (vi) A figure formed by two rays with a common initial point is called an angle
Answer» Solution :(i)TRUE(II) True (iii) True (iv) True (v) True as it FAILS on the curved SURFACES(vi) True

Discussion

1617.	To know the opinion of the students about the subject statistics , a survey of 200 students was conducted . The data is recorded in the following table : {:("Opinion ","Number of students"),("Like",135),("Dislike",65):} Find the probability that a student chosen at random Does not like it.
Answer» ANSWER :`13/40`

Discussion

1618.	To know the opinion of the students about the subject statistics , a survey of 200 students was conducted . The data is recorded in the following table : {:("Opinion ","Number of students"),("Like",135),("Dislike",65):} Find the probability that a student chosen at random Likes statistics
Answer» ANSWER :`27/40`

Discussion

1619.	If the mean of 10, 12, 18, 13, P and 17 is 15, find the value of P.
Answer» ANSWER :20

Discussion

1620.	A certain sum of money at simple interest increases by 50% in 5 years. What will be the compound interest, compounded annually on Rs 13,000 for 3 years at the same rate?
Answer» SOLUTION :RS 4303

Discussion

1621.	ABCD is a rectangle . If AB=10 cm and ar(ABCD)=150 cm^2 , then BC=____ cm.
Answer» 7.5 15 30 12 Answer :A

Discussion

1622.	Rationalise the denominator of (1)/(4+sqrt5)
Answer» ANSWER :`(4-sqrt5)/(11)`

Discussion

1623.	In a businessP,Q,R and S arefourpartners. Psinvestmentis twice R 'sinvestment Q 'sinvestment is (1)/(4) ofS'sinvestment and P and Qinvestedequally . If thetotalprofitat the end ofthe year is Rs 13,000then findthe sumof the shareof p andR in theprofit.
Answer» `Rs 10,000` `Rs 3000` `Rs 4000` `Rs 5000` Solution :(i) Usingthe GIVENDATA findthe ratioof theinvestments of P,Q,R and S (ii) LET THEINVESTMENT of A and B BERS x each (iii) Now , find theinvestment of C and Din termsof x (iv) Ratioof shares ofprofits is equalto theratioof theirinvestments

Discussion

1624.	If the mean of the following frequency distribution is 26.7, find the missing frequency f:
Answer» ANSWER :10

Discussion

1625.	100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having nogirl
Answer» ANSWER :0.08

Discussion

1626.	100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having One girl.
Answer» ANSWER :0.8

Discussion

1627.	100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having two girls
Answer» ANSWER :0.12

Discussion

1628.	If 4cos^(2)x=3 and x is an acute angle, find the value of : sin2x
Answer» ANSWER :`SQRT(3)/2`

Discussion

1629.	Find the value of x in the given figure.
Answer» ANSWER :`30^(@)`

Discussion

1630.	Find an irrational number between (5)/(7) and (7)/(9). How many more there may be?
Answer» ANSWER :`(SQRT5)/(3)`, INFINITE SOLUTIONS

Discussion

1631.	State the coefficient of x^(2) in each of the following polynomials : (3)/(2)x^(2) - (5)/(4)x +1
Answer» ANSWER :`(3)/(2)`

Discussion

1632.	Ramapada had just enough money to purchase either 30 pens or 50 pencils . He decides tospends only 80% of his money and buys 10 pens . At themaximum howmanypencils can he buy with theremainingmoney that he has ?
Answer» 23 24 25 26 Solution :ASSUMETHAT Ramapada have RS 150 .then findthe CP of penand pencil.

Discussion

1633.	Find the angle in radian through which a pendulum swings if its length is 75cm and the tip describes an arc of length 10cm.
Answer» ANSWER :.5.6 SECOND

Discussion

1634.	Find the remainder when x^(4) + x^(3) - 2x^(2) + x +1 is divide by x-1.
Answer» ANSWER :2

Discussion

1635.	In triangle ABC, AD is the perpendicular bisector of BC (see the given figure). Show that triangle ABC is an isosceles triangle in which AB = AB .
Answer» ANSWER :AC

Discussion

1636.	(a) The total surface of a sphere is 676 pi cm^(2). Find the radius of the sphere. (b) The total surface of a sphere is 4 pi cm^(2). Find the volume and diameter of the sphere. (c ) The total surface of a sphere is 1386 cm^(2). Find the diameter of the sphere. (d) The total surface of a sphere is 3600 pi cm^(2). Find the volume of the sphere.
Answer» Answer :(a) 13 CM (B) `(4PI)/(3)cm^(3), 2cm` (c )21 cm (d) `36000 pi cm^(3)`

Discussion

1637.	State true or false .The region enclosed by a chord and the minor arc isminor segment
Answer» ANSWER :1

Discussion

1638.	Find p(0), p(1) and p(2) for each of the following polynomials : p(y) = y^(2) - y +1
Answer» ANSWER :1,1,3

Discussion

1639.	Prove that the successive joiningof the points (4,3) (5,6) and (3,5) produce a square.
Answer» ANSWER :N/A

Discussion

1640.	Given that angleA and angleB are complementary angles. If angleA=angleB+20^(@), then find angleA and angleB
Answer» ANSWER :`angleA=55^(@),angleB=35^(@)`

Discussion

1641.	In trianglePQR , PM is an altitude and QR is the hypotenuse. If QR=12 cm and PM=6 cm, then ar(PQR)=___ cm^2
Answer» 18 72 36 24 Answer :C

Discussion

1642.	For a given cylinder, the radius of the base is 7 cm and its height is 15 cm. What will be the area of its base and its top ?
Answer» ANSWER :154 `CM^(2)`, 154 `cm^(2)`

Discussion

1643.	If sqrt((sqrt10 +1)/(sqrt10-1)) thenfind the value of (x 1/x)
Answer» ANSWER :(a) ` 2/3`

Discussion

1644.	Find x, if 9,x,14,18,x,x,8,10 and 4 have a mean of 11.
Answer» ANSWER :`x=12`

Discussion

1645.	If the polynomials x ^(3) + ax ^(2) + 5 and x ^(3) - 2x ^(2)+a are divided by (x +2)leave the same remainder. Find the value of a.
Answer» ANSWER :`(-13)/(3)`

Discussion

1646.	Draw the graph for each of the equations x+y=6 and x-y=2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.
Answer» ANSWER :(4,1)

Discussion

1647.	Evaluate each of the following using proper identity :15^(3) + 35^(3) - 50^(3)
Answer» ANSWER :`-78,750`

Discussion

1648.	Every surd is an irrational, but every irrational need not be a surd. Justify your answer.
Answer» ANSWER :`PI` is an IRRATIONAL NUMBER, but not a SURD.

Discussion

1649.	find the arithmetic mean of the following data.
Answer» ANSWER :15.55

Discussion

1650.	Plot the points (0,0), (0,3), (4,3), (4,0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.
Answer» ANSWER :12 SQ. UNITS

Discussion

Explore topic-wise InterviewSolutions in .

Find the total surface area of a hemisphere of radius 10 cm . (use pi =3.14

Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

Axioms are assumed

Factorise : x^(3) - 3x^(2) - 9x - 5

A loan of Rs 18900 is to be paid back in two equal half yearly instalment if the interest is compounded half yearly at 20% per annum then the interest is (in rupees)

Find A, if : sin2A=1

A metal pipe is 77 cm .long .The inner diameter of a cross section is 4 cm. the outer diameter being 4.4 cm .Find its (i) inner curved surface area outer curved surface area Total surface area.

Find the value of : tan30^(@)tan60^(@)

Without actual calculating the cubes, find the vlaue of each of the following (i) (-10) ^(3) + (7) ^(3) + (3)^(3) (ii) (28) ^(3) + (-15)^(3) + (-13)^(3) (iii)((1)/(2)) ^(3) + ((1)/(3)) ^(3) -((5)/(6)) ^(3) (iv) (0.2)^(3) - (0.3) ^(3) +(0.1)^(3)

Construct a Delta ABC in which AB=4.5 cm, BC=6 cm and median AD=4 cm.

In triangle PQR, ifangle R gt angleQ then

ABC is a triangle. Locate a point in the interior of triangle ABC which is equidistant from all the vertices of triangle ABC

Simplify the following expressions : (sqrt5+sqrt2)^(2)

Calculate the amount, if Rs 15,000 is lent at compound interest for 2 years and the rates for the successive years are 8% p.a. and 10% p.a. respectively.

To know the opinion of the students about the subject statistics , a survey of 200 students was conducted . The data is recorded in the following table : {:("Opinion ","Number of students"),("Like",135),("Dislike",65):} Find the probability that a student chosen at random Does not like it.

To know the opinion of the students about the subject statistics , a survey of 200 students was conducted . The data is recorded in the following table : {:("Opinion ","Number of students"),("Like",135),("Dislike",65):} Find the probability that a student chosen at random Likes statistics

If the mean of 10, 12, 18, 13, P and 17 is 15, find the value of P.

A certain sum of money at simple interest increases by 50% in 5 years. What will be the compound interest, compounded annually on Rs 13,000 for 3 years at the same rate?

ABCD is a rectangle . If AB=10 cm and ar(ABCD)=150 cm^2 , then BC=____ cm.

Rationalise the denominator of (1)/(4+sqrt5)

In a businessP,Q,R and S arefourpartners. Psinvestmentis twice R 'sinvestment Q 'sinvestment is (1)/(4) ofS'sinvestment and P and Qinvestedequally . If thetotalprofitat the end ofthe year is Rs 13,000then findthe sumof the shareof p andR in theprofit.

If the mean of the following frequency distribution is 26.7, find the missing frequency f:

100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having nogirl

100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having One girl.

100 families with two children were selected randomly and the following data were recorded : {:("No. of girls in family",2,1,0),("No. of families",12,80,8):} Calculate the probability of a family chosen at random having two girls

If 4cos^(2)x=3 and x is an acute angle, find the value of : sin2x

Find the value of x in the given figure.

Find an irrational number between (5)/(7) and (7)/(9). How many more there may be?

State the coefficient of x^(2) in each of the following polynomials : (3)/(2)x^(2) - (5)/(4)x +1

Ramapada had just enough money to purchase either 30 pens or 50 pencils . He decides tospends only 80% of his money and buys 10 pens . At themaximum howmanypencils can he buy with theremainingmoney that he has ?

Find the angle in radian through which a pendulum swings if its length is 75cm and the tip describes an arc of length 10cm.

Find the remainder when x^(4) + x^(3) - 2x^(2) + x +1 is divide by x-1.

In triangle ABC, AD is the perpendicular bisector of BC (see the given figure). Show that triangle ABC is an isosceles triangle in which AB = AB .

State true or false .The region enclosed by a chord and the minor arc isminor segment

Find p(0), p(1) and p(2) for each of the following polynomials : p(y) = y^(2) - y +1

Prove that the successive joiningof the points (4,3) (5,6) and (3,5) produce a square.

Given that angleA and angleB are complementary angles. If angleA=angleB+20^(@), then find angleA and angleB

In trianglePQR , PM is an altitude and QR is the hypotenuse. If QR=12 cm and PM=6 cm, then ar(PQR)=___ cm^2

For a given cylinder, the radius of the base is 7 cm and its height is 15 cm. What will be the area of its base and its top ?

If sqrt((sqrt10 +1)/(sqrt10-1)) thenfind the value of (x 1/x)

Find x, if 9,x,14,18,x,x,8,10 and 4 have a mean of 11.

If the polynomials x ^(3) + ax ^(2) + 5 and x ^(3) - 2x ^(2)+a are divided by (x +2)leave the same remainder. Find the value of a.

Draw the graph for each of the equations x+y=6 and x-y=2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.

Evaluate each of the following using proper identity :15^(3) + 35^(3) - 50^(3)

Every surd is an irrational, but every irrational need not be a surd. Justify your answer.

find the arithmetic mean of the following data.

Plot the points (0,0), (0,3), (4,3), (4,0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.